diff --git a/2.1.1/2.1.1(q1).txt b/2.1.1/2.1.1(q1).txt
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diff --git a/2.1.1/2.1.1(q2).txt b/2.1.1/2.1.1(q2).txt
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diff --git a/2.1.1/2.1.1.graph b/2.1.1/2.1.1.graph
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+#!/usr/bin/gnuplot -persist
+set terminal postscript solid color eps enhanced
+#set terminal png enhanced
+set output "2.1.1.ps"
+set encoding koi8r
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+#set label 11 center at graph 0.5,char 0.5 "Рис.2 Результаты измерений напряжения V_{B} в зависимости от тока I_{A} для проволок разной длины l и их линейная аппроксимация y = kx" font "Arial,10"
+set grid
+set xlabel "N, Вт"
+set ylabel '/Symbol D T, ^\circ C'
+
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+set style line 4 lc black 
+
+set key box linestyle 4
+set key opaque Left
+
+plot "2.1.1(q1).txt" using 1:2:3  notitle with yerrorbars linestyle 1
+plot "2.1.1(q2).txt" using 1:2:3  notitle with yerrorbars linestyle 2 
+#plot "1.1.1(20).txt" using 2:1:3  notitle with yerrorbars linestyle 3 
+
+plot	3.68*x smooth csplines title "q_{1}" linestyle 1, \
+	4.6*x smooth csplines title "q_{2}" linestyle 2
+#	2.006*x smooth csplines title "l = 20 см\nk=2.006^+/-0.023 Ом" linestyle 3
diff --git a/2.1.1/2.1.1.png b/2.1.1/2.1.1.png
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diff --git a/2.1.1/data.txt b/2.1.1/data.txt
index 5506481..a2715b6 100644
--- a/2.1.1/data.txt
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@@ -1,68 +1,4 @@
 Влажность - 64%
-Давление - 745.5 мм. рт. ст.
-t = 22.3 C
+Давление - 745.5 мм. рт. ст. (99375.15 Па)
+t = 22.3 C (295.45 К)
 p0 = 1.17 кг/м^3
-
-______________
-delta T = 1.9656 К
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-
-___________________
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-
diff --git a/2.1.1/data_fucked_up.txt b/2.1.1/data_fucked_up.txt
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+Влажность - 64%
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+
+______________
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+
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+
+___________________
+
+delta T = 5.1597 К
+
+#1
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+eps = 0.21 мВ
+
+#2
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+
+#4 
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diff --git a/2.1.1/lab-gnuplottex-fig1.gnuplot b/2.1.1/lab-gnuplottex-fig1.gnuplot
new file mode 100644
index 0000000..30889c9
--- /dev/null
+++ b/2.1.1/lab-gnuplottex-fig1.gnuplot
@@ -0,0 +1,22 @@
+set terminal epslatex
+set output './lab-gnuplottex-fig1.tex'
+set grid
+set xlabel '$ N $, Вт'
+set ylabel '$ \Delta T $, C'
+
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+set xrange [0:7]
+set key spacing 2
+set key bottom right
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+set style line 2 lt 1 pt 7 ps 0.5 lc rgb "blue"
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diff --git a/2.1.1/lab-gnuplottex-fig1.tex b/2.1.1/lab-gnuplottex-fig1.tex
new file mode 100644
index 0000000..1c824cf
--- /dev/null
+++ b/2.1.1/lab-gnuplottex-fig1.tex
@@ -0,0 +1,215 @@
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+\begingroup
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+    }{Either use 'blacktext' in gnuplot or load the package
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+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\includegraphics[2][]{%
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+      Package graphicx or graphics not loaded%
+    }{See the gnuplot documentation for explanation.%
+    }{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
+    \renewcommand\includegraphics[2][]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
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+  \@ifundefined{ifGPblacktext}{%
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+    \GPblacktexttrue
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+      \expandafter\def\csname LT3\endcsname{\color{black}}%
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diff --git a/2.1.1/lab.aux b/2.1.1/lab.aux
new file mode 100644
index 0000000..6bea97a
--- /dev/null
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diff --git a/2.1.1/lab.gnuploterrors b/2.1.1/lab.gnuploterrors
new file mode 100644
index 0000000..c855d77
--- /dev/null
+++ b/2.1.1/lab.gnuploterrors
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+gnuplot: error while loading shared libraries: libcerf.so.2: cannot open shared object file: No such file or directory
diff --git a/2.1.1/lab.log b/2.1.1/lab.log
new file mode 100644
index 0000000..0344601
--- /dev/null
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diff --git a/2.1.1/lab.pdf b/2.1.1/lab.pdf
index 30a9eb0..281cf4a 100644
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diff --git a/2.1.1/lab.tex b/2.1.1/lab.tex
index 8b471dc..89ff41a 100644
--- a/2.1.1/lab.tex
+++ b/2.1.1/lab.tex
@@ -5,6 +5,8 @@
 \usepackage{epsf,amsmath,amsfonts,amssymb,amsbsy}
 \usepackage[mathscr]{eucal}
 \usepackage[english, russian]{babel}
+\usepackage{gnuplottex}
+
 \author{Гришаев Григорий С01-119}
 \title{Отчёт о выполнении лабораторной работы 2.1.1}
 \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
@@ -16,403 +18,255 @@
 \begin{document}
 	\maketitle
 	\begin{center}
-		{\Large Измерение удельной теплоёмкости воздуха при постоянном давленини}
+		{\Large Измерение удельной теплоёмкости воздуха при постоянном давлении}
 	\end{center}
-	\paragraph*{Цель работы:} 1) измерение повышения температуры воздуха в результате подвода тепла при стационарном течении через стеклянную трубу; 2) вычисление по результатам измерений теплоёмкости воздуха при постоянном давлении.  
-	\paragraph*{В работе используются:} теплоизолированная трубка; электронагреватель; источник питания постоянного тока; амперметр; вольтметр; термопара; компрессор; газовый счётчик;
-	секундомер.
+	\paragraph*{Цель работы:}измерить повышение температуры воздуха в зависимости от мощности подводимого тепла и расхода при стационарном течении через трубу; исключив тепловые потери, по результатам измерений определить теплоёмкость воздуха при постоянном давлении
+	\paragraph*{В работе используются:}теплоизолированная стеклянная трубка; электронагреватель; источник питания постоянного тока; амперметр, вольтметр (цифровые мультиметры); термопара, подключенная к микровольтметру; компрессор; газовый счётчик; секундомер.
+
+
 	\section{Теоретические сведения}
 		Определение теплоёмкости обычно производится в калориметрах. При этом регистрируется количество тепла {Q}, полученное телом, и изменение температуры этого тела $ {\Delta T} $.
-		Теплоёмкость тела определяется как их отношение: $$ C = \frac{Q}{\Delta T} \; (1).$$
-		 
-		Необходимо, чтобы количество тепла, затрачиваемое на нагревание исследуемого тела, существенно превосходило тепло, расходуемое на нагревание самого калориметра, а также на потери тепла из установки.
-		 
-		 Для увеличения количества нагреваемого газа при неизменных размерах установки в нашей работе исследуемый газ (воздух) продувается через калориметр, внутри которого установлен нагреватель. При этом
-		 измеряются мощность нагревателя, масса воздуха, протекающего в единицу
-		 времени (расход), и приращение его температуры.
-		 
+		Теплоёмкость тела определяется как их отношение:
+		\begin{equation}
+		\label{eq1}
+			C = \frac{\delta Q}{dT} \;
+		\end{equation}
+			Необходимо, чтобы количество тепла, затрачиваемое на нагревание исследуемого тела, существенно превосходило тепло, расходуемое на нагревание самого калориметра, а также на потери тепла из установки.		 
+		 Для увеличения количества нагреваемого газа при неизменных размерах установки в нашей работе исследуемый газ (воздух) продувается через калориметр, внутри которого установлен нагреватель. При этом измеряются мощность нагревателя, масса воздуха, протекающего в единицу времени (расход), и приращение его температуры.
+		 Рассмотрим газ, протекающий стационарно слева направо через трубу постоянного сечения, в которой установлен нагревательный элемент (см. рис. 1). Пусть за некоторое время $ dT $  через калориметр прошла малая порция газа массой $ dm = qdt $, где $ q $ [кг/с] — массовый расход газа в трубе. Если мощность нагрева равна $ N $, мощность тепловых потерь на обмен с окружающей средой $ N_{пот} $, то порция получила тепло $ \delta Q = (N - N_{пот})dt $. С другой стороны, по определению теплоёмкости \ref{eq1}, $ \delta Q = c dm \Delta T$, где $ \Delta T = T_{2} - T_{1}$ - приращение температуры газа, и $ c $ — удельная (на единицу массы) теплоёмкость газа в рассматриваемом процессе. При малых расходах газа и достаточно большом диаметре трубы перепад давления на её концах мал, поэтому можно принять, что $ P_{1} \approx P_{2} = P_{0} $, где $ P_{0} $ — атмосферное давление. Следовательно, в условиях опыта измеряется удельная теплоёмкость при постоянном давлении $ c_{p} $. Таким образом, получаем
+		\begin{equation}
+		\label{eq2}
+			c_{p} = \frac{N - N_{пот}}{q \Delta T};
+		\end{equation}
+		\begin{figure}[h!]
+			\center{\includegraphics[width=0.5\linewidth]{1}}
+			\caption{Нагрев газа при течении по трубе}
+		\end{figure}	 
+
+
 	\subsection{Экспериментальная установка:}
 	
-	Схема установки изображена на рис.1. Воздух, нагнетаемый компрессором, прокачивается через калориметр. Калориметр представляет собой стеклянную цилиндрическую трубку с двойными стенками, запаянными с торцов.
+	Схема установки изображена на рис.2. Воздух, нагнетаемый компрессором, прокачивается через калориметр. Калориметр представляет собой стеклянную цилиндрическую трубку с двойными стенками, запаянными с торцов.
 	
 		\begin{figure}[h]
-		\center{\includegraphics{1}}
+			\center{\includegraphics{3}}
+			\caption{Схема экспериментальной установки}
 		\end{figure}
 	
 		Нагреватель в виде намотанной на пенопласт нихромовой проволоки расположен внутри калориметра непосредственно в воздушном потоке. Нагрев проволоки производится от регулируемого источника постоянного тока (ИП).
 		Напряжение $U$ на нагревателе и ток $I$ через него регистрируются цифровыми мультиметрами. Таким образом, мощность нагрева равна 
-		$$N= UI \; (3).$$ 
+	\begin{equation}
+		\label{eq3}
+		N= UI \; 
+	\end{equation}
 		Для измерения разности температур $\Delta T$ служит медно-константановая
 		термопара. Один спай термопары расположен в струе воздуха, входящего в
-		калориметр, и находится при комнатной температуре, а второй — в струе выходящего нагретого воздуха. Константановая проволока термопары расположена внутри калориметра, а медные проводники подключены к цифровому вольтметру. Возникающая в термопаре ЭДС $\varepsilon$ пропорциональна разности температур $\Delta T$ спаев: $$\varepsilon =\beta \Delta T \; (4),$$ где $\beta = 42.3 \frac{мкВ}{^\circ C}$ — чувствительность медно-константановой термопары в рабочем диапазоне температур (20–30 $^\circ C$ ). ЭДС регистрируется с помощью микровольтметра.
-		
-		Вычислим работу, совершаемую при протекании газа через калориметр. Внешняя работа по перемещению моля газа в направлении течения в начале трубки равна $ A_{1} = P_{1}V_{1} $, а в конце трубки давление препятствует движению и внешняя работа над газом отрицательна: $ A_{2}=-P_{2}V_{2}$. Полная работа над газом равна $ A_{1}+A_{2}=P_{1}V_{1}-P_{2}V_{2}$, а работа самого газа равна этой же величине, но с обратным знаком: $$  A =P_{2}V_{2}-P_{1}V_{1}$$
-		Внутренняя энергия газа изменяется на величину $ \Delta U = U_{2} - U_{1} $.
-		Из первого начала термодинамики: $$ Q = U_{2}-U_{1}+P_{2}V_{2}-P_{1}V_{1}=H_{2}-H_{1}$$,
-		где $H=U+PV$ - энтальпия.
-		Для идеального газа $ H = C_{p}T$, поэтому $$ Q = C_{p}(T_{2}-T_{1})$$.
-		Следовательно, в данном эксперименте измеряется теплоемкость при постоянном давлении.
-		Расчет удельной теплоемкости воздуха: $$ c_{p} = \frac{Q}{m \Delta T}= \frac{IU-N}{m \Delta T}$$,
-%		Объём воздуха, прошедшего через калориметр, измеряется газовым счётчиком ГС. Для регулировки расхода служит кран К. Время $\Delta t$ прохождения некоторого объема $\Delta V$ воздуха измеряется секундомером. Объёмный расход равен $\frac{\Delta V}{\Delta t} $, массовый расход может быть найден как $$q = \rho_{0} \frac{\Delta V}{\Delta t} \; (5),$$ где $rho_{0}$ — плотность воздуха при комнатной температуре, которая в свою очередь может быть получена из уравнения Менделеева–Клапейрона: $\rho_{0}= \frac{\mu P_{0} }{R T_{0}},$ где $P_{0}$ — атмосферное давление, $T_{0}$ — комнатная температура (в Кельвинах), $\mu = 29,0 {г/моль}$ — средняя молярная масса (сухого) воздуха.
-		
-%		Учитывая особенности устройства калориметра, следует ожидать, что мощность нагревателя расходуется не только на нагрев массы прокачиваемого воздуха, но и частично теряется за счет нагрева внутренних стенок термостата и рассеяния тепла через торцы термостата. Можно предположить, что при небольшом нагреве ($\Delta T \ll T_{0}$) мощность потерь тепла $N_{пот}$ прямо пропорциональна разности температур:$$ N_{пот} = \alpha \Delta T \; (6),$$ где $\alpha$ — некоторая константа. При этом условии основное соотношение (2) принимает вид $$N = (c_{P}q +\alpha)\Delta T \;(7)$$
-%		Следовательно, при фиксированном расходе воздуха ($q = const$ ) подводимая мощность и разность температур связаны прямой пропорциональностью($\Delta T(N)$ — линейная функция).
+		калориметр, и находится при комнатной температуре, а второй — в струе выходящего нагретого воздуха. Константановая проволока термопары расположена внутри калориметра, а медные проводники подключены к цифровому вольтметру. Возникающая в термопаре ЭДС $\varepsilon$ пропорциональна разности температур $\Delta T$ спаев: 
+		\begin{equation}
+			\label{eq4}
+			\varepsilon =\beta \Delta T \;
+		\end{equation}
+			где $\beta = 40.7 \frac{мкВ}{^\circ C}$ — чувствительность медно-константановой термопары в рабочем диапазоне температур (20–30 $^\circ C$ ). ЭДС регистрируется с помощью микровольтметра.
 		
+	Объём воздуха, прошедшего через калориметр, измеряется газовым счётчиком ГС. Для регулировки расхода служит кран К. Время $ \Delta t $ прохождения некоторого объема $ \Delta V $ воздуха измеряется секундомером. Объёмный расход равен $ \Delta V/\Delta T $, массовый расход может быть найден как
+	\begin{equation}
+		\label{eq5}
+		q = \rho_{o}\frac{\Delta V}{\Delta t} \;
+	\end{equation}
+	где $ \rho_{0} $ — плотность воздуха при комнатной температуре, которая в свою очередь может быть получена из уравнения Менделеева–Клапейрона: $ \rho_{0} = \frac{\mu P_{0}}{R T_{0}} $, где $ P_{0} $ — атмосферное давление, $ T_{0} $ — комнатная температура (в Кельвинах), $ \mu $= 29,0 г/моль — средняя молярная масса (сухого) воздуха.
+	Учитывая особенности устройства калориметра, следует ожидать, что мощность нагревателя расходуется не только на нагрев массы прокачиваемого воздуха, но и частично теряется за счет нагрева внутренних стенок термостата и рассеяния тепла через торцы термостата. Можно предположить, что при небольшом нагреве ($ \Delta T << T_{0} $) мощность потерь тепла $ N_{пот} $ прямо
+пропорциональна разности температур:
+\begin{equation}
+	\label{eq6}
+	N_{пот} = \alpha \Delta T \;
+\end{equation}
+где $ \alpha $ — некоторая константа. При этом условии основное соотношение \ref{eq2} принимает вид
+\begin{equation}
+	\label{eq7}
+	N = (c_{p}q + \alpha)\Delta T \;
+\end{equation}
+Следовательно, при фиксированном расходе воздуха ($ q $ = const) подводимая мощность и разность температур связаны прямой пропорциональностью ($ \Delta T{N} $ — линейная функция).
+	\subsection{Оборудование и инструментальные погрешности}
+	Для измерения $ \varepsilon $ использовался вольтметр универсальный В7-78/1, его абсолютная погрешность равна $ \pm (0.005 \frac{\varepsilon}{100} + 3.5) \; мкВ$.
+
+	Для измерения $ U $ использовался цифровой универсальный вольтметр GDM-8145, абсолютная погрешность которого равна $ \pm (0.0003U \pm 4 \; мВ) $. 
+	Его же мы использовали для измерения $ I $, абсолютная погрешность: $ \pm (0.002I+20 \; мкА) $.
 	\subsection{Ход работы}
-%	\begin{enumerate}
-%		\item Подготовим к работе газовый счетчик: проверим, что он заполнен  водой, установим счетчик по уровню.
-%		\item Охладим калориметр до комнатной температуры.
-%		\item Включим вольтметр, предназначенный для измерения ЭДС термопары. 
-%		\item Запишем показания компнатной температуры и давления. $$T_{0} = 297.05 \; ^\circ C, P_{0} = 99325 \pm 13 \; {Па} $$
-%		\item С помощью газового счетчика и секундомера измерим максимальный расход воздуха $\frac{\Delta V}{\Delta T}$ (в л/с). Измерения представлены в таблице 1. По найденным значениям определим среднее значение расхода и массовый расход воздуха $q_{max}$ [г/с].
-%		
-%		$$q = \rho_0 \frac{\Delta V}{\Delta t} = \frac{\mu P_0}{RT_0} \frac{\Delta V}{\Delta t}.$$
-%		
-%		Относительная погрешность косвенных измерений может быть найдена по формуле $$\frac{\sigma_{q_{max}кос}}{q_{max}} = \sqrt{(\frac{\sigma_{T_0}}{T_{0}})^2+(\frac{\sigma_{P_0}}{P_{0}})^2+ (\frac{\sigma_t}{t})^2}$$ 
-%
-%
-%	\begin{table}
-%	\begin{center}
-%	\begin{tabular}{|c|c|c|c|c|}
-%				\hline
-%				$\Delta V, л$ & $\Delta t, c$ & $\frac{\Delta V}{\Delta t},\frac{л}{с}$ & $q_{max},\frac{г}{c} $ & $\sigma_{q_{max}кос}, \; \frac{г}{с} \cdot 10^{-3}$ \\
-%				\hline
-%				x & 0 & 0 & 0 & 0  \\
-%				\hline
-%				x & 0 & 0 & 0 & 0\\
-%				\hline
-%				x & 0 &  0 & 0 & 0\\
-%				\hline
-%				x & 0 & 0 & 0 &0 \\
-%				\hline
-%	
-%	\end{tabular}
-%	\end{center}
-%	\caption{Измерение расхода воздуха}
-%	\end{table}
-%	$$\overline{\frac{\Delta V}{\Delta t}} = 0.1951 \; \frac{л}{с} ,\; \overline{q_{max}} = 0.2276 \; \frac{г}{с} $$
-%	
-%	Случайная погрешность массового расхода может быть найдена по формуле: $$\sigma_{q_{max}сл} =  \sqrt{\frac{\sum_{i=1}^{7} (q_{max,i}-\overline{q_{max}})^2}{6}} = 0.0003 \; \frac{г}{c}.$$
-%	
-%	Косвенная погрещность для среднего значения: $q_{max}$ $$\sigma_{\overline{q_{max}}кос} = \sqrt{\frac{\sum_{i=1}^{7} (\sigma_{q_{max}кос})^2}{7^2}} = 0.0003 \; \frac{г}{c}.$$
-%	
-%	Суммарная погрешность: $$\sigma_{\overline{q_{max}}} = \sqrt{(\sigma_{q_{max}сл})+(\sigma_{\overline{q_{max}}кос})^2} = 0.0004 \; \frac{г}{c}.$$
-%	
-%	Окончательное значение: $$q_{max} = 0.2276 \pm 0.0004 \; \frac{г}{с} $$
-%	
-%	\item Оценим величину тока нагревателя $I_{0}$, требуемого для нагрева воздуха на $\delta T = 1 {К}$.
-%	
-%	Определим теоретическое значение удельной теплоемкости воздуха при постоянном давлении $C_{теорp} \; \frac{Дж}{г\cdot K}$, считая воздух смесью двухатомных идеальных газов: $Cp = 3.5R\mu \approx 1 \; \frac{Дж}{г\cdot K}.$
-% 	
-% 	Оценим минимальную мощность $N_0$, необходимую для нагрева газа при максимальном расходе. $N_{0} = c_{p}q\Delta T \approx 0.227 {Вт}.$
-%	
-%	Учитывая, что сопротивление проволоки нагревателя составляет приблизительно $R_{н} \approx 35 {Ом}$ и в процессе опыта практически не меняется, искомое значение тока $I_{0} = q N_{0} R_{н} \approx 0.08 \; {А}.$
-%	
-%	\item Проведем измерение зависимости разности температур от мощности нагрева $\Delta T(N)$ при максимальном расходе воздуха $q_0 = q_{max}.$
-%	\begin{table}
-%
-%	\begin{center}
-%	\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
-%		\hline
-%		$I, мA$ & $U, B$ & $N, Вт$ & $R_н, Ом$ & $\varepsilon, \muВ$ & $ \Delta T, K$
-%		\\
-%		\hline
-%		108.18 & 3.19 & 0.345 & 29.49 & 52 & 1.28 
-%		\\
-%		\hline
-%		141.62 & 4.18 & 0.592 & 29.52 & 88 & 2.16 
-%		\\
-%		\hline
-%		165.70 & 4.89 & 0.810 & 29.51 & 118 & 2.90 
-%		\\
-%		\hline
-%		181.06 & 5.34 & 0.967 & 29.49 & 141 & 3.46 
-%		\\
-%		\hline
-%		210.7 & 6.21 & 1.308 & 29.48 & 188 & 4.61 
-%		\\
-%		\hline
-%	\end{tabular}
-%	\end{center}
-%	\caption{Измерение $\Delta T (N) \; {при} \; q_{max}$}
-%	\end{table}
-%	Следует отметить, что погрешность измерения тока: $\sigma_{I} = 0.01 \; мA$, а  напряжения: $\sigma_{U}= 0.01 \; В$, $\sigma_{\varepsilon}= 1 \; \muВ$
-%
-%	Завершив первую серию измерении, охладим калориметр до комнатнои температуры.
-%	Для этого отключим источник питания нагревателя, откроем кран К и продуем калориметр при максимальном расходе воздуха до тех пор, пока показания ЭДС не достигнут нуля.
-%	
-%	Данные представлены в таблице 2.
-%	
-%	\begin{table}
-%	\begin{center}
-%	\begin{tabular}{lr}
-%	\begin{tabular}{|c|c|c|c|c|}
-%	\hline
-%	$\Delta V, л$ & $\Delta t, c$  & $\frac{\Delta V}{\Delta t},\frac{л}{с}$ & $q_1, \frac{г}{c}$ & $Z, \; \frac{г}{с} \cdot 10^{-3}$ \\
-%	\hline
-%	5 & 46.02 & 0.1086 & 0.1266 & 0.550 \\
-%	\hline
-%	10 & 91.4 &  0.1094 & 0.1275 & 0.279 \\
-%	\hline
-%	15 & 134.78 & 0.1113 & 0.1297& 0.192 \\
-%	\hline
-%	20 & 178.96 & 0.1117 & 0.1302 & 0.146\\
-%	\hline
-%	25 & 221.14 & 0.1130 & 0.1317 & 0.119 \\
-%	\hline
-%	30 & 266.36 & 0.1126 & 0.1312 & 0.099\\
-%	\hline
-%	35 & 311.83 & 0.1122 & 0.1308 & 0.084\\
-%	\hline
-%	\end{tabular}
-%	
-%	\begin{tabular}{|c|c|c|c|c|}
-%	\hline
-%	$\Delta V, л$ & $\Delta t, c$  & $\frac{\Delta V}{\Delta t},\frac{л}{с}$ & $q_2, \frac{г}{c}$ & $Z, \; \frac{г}{с} \cdot 10^{-3}$ \\
-%	\hline
-%	1 & 13.40 & 0.0747 & 0.0870 & 1.30\\
-%	\hline
-%	2 & 27.56 & 0.0726 & 0.0846 & 0.61\\
-%	\hline
-%	3 & 41.31 & 0.0726 & 0.0846 & 0.41\\
-%	\hline
-%	4 & 54.95 & 0.0733 & 0.0855 & 0.31 \\
-%	\hline
-%	5 & 69.05 & 0.0724 & 0.0844 & 0.24\\
-%	\hline
-%	6 & 82.24 & 0.0729 & 0.0850 & 0.21\\
-%	\hline
-%	7 & 96.18 & 0.0728 & 0.0848 & 0.18 \\
-%	\hline
-%\end{tabular}
-%\end{tabular}
-%\end{center}
-%\caption{Измерения других расходов; $q_1 = 0.123  \pm 0.002 \; \frac{г}{с}; \; q_2 = 0.085 \pm 0.001 \; \frac{г}{с} $ }
-%\end{table}
-%	Проведем аналогичные измерения для других значений расхода воздуха. Новая температура $T_{0} = 297.4 ^\circ C$.
-%	Данные представлены в таблице 3 и 4.  ($Z \equiv \sigma_{q_{max}кос}$). Погрешности рассчитаны аналогично $q_{max}.$
-%
-%\begin{table}
-%	\begin{center}
-%		\begin{tabular}{lr}
-%			\begin{tabular}{|c|c|c|c|c|c|}
-%				\hline
-%				$I, A$ & $U, B$ & $N, Вт$ & $R_н, Ом$ & $\varepsilon, \muВ$ & $ \Delta T, K$\\
-%				\hline
-%				91.34 & 2.69 & 0.246 & 29.45 & 50 & 1.23 \\
-%				\hline
-%				120.30 & 3.55 & 0.427 & 29.51 & 89 & 2.19 \\
-%				\hline
-%				145.11 & 4.28 & 0.621 & 29.49 & 128 & 3.14 \\
-%				\hline
-%				176.45 & 5.20 & 0.918 & 29.47 & 184 & 4.52 \\
-%				\hline
-%				212.20 & 6.23 & 1.322 & 29.36 & 261 & 6.41 \\
-%				\hline	
-%			
-%			\end{tabular}
-%			\begin{tabular}{|c|c|c|c|c|c|}
-%				\hline
-%				$I, A$ & $U, B$ & $N, Вт$ & $R_н, Ом$ & $\varepsilon, \muВ$ & $ \Delta T, K$\\
-%				\hline
-%				105.95 & 3.13 & 0.332 & 29.54 & 81 & 1.99 \\
-%				\hline
-%				125.74 & 3.71 & 0.466 & 29.51 & 128 & 3.14 \\
-%				\hline
-%				149.46 & 4.41 & 0.659 & 29.50 & 175 & 4.30 \\
-%				\hline
-%				177.33 & 5.23 & 0.927 & 29.49 & 236 & 5.80 \\
-%				\hline
-%				211.5 & 6.25 & 1.322 & 29.55 & 310 & 7.62 \\
-%				\hline
-%			\end{tabular}
-%		\end{tabular}
-%	\end{center}
-%	\caption{Измерение $\Delta T (N) \; {при} \; q_{1} \; и \; q_{2}$}
-%\end{table}
-%
-%		Погрешности будем считать по слудующим формулам: $$ \sigma_{\Delta T} = \Delta T \frac{\sigma_{\varepsilon}}{\varepsilon}, \sigma_{N}= N\sqrt{( \frac{\sigma_{I}}{I})^2 + (\frac{\sigma_{U}}{U})^2} \approx N \frac{\sigma_{U}}{U}$$
-%	
-%		\begin{table}
-%		\begin{tabular}{lr}
-%		\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
-%			\hline
-%			q, $\frac{г}{с}$ & \multicolumn{4}{|c|}{0.2276} & \multicolumn{4}{|c|}{0.123}
-%			\\
-%			\hline
-%			k &  $\Delta T, \; ^\circ C$& $\sigma_{\Delta T}\; ^\circ C$ & $N$, мВт & $\sigma_{N}$, мВт & $\Delta T, \; ^\circ C$& $\sigma_{\Delta T}\; ^\circ C$ & $N$, мВт & $\sigma_{N}$, мВт
-%			\\
-%			
-%			\hline
-%			0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
-%			\\
-%			\hline
-%			1 & 1.28 & 0.02 & 345 & 1.1 & 1.23 &  0.02 & 246 & 0.9
-%			\\
-%			\hline
-%			2 & 2.16 & 0.02 & 592 & 1.4 & 2.19 & 0.02 & 427 & 1.2
-%			\\
-%			\hline
-%			3 & 2.90 & 0.02 & 810 & 1.7 & 3.14 & 0.02 & 621 & 1.5
-%			\\
-%			\hline
-%			4 & 3.46 & 0.02 & 967 & 1.8 & 4.52 & 0.02 & 918 & 1.8
-%			\\
-%			\hline
-%			5 & 4.61 & 0.02 & 1308 & 2.1 & 6.41 & 0.02 & 1322 & 2.1
-%			\\
-%			\hline
-%		\end{tabular}
-%
-%		\\
-%
-%		\begin{tabular}	{|l|l|l|l|l|l|l|l|l|l|l|}
-%		\hline
-%		q, $\frac{г}{с}$ & \multicolumn{4}{|c|}{0.085} 
-%		\\
-%		\hline 
-%		k &  $\Delta T, \; ^\circ C$& $\sigma_{\Delta T}\; ^\circ C$ & $N$, мВт & $\sigma_{N}$, мВт
-%		\\
-%		\hline
-%		0 & 0 & 0 & 0 & 0
-%		\\
-%		\hline
-%		1 & 1.99 & 0.02 & 332 & 1.1 
-%		\\
-%		\hline
-%		2 & 3.14 & 0.02 & 466 & 1.3 
-%		\\
-%		\hline
-%		3 & 4.30 & 0.02 & 659 & 1.5 
-%		\\
-%		\hline
-%		4 & 5.80 & 0.02 & 927 & 1.8
-%		\\
-%		\hline
-%		5 & 7.62 & 0.02 & 1322 & 2.1
-%		\\
-%		\hline	
-%	\end{tabular}
-%
-%
-%
-%		\end{tabular}
-%	\caption{ погрешности, $\Delta T \; и \; N$}
-%	\end{table}
-%
-%
-%	После завершения опытов выключим источник питания нагревателя и мультиметры. Кран К откроем для максимального продува воздуха через калориметр.
-%	
-%\item Построим на одном графике зависимости $\Delta T (N)$ при разных значениях $q$.
-%	\begin{center}
-%			\begin{tikzpicture}[scale = 2]
-%			\begin{axis}[
-%			axis lines = left,
-%			legend style={at={(1,0.3)}},
-%			xlabel = {$N$, {мВт}},
-%			ylabel = {$\Delta T, {^\circ C} $
-%			},
-%			xmin=0, xmax=1350,
-%			ymin=0, ymax=8,
-%			ymajorgrids = true,
-%			xmajorgrids = true,
-%			minor tick num = 4
-%			]
-%			\addplot+[only marks ] plot[error bars/.cd, y dir=both, y explicit]
-%			coordinates {
-%				(0,0)
-%				(345,1.28) 
-%				(592, 2.16)
-%				(810, 2.90)
-%				(967 , 3.46)
-%				(1308, 4.61)
-%			};
-%			\addplot+[only marks ] plot[error bars/.cd, y dir=both, y explicit] coordinates {
-%				(0,0)
-%				(246,1.23) 
-%				(427, 2.19)
-%				(621, 3.14)
-%				(918 , 4.52)
-%				(1322, 6.41)
-%			};	
-%			\addplot+[only marks ] plot[error bars/.cd, y dir=both, y explicit]
-%			coordinates {
-%				(0,0)
-%				(332,1.99) 
-%				(466, 3.14)
-%				(659, 4.30)
-%				(927 , 5.80)
-%				(1322, 7.62)
-%			};
-%		
-%
-%			\addplot[blue, domain=0:1350]{0.042+0.0035*x};
-%			\addplot[red, domain=0:1350]{0.0619+0.0048*x};
-%			\addplot[brown, domain=0:1350]{0.0210+0.0063*x};
-%			\legend{
-%				$q_{max} = 0.2276 \frac{г}{с}$, $q_{1} = 0.123 \frac{г}{с};$ , $ q_{2} = 0.085 \frac{г}{с};$
-%			};
-% 			\end{axis}
-%			\end{tikzpicture}
-%		\end{center}
-%		${y_{max} = (3.5 \pm 0.3 )10^{-3}x+0.042 \pm 0.027}$,\\
-%		$\; {y_{1} = (4.8 \pm 0.1)10^{-3}x+0.062 \pm 0.044}$,\\
-%		$\; {y_{2} = (6.3 \pm 0.2)10^{-3}x+0.021 \pm 0.12}.$
-%		$Чтобы \; найти \; k_{max},\; k_1, \; k_2$, необходимо перевернуть соотвествующие коэффициенты $k'$ наклонов прямых, а погрешность считать по формуле: $$\sigma_k = k^2 \sigma_{k'}.$$
-%		$k_{max} = 0.286 \pm 0.025 \; \frac{Вт}{К}, \; k_{1} = 0.208 \pm 0.004 \; \frac{Вт}{К}, \; k_{2} = 0.159 \pm 0.005 \; \frac{Вт}{К} $
-%
-%		Прямая для расхода $q_2$ не идёт из нуля, вероятно, из-за поспешного начала третей серии измерений (начальная температура была несколько больше комнатной). Однако в целом из вида наших прямых, можно сделать вывод о том, что тепловые потери пропорциональны разности температур.
-%
-%	
-%		Построим график зависимости $k(q)$ и по его наклону определим теплоёмкость воздуха при постоянном давлении $c_p$
-%		
-%		\begin{center}
-%		\begin{tikzpicture}[scale = 1]
-%		\begin{axis}[
-%		axis lines = left,
-%		legend style={at={(1,1)}},
-%		xlabel = {$q, \; \frac{г}{с} \cdot 10^{-1}$},
-%		ylabel = {$k, \frac{Вт}{К}$
-%		},
-%		xmin=0, xmax=3,
-%		ymin=0, ymax=0.5,
-%		ymajorgrids = true,
-%		xmajorgrids = true,
-%		minor tick num = 4
-%		]
-%		\addplot+[only marks ] plot[error bars/.cd, x dir=both, x explicit ,y dir=both, y explicit]
-%		coordinates {
-%			(2.276,0.286) +- (0.004,0.025)
-%			(1.23, 0.208 ) +- (0.02,0.004)
-%			( 0.85,0.159) +- (0.01,0.005)
-%		};
-%		\addplot [red, domain=0:3]{0.0928+0.0860*x};
-%		
-%		\legend{
-%			$$y=0.0928+0.0860x$$
-%		};
-%		\end{axis}
-%		\end{tikzpicture}
-%		\end{center}
-%	
-%Итак, из графика найдём $c_p = (0.86 \pm 0.1) \; \frac{Дж}{К \cdot г} \cdot 29 \frac{г}{моль} = 24.94 \pm 2.29 \; \frac{Дж}{К моль}.$ A также $\alpha = 0.093 \pm 0.018 \; \frac{Вт}{К}.$ К сожалению, теплоёмкость значительно отличается от теоретического значения $29.09 \; \frac{Дж}{К моль}.$ Измерения необходимо было проводить более тщательно, ждать установления термодинамического равновесия более длительное время. Однако не смотря на это, результаты, полученные при обработке данных совпадают (почти) с теоретическими с учётом погрешностей.
-%
-%Посчитаем доли тепловых потерь в опытах : $\frac{N_{пот}}{N} =\frac{\alpha}{k}$
-%
-%	\begin{center}
-%	\begin{tabular}{|c|c|}
-%		\hline
-%		$q, \; \frac{г}{с}$ & $\frac{N_{пот}}{N}$ \\
-%		\hline
-%		0.085 & $0.59 \pm 0.11$ \\
-%		\hline
-%		0.123 & $0.45 \pm 0.09$\\
-%		\hline
-%		0.2276 & $0.33 \pm 0.06$ \\
-%		\hline
-%	\end{tabular}
-%	\end{center}
-%
-%\end{enumerate}
+	\begin{enumerate}
+		\item Запишем показания комнатной температуры, давления и влажности воздуха.
+			\begin{table}[h]
+	\begin{center}
+	\begin{tabular}{|c|c|c|}
+				\hline
+				& Значение & $ \sigma $ \\
+				\hline
+				$ T_{0} $, К & 295.45 & 0.1 \\
+				\hline
+				$ p $, Па & 99375.15 & 1 \\
+				\hline
+				$ \phi $ & 64\% & 1\% \\
+				\hline
+
+	\end{tabular}
+	\end{center}
+	\end{table}
+
+Рассчитываем плотность воздуха $ \rho_{0} $:
+			$$ \rho_{0} = \frac{2.9 * 10^{-3}*99375.15}{8.31*295.45} \approx 1.17 \; кг/м^{3} $$
+			Относительную погрешность вычисления плотности воздуха вычислим по формуле:
+			$$ \frac{\sigma_{\rho_{0}}}{\rho_{0}} = \sqrt{(\frac{\sigma_{P_{0}}}{P_{0}})^{2}+(\frac{\sigma_{\phi}}{\phi})^{2}+(\frac{\sigma_{T}}{T})^{2}} $$
+			$$ \Rightarrow \sigma_{\rho_{0}} = 0.018 \; \frac{кг}{м^{3}} $$
+		\item Рассчитываем теоретическую теплоемкость воздуха при постоянном давлении (в предположении, что воздух - смесь двух идеальных двухатомных газов):
+			$$ C_{p} = \frac{7}{2}R \approx 29.09 \; \frac{Дж}{моль*К} $$
+			$$ C_{p}^{\mu} = \frac{C_{p}}{\mu} \approx 1 \; \frac{Дж}{г*К} $$
+
+		\item С помощью газового счетчика и секундомера измерим расход воздуха для двух случаев, пользуясь формулой \ref{eq5} ($ q_{1} $ и $ q_{2} $). Результаты измерений представлены в таблице.
+			\begin{table}[h]
+				\begin{center}
+				\begin{tabular}{|c|c|c|c|c|}
+				\hline
+					$ \Delta V $, л & $ \Delta t $, с & $ \frac{\Delta V}{\Delta t} \; , \frac{л}{с} $ & $ q_{1} \; , \frac{г}{с}$  & $ \sigma_{q_{1}кос}, \; \frac{г}{с}*10^{-3} $\\
+				\hline
+					5 & 24.9 & 0.2 & 0.234  & 0.47 \\
+				\hline
+					5 & 25.6 & 0.2 & 0.234 & 0.47 \\
+				\hline
+					5 & 26.0 & 0.19 & 0.222 & 0.45 \\	
+				\hline
+				\end{tabular}
+					\caption{Измерение $ q_{1} $}
+				\end{center}
+			\end{table}
+			\begin{table}[h]
+				\begin{center}
+				\begin{tabular}{|c|c|c|c|c|}
+				\hline
+					$ \Delta V $, л & $ \Delta t $, с & $ \frac{\Delta V}{\Delta t} \; , \frac{л}{с} $ & $ q_{2} \; , \frac{г}{с}$ & $ \sigma_{q_{2}кос}, \; \frac{г}{с}*10^{-3} $ \\
+				\hline
+					5 & 32.7 & 0.15 & 0.176 & 0.35 \\
+				\hline
+					5 & 33.1 & 0.15 & 0.176 & 0.35 \\
+				\hline
+					5 & 33.2 & 0.15 & 0.176 & 0.35 \\	
+				\hline
+				\end{tabular}
+					\caption{Измерение $ q_{2} $}
+				\end{center}
+			\end{table}
+			Итого, $ q_{1} = \overline{q_{1}} = 0.23 \; г/с $, $ q_{2} = \overline{q_{2}} = 0.176 \; г/с $.
+
+			Вычислим случайную погрешность измерения $ q $:
+			$$ \sigma_{q} = \sqrt{\frac{1}{n(n-1)}\sum_{i=1}^{n}(q_{i}-\overline q)^{2}} $$
+			Итак, $ \sigma_{q_{1}} = 4*10^{-3} \; \frac{г}{с} $, $ \sigma_{q_{2}} \approx 0\; \frac{г}{с} $
+			
+			Вычислим величину относительной косвенной погрешности измерения $ q_{1} $ и $ q_{2} $:
+			$$ \frac{\sigma_{qкос}}{q} = \sqrt{(\frac{\sigma_{T_{0}}}{T_{0}})^{2} + (\frac{\sigma_{P_{0}}}{P_{0}})^{2} + (\frac{\sigma_{t}}{t})^{2}} $$
+			Косвенная погрешность для среднего значения $ q $: $ \sigma_{q_{1}кос} = 0.00046 \; \frac{г}{с} $, $ \sigma_{q_{2}кос} = 0.00035 \; \frac{г}{с}$
+
+			Суммарная погрешность: 
+			$$ \sigma_{\overline{q}} = \sqrt{(\sigma_{q})^{2}+(\sigma_{qкос})^2 } $$
+			$$ \sigma_{\overline{q_{1}}} = 0.0006 \; \frac{г}{с} $$
+			$$ \sigma_{\overline{q_{2}}} = 0.0004 \; \frac{г}{с} $$
+
+		\item Оценим величину тока нагревателя $ I_{0} $, требуемого для нагрева воздуха на $ \delta Q = 1К $. Оценим минимальную мощность $ N_{0} $, необходимую для нагрева газа при максимальном расходе $ N_{0} = c_{p}q\Delta T \approx 0.23 \; Вт $ в первом случае, $ N_{0} = c_{p}q\Delta T \approx 0.176 \; Вт $ во втором случае.
+		
+			Учитывая, что сопротивление проволоки нагревателя составляет приблизительно $ R_{н} \approx 35 \; Ом $ и в процессе опыта практически не меняется, искомое значение тока: $ I_{0}=\sqrt{\frac{N_{0}}{R_{н}}} \approx 0.08 \; А $ (в первом случае), $ I_{0}=\sqrt{\frac{N_{0}}{R_{н}}} \approx 0.07 \; А $(во втором случае).
+		\item Зафиксируем $ \Delta T(N) $ для двух значений $ q $ (между измерениями калориметр надлежит остудить):
+		$ q_{1} = 0.236 \; г/с $, $ q_{2} = 0.179 \; г/с $.
+	\begin{table}[h]
+	\begin{center}
+	\begin{tabular}{|c|c|c|c|c|}
+				\hline
+				$U, В$ & $I, мА$ & $ N $, Вт & $ \varepsilon, мкВ $ & $ \Delta T, К $ \\
+				\hline
+				6.105 & 169.81 & 1.0367 & 154 & 3.78 \\
+				\hline
+				5.576 & 155.02 & 0.8644 & 127 & 3.12 \\
+				\hline
+				5.334 & 148.46 & 0.7919 & 120 & 2.95 \\
+				\hline
+				4.947 & 133.77 & 0.6618 & 102 & 2.51 \\
+				\hline
+	
+	\end{tabular}
+	\end{center}
+		\caption{Зависимость $ \Delta T(N)$ для $ q_{1} $}
+	\end{table}
+	\begin{table}[h]
+	\begin{center}
+	\begin{tabular}{|c|c|c|c|c|}
+				\hline
+				$U, В$ & $I, мА$ & $ N $, Вт & $ \varepsilon, мкВ $ & $ \Delta T, К $ \\
+				\hline
+				5.934 & 165.82 & 0.984 & 186 & 4.57 \\
+				\hline
+				5.021 & 140.4 & 0.7049 &131 & 3.22 \\
+				\hline
+				4.572 & 127.83 & 0.5844 & 108 & 2.65 \\
+				\hline
+				4.231 & 118.3 & 0.5005 & 93 & 2.29 \\
+				\hline
+	
+	\end{tabular}
+	\end{center}
+		\caption{Зависимость $ \Delta T(N)$ для $ q_{2} $}
+	\end{table}
+
+\end{enumerate}
+\subsection{Обработка данных}
+Построим на одном графике зависимости $ \Delta T(N) $ при $ q_{1} $ и $ q_{2} $.
+Коэффициент аппроксимирующей прямой найдем по формуле $$ k = \frac{\overline{\Delta T N}}{\overline{N^{2}}} $$
+
+Итого, $ k_{1} = 3.68 $, $ k_{2} = 4.6 $.
+$$ \sigma_{k} = \sqrt{\frac{1}{n-1}(\frac{\overline{\Delta T^{2}}}{\overline{N^{2}}}-k^{2})} $$ 
+$$ \sigma_{k_{1}} \approx 0.023 \; \frac{К}{Вт} $$, $$ \sigma_{k_{2}} \approx 0.0188 \; \frac{К}{Вт} $$
+\begin{figure}[h!]
+	\centering
+	\begin{gnuplot}[terminal=epslatex]
+		set grid
+set xlabel '$ N $, Вт'
+set ylabel '$ \Delta T $, C'
+
+set multiplot
+set yrange [0:1500]
+set xrange [0:7]
+set key spacing 2
+set key bottom right
+set key off
+
+set style line 1 lt 1 pt 7 ps 0.5 lc rgb "red" 
+set style line 2 lt 1 pt 7 ps 0.5 lc rgb "blue"
+set style line 4 lc black 
+
+set key box linestyle 4
+set key opaque Left
+
+plot "2.1.3(22.8).data" using 1:2  notitle linestyle 1 
+
+	\end{gnuplot}
+\end{figure}
+
+Воспользуемся соотношениями $ C_{p}q_{1} + \alpha = \frac{1}{k_{1}}, \; C_{p}q_{2} + \alpha = \frac{1}{k_{2}} $, откуда имеем 
+$$ C_{p} = \frac{k_{2}-k_{1}}{k_{2}k_{1}(q_{1}-q_{2})} $$
+$$ \alpha = \frac{1}{k_{1}} - C_{p}q_{1} $$
+Отсюда имеем: $ C_{p} \approx 1.006 \; \frac{Дж}{г*К} $, $ \alpha \approx 0.042 \; \frac{Вт}{К} $
+
+Определим долю тепловых потерь: $ \frac{N_{пот}}{N} = \frac{\alpha}{C_{p}q + \alpha}$.
+$$ \frac{N_{пот}}{N_{1}} \approx 0.153$$
+$$ \frac{N_{пот}}{N_{2}} \approx 0.189$$
+
+Определим погрешность измерения $ C_{p} $:
+$$ \sigma_{C_{p}} = \sqrt{(\frac{\sigma_{k_{1}}}{k_{1}^{2}(q_{1}-q_{2})})^{2}+(\frac{\sigma_{k_{2}}}{k_{2}^{2}(q_{1}-q_{2})})^{2}+ (\frac{k_{2}-k_{1}}{k_{2}k_{1}(q_{1}-q_{2})^{2}})^{2}(\sigma_{q_{1}}^{2}+\sigma_{q_{2}}^{2})^{2}} $$
+Итого, $\sigma_{C_{p}} \approx 0.165 \;\frac{Дж}{г*К}$
+
+$$ \sigma_{\alpha} = \sqrt{(\frac{\sigma_{k_{1}}}{k_{1}^{2}})^{2} + (q_{1}\sigma_{C_{p}})^{2} + (C_{p}\sigma_{q_{1}})^{2} } \approx 0.002 \; \frac{Вт}{К} $$
+
+$$ \frac{\sigma_{N_{пот}}}{N} = \frac{1}{(C_{p}q+\alpha)^{2}}\sqrt{(C_{p}q\sigma_{\alpha})^{2}+(\alpha q \sigma_{C_{p}})^{2} + (\alpha C_{p} \sigma_{q})^{2} }$$
+$$ \frac{\sigma_{N_{пот}}}{N_{1}} \approx 0.0217, \; \frac{\sigma_{N_{пот}}}{N_{2}} \approx 0.0257 $$
+\subsection{Обсуждение результатов}
+Полученное значение $ C_{p} = 1.006 \pm 0.165 \; \frac{Дж}{г*К} $ практически совпадает с табличным $ C_{p}^{табл} = 1.004 \; \frac{Дж}{г*К} $
+Предположение о линейной зависимости $ \Delta T (N) $ подтвердилось.
 
+\subsection{Вывод}
+Экспериментальным путем мы смогли определить крайне близкое к реальному значение удельной теплоемкости воздуха при постоянном давлении.
 \end{document}
diff --git a/2.1.1/lab.tex1 b/2.1.1/lab.tex1
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+++ b/2.1.1/lab.tex1
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+\documentclass[a4paper,12pt]{article}
+\usepackage{cmap}
+\usepackage[utf8]{inputenc}
+\usepackage[warn]{mathtext}
+\usepackage{epsf,amsmath,amsfonts,amssymb,amsbsy}
+\usepackage[mathscr]{eucal}
+\usepackage[english, russian]{babel}
+\usepackage{gnuplottex}
+
+\author{Гришаев Григорий С01-119}
+\title{Отчёт о выполнении лабораторной работы 2.1.1}
+\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
+\usepackage{graphicx}
+\usepackage{indentfirst}
+\graphicspath{{images/}}
+\DeclareGraphicsExtensions{.pdf,.png,.jpg}
+\usepackage{pgfplots}
+\begin{document}
+	\maketitle
+	\begin{center}
+		{\Large Измерение удельной теплоёмкости воздуха при постоянном давлении}
+	\end{center}
+	\paragraph*{Цель работы:}измерить повышение температуры воздуха в зависимости от мощности подводимого тепла и расхода при стационарном течении через трубу; исключив тепловые потери, по результатам измерений определить теплоёмкость воздуха при постоянном давлении
+	\paragraph*{В работе используются:}теплоизолированная стеклянная трубка; электронагреватель; источник питания постоянного тока; амперметр, вольтметр (цифровые мультиметры); термопара, подключенная к микровольтметру; компрессор; газовый счётчик; секундомер.
+
+
+	\section{Теоретические сведения}
+		Определение теплоёмкости обычно производится в калориметрах. При этом регистрируется количество тепла {Q}, полученное телом, и изменение температуры этого тела $ {\Delta T} $.
+		Теплоёмкость тела определяется как их отношение:
+		\begin{equation}
+		\label{eq1}
+			C = \frac{\delta Q}{dT} \;
+		\end{equation}
+			Необходимо, чтобы количество тепла, затрачиваемое на нагревание исследуемого тела, существенно превосходило тепло, расходуемое на нагревание самого калориметра, а также на потери тепла из установки.		 
+		 Для увеличения количества нагреваемого газа при неизменных размерах установки в нашей работе исследуемый газ (воздух) продувается через калориметр, внутри которого установлен нагреватель. При этом измеряются мощность нагревателя, масса воздуха, протекающего в единицу времени (расход), и приращение его температуры.
+		 Рассмотрим газ, протекающий стационарно слева направо через трубу постоянного сечения, в которой установлен нагревательный элемент (см. рис. 1). Пусть за некоторое время $ dT $  через калориметр прошла малая порция газа массой $ dm = qdt $, где $ q $ [кг/с] — массовый расход газа в трубе. Если мощность нагрева равна $ N $, мощность тепловых потерь на обмен с окружающей средой $ N_{пот} $, то порция получила тепло $ \delta Q = (N - N_{пот})dt $. С другой стороны, по определению теплоёмкости \ref{eq1}, $ \delta Q = c dm \Delta T$, где $ \Delta T = T_{2} - T_{1}$ - приращение температуры газа, и $ c $ — удельная (на единицу массы) теплоёмкость газа в рассматриваемом процессе. При малых расходах газа и достаточно большом диаметре трубы перепад давления на её концах мал, поэтому можно принять, что $ P_{1} \approx P_{2} = P_{0} $, где $ P_{0} $ — атмосферное давление. Следовательно, в условиях опыта измеряется удельная теплоёмкость при постоянном давлении $ c_{p} $. Таким образом, получаем
+		\begin{equation}
+		\label{eq2}
+			c_{p} = \frac{N - N_{пот}}{q \Delta T};
+		\end{equation}
+		\begin{figure}[h!]
+			\center{\includegraphics[width=0.5\linewidth]{1}}
+			\caption{Нагрев газа при течении по трубе}
+		\end{figure}	 
+
+
+	\subsection{Экспериментальная установка:}
+	
+	Схема установки изображена на рис.2. Воздух, нагнетаемый компрессором, прокачивается через калориметр. Калориметр представляет собой стеклянную цилиндрическую трубку с двойными стенками, запаянными с торцов.
+	
+		\begin{figure}[h]
+			\center{\includegraphics{3}}
+			\caption{Схема экспериментальной установки}
+		\end{figure}
+	
+		Нагреватель в виде намотанной на пенопласт нихромовой проволоки расположен внутри калориметра непосредственно в воздушном потоке. Нагрев проволоки производится от регулируемого источника постоянного тока (ИП).
+		Напряжение $U$ на нагревателе и ток $I$ через него регистрируются цифровыми мультиметрами. Таким образом, мощность нагрева равна 
+	\begin{equation}
+		\label{eq3}
+		N= UI \; 
+	\end{equation}
+		Для измерения разности температур $\Delta T$ служит медно-константановая
+		термопара. Один спай термопары расположен в струе воздуха, входящего в
+		калориметр, и находится при комнатной температуре, а второй — в струе выходящего нагретого воздуха. Константановая проволока термопары расположена внутри калориметра, а медные проводники подключены к цифровому вольтметру. Возникающая в термопаре ЭДС $\varepsilon$ пропорциональна разности температур $\Delta T$ спаев: 
+		\begin{equation}
+			\label{eq4}
+			\varepsilon =\beta \Delta T \;
+		\end{equation}
+			где $\beta = 40.7 \frac{мкВ}{^\circ C}$ — чувствительность медно-константановой термопары в рабочем диапазоне температур (20–30 $^\circ C$ ). ЭДС регистрируется с помощью микровольтметра.
+		
+	Объём воздуха, прошедшего через калориметр, измеряется газовым счётчиком ГС. Для регулировки расхода служит кран К. Время $ \Delta t $ прохождения некоторого объема $ \Delta V $ воздуха измеряется секундомером. Объёмный расход равен $ \Delta V/\Delta T $, массовый расход может быть найден как
+	\begin{equation}
+		\label{eq5}
+		q = \rho_{o}\frac{\Delta V}{\Delta t} \;
+	\end{equation}
+	где $ \rho_{0} $ — плотность воздуха при комнатной температуре, которая в свою очередь может быть получена из уравнения Менделеева–Клапейрона: $ \rho_{0} = \frac{\mu P_{0}}{R T_{0}} $, где $ P_{0} $ — атмосферное давление, $ T_{0} $ — комнатная температура (в Кельвинах), $ \mu $= 29,0 г/моль — средняя молярная масса (сухого) воздуха.
+	Учитывая особенности устройства калориметра, следует ожидать, что мощность нагревателя расходуется не только на нагрев массы прокачиваемого воздуха, но и частично теряется за счет нагрева внутренних стенок термостата и рассеяния тепла через торцы термостата. Можно предположить, что при небольшом нагреве ($ \Delta T << T_{0} $) мощность потерь тепла $ N_{пот} $ прямо
+пропорциональна разности температур:
+\begin{equation}
+	\label{eq6}
+	N_{пот} = \alpha \Delta T \;
+\end{equation}
+где $ \alpha $ — некоторая константа. При этом условии основное соотношение \ref{eq2} принимает вид
+\begin{equation}
+	\label{eq7}
+	N = (c_{p}q + \alpha)\Delta T \;
+\end{equation}
+Следовательно, при фиксированном расходе воздуха ($ q $ = const) подводимая мощность и разность температур связаны прямой пропорциональностью ($ \Delta T{N} $ — линейная функция).
+	\subsection{Оборудование и инструментальные погрешности}
+	Для измерения $ \varepsilon $ использовался вольтметр универсальный В7-78/1, его абсолютная погрешность равна $ \pm (0.005 \frac{\varepsilon}{100} + 3.5) \; мкВ$.
+
+	Для измерения $ U $ использовался цифровой универсальный вольтметр GDM-8145, абсолютная погрешность которого равна $ \pm (0.0003U \pm 4 \; мВ) $. 
+	Его же мы использовали для измерения $ I $, абсолютная погрешность: $ \pm (0.002I+20 \; мкА) $.
+	\subsection{Ход работы}
+	\begin{enumerate}
+		\item Запишем показания комнатной температуры, давления и влажности воздуха.
+			\begin{table}[h]
+	\begin{center}
+	\begin{tabular}{|c|c|c|}
+				\hline
+				& Значение & $ \sigma $ \\
+				\hline
+				$ T_{0} $, К & 295.45 & 0.1 \\
+				\hline
+				$ p $, Па & 99375.15 & 1 \\
+				\hline
+				$ \phi $ & 64\% & 1\% \\
+				\hline
+
+	\end{tabular}
+	\end{center}
+	\end{table}
+
+Рассчитываем плотность воздуха $ \rho_{0} $:
+			$$ \rho_{0} = \frac{2.9 * 10^{-3}*99375.15}{8.31*295.45} \approx 1.17 \; кг/м^{3} $$
+			Относительную погрешность вычисления плотности воздуха вычислим по формуле:
+			$$ \frac{\sigma_{\rho_{0}}}{\rho_{0}} = \sqrt{(\frac{\sigma_{P_{0}}}{P_{0}})^{2}+(\frac{\sigma_{\phi}}{\phi})^{2}+(\frac{\sigma_{T}}{T})^{2}} $$
+			$$ \Rightarrow \sigma_{\rho_{0}} = 0.018 \; \frac{кг}{м^{3}} $$
+		\item Рассчитываем теоретическую теплоемкость воздуха при постоянном давлении (в предположении, что воздух - смесь двух идеальных двухатомных газов):
+			$$ C_{p} = \frac{7}{2}R \approx 29.09 \; \frac{Дж}{моль*К} $$
+			$$ C_{p}^{\mu} = \frac{C_{p}}{\mu} \approx 1 \; \frac{Дж}{г*К} $$
+
+		\item С помощью газового счетчика и секундомера измерим расход воздуха для двух случаев, пользуясь формулой \ref{eq5} ($ q_{1} $ и $ q_{2} $). Результаты измерений представлены в таблице.
+			\begin{table}[h]
+				\begin{center}
+				\begin{tabular}{|c|c|c|c|c|}
+				\hline
+					$ \Delta V $, л & $ \Delta t $, с & $ \frac{\Delta V}{\Delta t} \; , \frac{л}{с} $ & $ q_{1} \; , \frac{г}{с}$  & $ \sigma_{q_{1}кос}, \; \frac{г}{с}*10^{-3} $\\
+				\hline
+					5 & 24.9 & 0.2 & 0.234  & 0.47 \\
+				\hline
+					5 & 25.6 & 0.2 & 0.234 & 0.47 \\
+				\hline
+					5 & 26.0 & 0.19 & 0.222 & 0.45 \\	
+				\hline
+				\end{tabular}
+					\caption{Измерение $ q_{1} $}
+				\end{center}
+			\end{table}
+			\begin{table}[h]
+				\begin{center}
+				\begin{tabular}{|c|c|c|c|c|}
+				\hline
+					$ \Delta V $, л & $ \Delta t $, с & $ \frac{\Delta V}{\Delta t} \; , \frac{л}{с} $ & $ q_{2} \; , \frac{г}{с}$ & $ \sigma_{q_{2}кос}, \; \frac{г}{с}*10^{-3} $ \\
+				\hline
+					5 & 32.7 & 0.15 & 0.176 & 0.35 \\
+				\hline
+					5 & 33.1 & 0.15 & 0.176 & 0.35 \\
+				\hline
+					5 & 33.2 & 0.15 & 0.176 & 0.35 \\	
+				\hline
+				\end{tabular}
+					\caption{Измерение $ q_{2} $}
+				\end{center}
+			\end{table}
+			Итого, $ q_{1} = \overline{q_{1}} = 0.23 \; г/с $, $ q_{2} = \overline{q_{2}} = 0.176 \; г/с $.
+
+			Вычислим случайную погрешность измерения $ q $:
+			$$ \sigma_{q} = \sqrt{\frac{1}{n(n-1)}\sum_{i=1}^{n}(q_{i}-\overline q)^{2}} $$
+			Итак, $ \sigma_{q_{1}} = 4*10^{-3} \; \frac{г}{с} $, $ \sigma_{q_{2}} \approx 0\; \frac{г}{с} $
+			
+			Вычислим величину относительной косвенной погрешности измерения $ q_{1} $ и $ q_{2} $:
+			$$ \frac{\sigma_{qкос}}{q} = \sqrt{(\frac{\sigma_{T_{0}}}{T_{0}})^{2} + (\frac{\sigma_{P_{0}}}{P_{0}})^{2} + (\frac{\sigma_{t}}{t})^{2}} $$
+			Косвенная погрешность для среднего значения $ q $: $ \sigma_{q_{1}кос} = 0.00046 \; \frac{г}{с} $, $ \sigma_{q_{2}кос} = 0.00035 \; \frac{г}{с}$
+
+			Суммарная погрешность: 
+			$$ \sigma_{\overline{q}} = \sqrt{(\sigma_{q})^{2}+(\sigma_{qкос})^2 } $$
+			$$ \sigma_{\overline{q_{1}}} = 0.0006 \; \frac{г}{с} $$
+			$$ \sigma_{\overline{q_{2}}} = 0.0004 \; \frac{г}{с} $$
+
+		\item Оценим величину тока нагревателя $ I_{0} $, требуемого для нагрева воздуха на $ \delta Q = 1К $. Оценим минимальную мощность $ N_{0} $, необходимую для нагрева газа при максимальном расходе $ N_{0} = c_{p}q\Delta T \approx 0.23 \; Вт $ в первом случае, $ N_{0} = c_{p}q\Delta T \approx 0.176 \; Вт $ во втором случае.
+		
+			Учитывая, что сопротивление проволоки нагревателя составляет приблизительно $ R_{н} \approx 35 \; Ом $ и в процессе опыта практически не меняется, искомое значение тока: $ I_{0}=\sqrt{\frac{N_{0}}{R_{н}}} \approx 0.08 \; А $ (в первом случае), $ I_{0}=\sqrt{\frac{N_{0}}{R_{н}}} \approx 0.07 \; А $(во втором случае).
+		\item Зафиксируем $ \Delta T(N) $ для двух значений $ q $ (между измерениями калориметр надлежит остудить):
+		$ q_{1} = 0.236 \; г/с $, $ q_{2} = 0.179 \; г/с $.
+	\begin{table}[h]
+	\begin{center}
+	\begin{tabular}{|c|c|c|c|c|}
+				\hline
+				$U, В$ & $I, мА$ & $ N $, Вт & $ \varepsilon, мкВ $ & $ \Delta T, К $ \\
+				\hline
+				6.105 & 169.81 & 1.0367 & 154 & 3.78 \\
+				\hline
+				5.576 & 155.02 & 0.8644 & 127 & 3.12 \\
+				\hline
+				5.334 & 148.46 & 0.7919 & 120 & 2.95 \\
+				\hline
+				4.947 & 133.77 & 0.6618 & 102 & 2.51 \\
+				\hline
+	
+	\end{tabular}
+	\end{center}
+		\caption{Зависимость $ \Delta T(N)$ для $ q_{1} $}
+	\end{table}
+	\begin{table}[h]
+	\begin{center}
+	\begin{tabular}{|c|c|c|c|c|}
+				\hline
+				$U, В$ & $I, мА$ & $ N $, Вт & $ \varepsilon, мкВ $ & $ \Delta T, К $ \\
+				\hline
+				5.934 & 165.82 & 0.984 & 186 & 4.57 \\
+				\hline
+				5.021 & 140.4 & 0.7049 &131 & 3.22 \\
+				\hline
+				4.572 & 127.83 & 0.5844 & 108 & 2.65 \\
+				\hline
+				4.231 & 118.3 & 0.5005 & 93 & 2.29 \\
+				\hline
+	
+	\end{tabular}
+	\end{center}
+		\caption{Зависимость $ \Delta T(N)$ для $ q_{2} $}
+	\end{table}
+
+\end{enumerate}
+\subsection{Обработка данных}
+Построим на одном графике зависимости $ \Delta T(N) $ при $ q_{1} $ и $ q_{2} $.
+Коэффициент аппроксимирующей прямой найдем по формуле $$ k = \frac{\overline{\Delta T N}}{\overline{N^{2}}} $$
+
+Итого, $ k_{1} = 3.68 $, $ k_{2} = 4.6 $.
+$$ \sigma_{k} = \sqrt{\frac{1}{n-1}(\frac{\overline{\Delta T^{2}}}{\overline{N^{2}}}-k^{2})} $$ 
+$$ \sigma_{k_{1}} \approx 0.023 \; \frac{К}{Вт} $$, $$ \sigma_{k_{2}} \approx 0.0188 \; \frac{К}{Вт} $$
+\begin{figure}[h!]
+	\centering
+	\begin{gnuplot}[terminal=epslatex]
+		set grid
+set xlabel '$ N $, Вт'
+set ylabel '$ \Delta T $, C'
+
+set multiplot
+set yrange [0:8]
+set xrange [0:1.5]
+set key spacing 2
+set key bottom right
+set key off
+
+set style line 1 lt 1 pt 7 ps 0.5 lc rgb "red" 
+set style line 2 lt 1 pt 7 ps 0.5 lc rgb "blue"
+set style line 4 lc black 
+
+set key box linestyle 4
+set key opaque Left
+
+plot "2.1.1(q1).txt" using 1:2  notitle linestyle 1
+plot "2.1.1(q2).txt" using 1:2  notitle linestyle 2 
+
+plot	3.68*x smooth csplines title "$ q_{1} $" linestyle 1, \
+	4.6*x smooth csplines title "$ q_{2} $" linestyle 2
+	\end{gnuplot}
+\end{figure}
+
+Воспользуемся соотношениями $ C_{p}q_{1} + \alpha = \frac{1}{k_{1}}, \; C_{p}q_{2} + \alpha = \frac{1}{k_{2}} $, откуда имеем 
+$$ C_{p} = \frac{k_{2}-k_{1}}{k_{2}k_{1}(q_{1}-q_{2})} $$
+$$ \alpha = \frac{1}{k_{1}} - C_{p}q_{1} $$
+Отсюда имеем: $ C_{p} \approx 1.006 \; \frac{Дж}{г*К} $, $ \alpha \approx 0.042 \; \frac{Вт}{К} $
+
+Определим долю тепловых потерь: $ \frac{N_{пот}}{N} = \frac{\alpha}{C_{p}q + \alpha}$.
+$$ \frac{N_{пот}}{N_{1}} \approx 0.153$$
+$$ \frac{N_{пот}}{N_{2}} \approx 0.189$$
+
+Определим погрешность измерения $ C_{p} $:
+$$ \sigma_{C_{p}} = \sqrt{(\frac{\sigma_{k_{1}}}{k_{1}^{2}(q_{1}-q_{2})})^{2}+(\frac{\sigma_{k_{2}}}{k_{2}^{2}(q_{1}-q_{2})})^{2}+ (\frac{k_{2}-k_{1}}{k_{2}k_{1}(q_{1}-q_{2})^{2}})^{2}(\sigma_{q_{1}}^{2}+\sigma_{q_{2}}^{2})^{2}} $$
+Итого, $\sigma_{C_{p}} \approx 0.165 \;\frac{Дж}{г*К}$
+
+$$ \sigma_{\alpha} = \sqrt{(\frac{\sigma_{k_{1}}}{k_{1}^{2}})^{2} + (q_{1}\sigma_{C_{p}})^{2} + (C_{p}\sigma_{q_{1}})^{2} } \approx 0.002 \; \frac{Вт}{К} $$
+
+$$ \frac{\sigma_{N_{пот}}}{N} = \frac{1}{(C_{p}q+\alpha)^{2}}\sqrt{(C_{p}q\sigma_{\alpha})^{2}+(\alpha q \sigma_{C_{p}})^{2} + (\alpha C_{p} \sigma_{q})^{2} }$$
+$$ \frac{\sigma_{N_{пот}}}{N_{1}} \approx 0.0217, \; \frac{\sigma_{N_{пот}}}{N_{2}} \approx 0.0257 $$
+\subsection{Обсуждение результатов}
+Полученное значение $ C_{p} = 1.006 \pm 0.165 \; \frac{Дж}{г*К} $ практически совпадает с табличным $ C_{p}^{табл} = 1.004 \; \frac{Дж}{г*К} $
+Предположение о линейной зависимости $ \Delta T (N) $ подтвердилось.
+
+\subsection{Вывод}
+Экспериментальным путем мы смогли определить крайне близкое к реальному значение удельной теплоемкости воздуха при постоянном давлении.
+\end{document}
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diff --git a/2.1.2/lab-gnuplottex-fig1.gnuplot b/2.1.2/lab-gnuplottex-fig1.gnuplot
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+set terminal epslatex
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+plot "2.1.3(50.0).data" using 1:2  notitle linestyle 4
diff --git a/2.1.2/lab-gnuplottex-fig1.tex b/2.1.2/lab-gnuplottex-fig1.tex
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+% pdflatex -shell-escape -enable-write18 lab.tex
+%\documentclass[a4paper,12pt]{article}
+
+\documentclass[a4paper,12pt]{article} 
+
+%%% Работа с русским языком
+
+%\usepackage{cmap}
+%\usepackage[utf8]{inputenc}
+%\usepackage[warn]{mathtext}
+\usepackage{epsf,amsmath,amsfonts,amssymb,amsbsy}
+\usepackage[mathscr]{eucal}
+\usepackage[english, russian]{babel}
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+
+
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+\usepackage[utf8]{inputenc}              % кодировка исходного текста
+%\usepackage[english,russian]{babel}  % локализация и переносы
+%\usepackage{gnuplottex}
+%Матеша
+%\usepackage{amsmath,amsfonts,amssymb,amsthm,mathtools} % AMS
+%\usepackage{icomma} % "Умная" запятая
+\usepackage{xcolor}
+%\mathtoolsset{showonlyrefs=true} % Показывать номера только у тех формул, на которые есть \eqref{} в тексте.
+
+%% Шрифты
+%\usepackage{euscript}	 % Шрифт Евклид
+%\usepackage{mathrsfs} % Красивый матшрифт
+
+%% Свои команды
+%\DeclareMathOperator{\sgn}{\mathop{sgn}}
+
+%% Перенос знаков в формулах (по Львовскому)
+%\newcommand*{\hm}[1]{#1\nobreak\discretionary{}
+%{\hbox{$\mathsurround=0pt #1$}}{}}
+
+%%% Заголовок
+\author{Гришаев Григорий С01-119}
+\title{Лабораторная работа 2.1.3}
+\date{\today}
+
+\begin{document}
+	
+\maketitle 
+	
+
+\paragraph*{Цель работы:}определение отношения $C_p / C_v$ углекислого газа  по измерения давления в стеклянном сосуде. Измерения производятся сначала после адиабатического расширения газа а затем после нагревания сосуда и газа до комнатной температуры. 
+\paragraph*{В работе используются:}стеклянный сосуд: U-образный жидкостный манометр; резиновая груша; газгольдер с углекислым газом. 
+
+\begin{figure}[b!]	\label{plan2}
+	
+	\center{\includegraphics[width=1 \linewidth]{1.jpg}}
+	\caption{Установка для определения $C_p / C_v$ методом адиабатического расширения газа}
+	
+\end{figure}
+
+
+
+\subparagraph*{Экспериментальная установка.} Используемая для опытов экспериментальня установка состоит из стеклянного сосуда А (объёмом около 20 л), снабженного краном К, и U-образного жидкостного манометра, измеряющего избыточное давление газа в сосуде. Схема установки показана на Рис. 1. 
+
+Избыточное давление создаётся с помощью резиновой груши, сосединённой с сосудом трубкой с краном $К_1$.
+
+В начале опыта  в стеклянном сосуде А находится исследуемый газ при комнатной температуре $T_1$ и давлении $P_1$, несколько превышающем атмосферное давление  $P_0$. После открытия крана К, соединяющего сосуд А с атмосферой, давление и температура газа будут понижаться. Это уменьшение температуры приближённо можно считать адиабатическим. 
+
+Для адиабатического процесса можно записать следующее уравнение: 
+
+\begin{equation}\label{mk}
+\left(\dfrac{P_1}{P_2}\right)^{\gamma - 1} = \left(\dfrac{T_1}{T_2}\right)^\gamma , 
+\end{equation} 
+
+где индексом "1" обозначено состояние после повышения давления в сосуде и выравнивания температуры с комнатной, а индексом "2"  $-$ сразу после открытия крана и выравнивания давления с атмосферным. 
+
+После того, как кран К вновь отсоединит сосуд от атмосферы , происходит медленное изохорическое нагревание газа со скоростью, определяемой теплопроводностью стеклянных стенок сосуда. Вместе с ростом температуры растёт и давление газа. З время порядка $\Delta t_T$  (время установления температуры) система достигает равновесия, и установившаяся температура газа $T_3$ становится равной комнатной температуре $T_1$. 
+
+Тогда используя закон Гей-Люссака для изохорического процесса и уравнение \eqref{mk} найдём $\gamma$:
+
+\begin{equation}\label{acc}
+\gamma = \dfrac{\ln(P_1 / P_0)}{\ln (P_1 / P_3)}.
+\end{equation}
+
+С учётом того, что $P_i = P_0 + \rho g h_i$ и пренебрегая членами второго порядка малости получим из \eqref{acc}:
+
+\begin{equation}\label{r}
+\gamma \approx \dfrac{h_1}{h_1 - h_2}.
+\end{equation}
+
+
+\newpage
+
+\section*{Ход работы}
+
+\subparagraph*{1.} Перед началом работы убедимся в том, что краны и места сочленений трубок достаточно герметичны. Для этого нужно наполнить баллон углекислым газом до давления, превышающего атмосферное  и перекроем кран $К_1$. По  U-образному манометру снимем зависимость давления $h$ в баллоне от времени $t$ и построим график зависимости $h = f(t)$. Из графика определим время установления термодинамического равновесия $\Delta t_T$. Стабильное избыточное давление воздуха $h_1$ в баллоне должно быть тщательно измерено.
+
+\subparagraph*{2.} Откроем кран К на короткое время и закроем его снова. Подождём, пока уровень жидкости в манометре перестанет изменяться. Это произойдёт, когда температура газа в сосуде сравняется с комнатной, примерно через время $\Delta t_T$. Запишем разность уровней жидкости в манометре $h_2$. Проведём серию из 5--8 измерений сначала для времени открытия крана $\Delta t = 0,5 с$, а затем для $\Delta t \approx 1,0 с и \Delta t \approx 1,5 с$. По полученным данным вычислим используя формулу \eqref{r} вычислим $\gamma$ и построим график зависимости $\gamma(\Delta t)$.
+
+\begin{table}[h!] 
+	\caption{Экспериментальные данные для $\Delta t = 0,5$}
+	\begin{center}
+	\begin{tabular}{|*{4}{l|}}
+		\hline
+	№ & $h_1$ , см & $h_2$, см & $\gamma$ \\ \hline
+	1& &  &  \\ \hline
+	2 &  &  &  \\ \hline
+	3 &  &  &  \\ \hline
+	4 &  &  &  \\ \hline
+	5 &  &  &  \\ \hline 
+	6 &  & &  \\ \hline
+	7 &  &  &  \\ \hline 
+	& & $\gamma_{ср} =  $ & $\sigma_{с, \gamma} = $ \\ \hline
+	\end{tabular}
+	\end{center}
+\end{table}
+
+\begin{table}[h!] 
+	\caption{Экспериментальные данные для $\Delta t = 1,0$}
+	\begin{center}
+		\begin{tabular}{|*{4}{l|}}
+			\hline
+			№ & $h_1$ , см& $h_2$, см & $\gamma$ \\ \hline
+			1 &  &  &  \\ \hline
+			2 &  &  &  \\ \hline 
+			3 &  &  &  \\ \hline
+			4 &  &  &  \\ \hline
+			5 &  &  &  \\ \hline
+			& & $\gamma_{ср} = 1.155 $ & $\sigma_{с, \gamma} = 0.003$ \\ \hline
+		\end{tabular}
+	\end{center}
+\end{table}
+
+
+
+\begin{table}[h!] 
+	\caption{Экспериментальные данные для $\Delta t = 2,0$}
+	\begin{center}
+		\begin{tabular}{|*{4}{l|}}
+			\hline
+			№ & $h_1$, см & $h_2$, см & $\gamma$ \\ \hline
+			1 & &  &  \\ \hline 
+			2 &  &  &  \\ \hline
+			3 &  &  &  \\ \hline 
+			4 &  &  &  \\ \hline
+			5 &  &  &  \\ \hline
+			6 &  &  &  \\ \hline 
+			& & $\gamma_{ср} = 1.124 $ & $\sigma_{с, \gamma} = 0.007$ \\ \hline			
+		\end{tabular}
+	\end{center}
+\end{table}
+\begin{figure}[ht]
+	\centering
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+	\end{gnuplot}
+\end{figure}
+\end{document}
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+\documentclass[a4paper,12pt]{article} % добавить leqno в [] для нумерации слева
+\usepackage[a4paper,top=1.3cm,bottom=2cm,left=1.5cm,right=1.5cm,marginparwidth=0.75cm]{geometry}
+%%% Работа с русским языком
+\usepackage{cmap}					% поиск в PDF
+\usepackage[warn]{mathtext} 		% русские буквы в фомулах
+\usepackage[T2A]{fontenc}			% кодировка
+\usepackage[utf8]{inputenc}			% кодировка исходного текста
+\usepackage[english,russian]{babel}	% локализация и переносы
+%\usepackage{physics}
+\usepackage{multirow}
+\usepackage{longtable}
+
+%%% Нормальное размещение таблиц (писать [H] в окружении таблицы)
+\usepackage{float}
+\restylefloat{table}
+
+
+
+\usepackage{graphicx}
+
+\usepackage{wrapfig}
+\usepackage{tabularx}
+
+\usepackage{hyperref}
+\usepackage[rgb]{xcolor}
+\hypersetup{
+	colorlinks=true,urlcolor=blue
+}
+
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.9}
+
+%%% Дополнительная работа с математикой
+\usepackage{amsmath,amsfonts,amssymb,amsthm,mathtools} % AMS
+\usepackage{icomma} % "Умная" запятая: $0,2$ --- число, $0, 2$ --- перечисление
+
+%% Номера формул
+\mathtoolsset{showonlyrefs=true} % Показывать номера только у тех формул, на которые есть \eqref{} в тексте.
+
+%% Шрифты
+\usepackage{euscript}	 % Шрифт Евклид
+\usepackage{mathrsfs} % Красивый матшрифт
+
+%% Свои команды
+\DeclareMathOperator{\sgn}{\mathop{sgn}}
+
+%% Перенос знаков в формулах (по Львовскому)
+\newcommand*{\hm}[1]{#1\nobreak\discretionary{}
+	{\hbox{$\mathsurround=0pt #1$}}{}}
+
+\date{\today}
+
+\usepackage{gensymb}
+
+\begin{document}
+
+\begin{titlepage}
+	
+	\vspace{4.5cm}
+	{\huge
+		\begin{center}
+			{\bf Отчёт о выполнении лабораторной работы 2.1.3}\\
+			Определение $ C_p/C_v $ по скорости звука в газе
+		\end{center}
+	}
+	\vspace{2cm}
+	\begin{flushright}
+		{\LARGE Автор:\\ Гришаев Григорий Павлович \\
+			\vspace{0.2cm}
+			С01-119}
+	\end{flushright}
+\end{titlepage}
+
+
+\section{Введение}
+\textbf{Цель работы:}  \begin{enumerate}
+\item измерение частоты колебаний и длины волны при резонансе звуковых колебаний в газе, заполняющем трубу;
+\item определение показателя адиабаты с помощью уравнения состояния идеального газа.
+\end{enumerate}
+
+\textbf{В работе используются:} звуковой генератор ГЗ; электронный осциллограф ЭО; микрофон; телефон; раздвижная труба; теплоизолированная труба, обогреваемая водой из термостата; баллон со сжатым углекислым газом; газгольдер.
+
+\section{Теоретические сведения}
+
+Скорость распространения звуковой волны в газах зависит от показателя адиабаты $ \gamma $. На измерении скорости звука основан один из наиболее точных методов определения показателя адиабаты.
+
+Скорость звука в газах определяется формулой:
+
+\begin{equation}\label{velocity}
+c=\sqrt{\gamma\frac{RT}{\mu}}.
+\end{equation}
+где $ R $ -- газовая постоянная, $ T $ -- температура газа, а $ \mu $ -- его молярная масса. Преобразуя эту формулу, найдем
+\begin{equation}\label{gamma}
+\boxed{\gamma = \frac{\mu}{RT}c^2}.
+\end{equation}
+
+Таким образом, для определения показателя адиабаты достаточно измерить температуру газа и скорость распространения звука (молярная масса газа предполагается известной).
+
+Звуковая волна, распространяющаяся вдоль трубы, испытывает многократные отражения от торцов. Звуковые колебания в трубе являются наложением всех отраженных волн и очень сложны. Картина упрощается, если длина трубы $ L $ равна целому числу полуволн, то есть когда \[ L=n\lambda/2, \] где $ \lambda $ -- длина волны звука в трубе, а $ n $ -- любое целое число. Если это условие выполнено, то волна, отраженная от торца трубы, вернувшаяся к ее началу и вновь отраженная, совпадает по фазе с падающей. Совпадающие по фазе волны усиливают друг друга. Амплитуда звуковых колебаний при этом резко возрастает -- наступает резонанс.
+
+При звуковых колебаниях слои газа, прилегающие к торцам трубы, не испытывают смещения. Узлы смещения повторяются по всей длине трубы через $ \lambda/2 $. Между узлами находятся максимумы смещения.
+
+Скорость звука c связана с его частотой $ f $ и длиной волны $ \lambda $ соотношением
+
+\begin{equation}\label{lambda_f}
+c=\lambda f.
+\end{equation}
+
+Подбор условий, при которых возникает резонанс, можно производить двояко:
+\begin{enumerate}
+	\item При неизменной частоте $ f $ звукового генератора (а следовательно, и неизменной длине звуковой волны $ \lambda $) можно изменять длину трубы $ L $. Для этого применяется раздвижная труба. Длина раздвижной трубы постепенно увеличивается, и наблюдается ряд последовательных резонансов. Возникновение резонанса легко наблюдать на осциллографе по резкому увеличению амплитуды колебаний. Для последовательных резонансов имеем \begin{equation}\label{first}
+	L_n=n\frac{\lambda}{2}, \quad L_{n+1}=(n+1)\frac{\lambda}{2}, \quad \dots, \quad L_{n+k} = n\frac{\lambda}{2}+k\frac{\lambda}{2},
+	\end{equation} т. е. $ \lambda/2 $ равно угловому коэффициенту графика, изображающего зависимость длины трубы $ L $ от номера резонанса $ k $. Скорость звука находится по формуле \eqref{lambda_f}.
+	\item При постоянной длине трубы можно изменять частоту звуковых колебаний. В этом случае следует плавно изменять частоту $ f $ звукового генератора, а следовательно, и длину звуковой волны $ \lambda $. Для последовательных резонансов получим 
+	\begin{equation}\label{4}
+	L=\frac{\lambda_1}{2}n=\frac{\lambda_2}{2}(n+1)=\dots=\frac{\lambda_{k+1}}{2}(n+k).
+	\end{equation}
+	
+	Из \eqref{lambda_f} и \eqref{4} имеем:
+	\[ f_1=\frac{c}{\lambda_1}=\frac{c}{2L}n, \quad f_2=\frac{c}{\lambda_2}=\frac{c}{2L}(n+1)=f_1+\frac{c}{2L},\quad \dots, \]
+	\begin{equation}\label{5}
+	f_{k+1}=\frac{c}{\lambda_{k+1}}=\frac{c}{2L}(n+k)=f_1+\frac{c}{2L}k.
+	\end{equation}
+	Скорость звука, деленная на $ 2L $, определяется, таким образом, по угловому коэффициенту графика зависимости частоты от номера резонанса.
+\end{enumerate}
+
+\section{Экспериментальная установка}
+
+Соответственно двум методам измерения скорости звука в работе имеются две установки (рис. \ref{img1} и \ref{img2}). В обеих установках звуковые колебания в трубе возбуждаются телефоном Т и улавливаются микрофоном М. Мембрана телефона приводится в движение переменным током звуковой частоты; в качестве источника переменной ЭДС используется звуковой генератор ГЗ. Возникающий в микрофоне сигнал наблюдается на осциллографе ЭО.
+
+Микрофон и телефон присоединены к установке через тонкие резиновые трубки. Такая связь достаточна для возбуждения и обнаружения звуковых колебаний в трубе и в то же время мало возмущает эти колебания: при расчетах оба торца трубы можно считать неподвижными, а влиянием соединительных отверстий пренебречь.
+
+Первая установка (рис. \ref{img1}) содержит раздвижную трубу с миллиметровой шкалой. Через патрубок (на рисунке не показан) труба может наполняться воздухом или углекислым газом из газгольдера. На этой установке производятся измерения $ \gamma $ для воздуха и для $ CO_2 $. Вторая установка (рис. \ref{img2}) содержит теплоизолированную трубу постоянной длины. Воздух в трубе нагревается водой из термостата. Температура газа принимается равной температуре омывающей трубу воды. На этой установке измеряется зависимость скорости звука от температуры.
+
+\begin{figure}[H]
+	\begin{center}
+		\includegraphics[width=12cm]{ust1.jpg}
+	\end{center}
+	\caption{\textit{Установка для измерения скорости звука при помощи раздвижной трубы}}
+	\label{img1}
+\end{figure}
+
+\begin{figure}[H]
+	\begin{center}
+		\includegraphics[width=12cm]{ust2.jpg}
+	\end{center}
+	\caption{\textit{Установка для изучения зависимости скорости звука от температуры}}
+	\label{img2}
+\end{figure}
+
+\section{Ход работы}
+
+\subsection{Измерение $ C_p/C_v $ для воздуха при различных температурах}
+
+Проведём измерения $ C_p/C_v $ для воздуха при различных температурах. Для этого будем использовать трубу постоянного размера $ L = (740 \pm 1) $ мм. Для фиксированной температуры будем изменять частоту звукового сигнала, тем самым изменяя и длину волны, так, чтобы мы могли наблюдать последовательные резонансы. Для каждого резонанса будем фиксировать частоту, при которой он возник. Полученные измерения занесём в таблицу \ref{tab:constL}.
+
+\begin{table}[H]
+	\centering
+	\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
+		\hline
+		$ T $, К & \multicolumn{2}{c|}{\textbf{303}} & \multicolumn{2}{c|}{\textbf{310}} & \multicolumn{2}{c|}{\textbf{317}} & \multicolumn{2}{c|}{\textbf{323}} & \multicolumn{2}{c|}{\textbf{328}} \\ \hline
+		k & $ \hat{f_k} $, Гц & $ f_k $, Гц & $ \hat{f_k} $, Гц & $ f_k $, Гц & $ \hat{f_k} $, Гц & $ f_k $, Гц & $ \hat{f_k} $, Гц & $ f_k $, Гц & $ \hat{f_k} $, Гц & $ f_k $, Гц \\ \hline
+		0 & 712 & 0 & 255 & 0 & 253 & 0 & 258 & 0 & 260 & 0 \\ \hline
+		1 & 941 & 229 & 489 & 234 & 493 & 240 & 488 & 230 & 496 & 236 \\ \hline
+		2 & 1171 & 459 & 718 & 463 & 725 & 472 & 732 & 474 & 731 & 471 \\ \hline
+		3 & 1410 & 698 & 944 & 689 & 963 & 710 & 971 & 713 & 977 & 717 \\ \hline
+		4 & 1640 & 928 & 1185 & 930 & 1201 & 948 & 1203 & 945 & 1216 & 956 \\ \hline
+		5 & 1875 & 1163 & 1423 & 1168 & 1436 & 1183 & 1450 & 1192 & 1463 & 1203 \\ \hline
+		6 & 2106 & 1394 & 1657 & 1402 & 1677 & 1424 & 1697 & 1439 & 1697 & 1437 \\ \hline
+		7 & 2337 & 1625 & 1897 & 1642 & 1917 & 1664 & 1937 & 1679 & 1950 & 1690 \\ \hline
+	\end{tabular}
+	\caption{Результаты измерений при разных температурах для воздуха}
+	\label{tab:constL}
+\end{table}
+
+Также занесём в таблицу величину $ f_k = \hat{f_k} - \hat{f_0} $. Погрешность измерения такой величины составит $ \sigma_{f_k} = \sigma_{\hat{f_k}}\sqrt{2} \approx 2,82 $ Гц.
+
+По полученным экспериментальным данным построим графики зависимости $ f_k(k) $.
+
+
+\begin{center}
+	\begin{tikzpicture}
+	\begin{axis}[
+	title={График зависимости $f_k(k)$ для воздуха},
+	xlabel={Номера резонанса $ k $},
+	ylabel={Резонансная частота $ f $, Гц},
+	legend pos=north west,
+	xmajorgrids=true,
+	ymajorgrids=true,
+	grid style=dashed,
+	/pgf/number format/.cd,%
+	set thousands separator={},
+	set decimal separator={,},
+	xmin = 0,
+	%xmax = 4.3,
+	ymin = 0,
+	%ymax = 5500,
+	width = 510,
+	height = 670,
+	]
+	\legend{ 
+		$ T = 303 $ К,,
+		$ T = 310 $ К,,
+		$ T = 317 $ К,,
+		$ T = 323 $ К,,
+		$ T = 328 $ К,,
+	};
+	
+	\addplot+ [black, only marks, mark size = 3pt,
+	mark=*, 
+	mark options = {
+		fill = red, 
+		draw = black},
+	error bars/.cd,
+	y dir=both, y explicit,
+	] table [x = k, y = L, y error = dL,] {
+		k	L	dL
+		0	0	3
+		1	229	3
+		2	459	3
+		3	698	3
+		4	928	3
+		5	1163	3
+		6	1394	3
+		7	1625	3
+	};
+	\addplot [red, domain=0:7.1, line width = 2.2pt] { 232.192857085818 * x};
+	
+	\addplot+ [black, only marks, mark size = 3pt, 
+	mark options = {
+		fill = blue, 
+		draw = black},
+	error bars/.cd,
+	y dir=both, y explicit,
+	] table [x = k, y = L, y error = dL,] {
+		k	L	dL
+		0	0	3
+		1	234	3
+		2	463	3
+		3	689	3
+		4	930	3
+		5	1168	3
+		6	1402	3
+		7	1642	3
+	};
+	\addplot [blue, domain=0:7.1, line width = 2.2pt] { 233.521428412963 * x};
+	
+	\addplot+ [black, only marks, mark size = 3pt, 
+	mark options = {
+		fill = green, 
+		draw = black},
+	error bars/.cd,
+	y dir=both, y explicit,
+	] table [x = k, y = L, y error = dL,] {
+		k	L	dL
+		0	0	3
+		1	240	3
+		2	472	3
+		3	710	3
+		4	948	3
+		5	1183	3
+		6	1424	3
+		7	1664	3
+	};
+	\addplot [green, domain=0:7.1, line width = 2.2pt] { 237.235714303741 * x};
+	
+	\addplot+ [black, only marks, mark size = 3pt, 
+	mark options = {
+		fill = orange, 
+		draw = black},
+	error bars/.cd,
+	y dir=both, y explicit,
+	] table [x = k, y = L, y error = dL,] {
+		k	L	dL
+		0	0	3
+		1	230	3
+		2	474	3
+		3	713	3
+		4	945	3
+		5	1192	3
+		6	1439	3
+		7	1679	3
+	};
+	\addplot [orange, domain=0:7.1, line width = 2.2pt] { 238.885714210443 * x};
+	
+	\addplot+ [black, mark=halfcircle*, only marks, mark size = 3pt, 
+	mark options = {
+		fill = violet, 
+		draw = black},
+	error bars/.cd,
+	y dir=both, y explicit,
+	] table [x = k, y = L, y error = dL,] {
+		k	L	dL
+		0	0	3
+		1	236	3
+		2	471	3
+		3	717	3
+		4	956	3
+		5	1203	3
+		6	1437	3
+		7	1690	3
+	};
+	\addplot [violet, domain=0:7.1, line width = 2.2pt] { 240.142856845106 * x};
+	
+	\end{axis}
+	\end{tikzpicture}
+\end{center}
+
+Аппроксимируем полученные зависимости прямыми $ y=ax $ используя метод наименьших квадратов. Коэффициент $ a $ и погрешности его определения находим согласно формулам \eqref{mnk:a}, \eqref{mnk:sigma_a} и \eqref{mnk:full_sigma}. Результаты вычислений для каждой температуры заносим в таблицу \ref{tab:resConstL}.
+
+\begin{table}[H]
+	\centering
+	\begin{tabular}{|c|c|c|c|c|c|c|}
+		\hline
+		$ T $, К & $ a $, с$ ^{-1} $ & $ \sigma_a $, с$ ^{-1} $ & $ c $, м/с & $ \sigma_c $, м/с & $ \gamma $ & $ \sigma_\gamma $ \\ \hline
+		303 & 232,2 & 0,3 & 343,6 & 0,6 & 1,358 & 0,005 \\ \hline
+		310 & 233,5 & 0,3 & 345,6 & 0,6 & 1,343 & 0,005 \\ \hline
+		317 & 237,2 & 0,3 & 351,1 & 0,6 & 1,355 & 0,005 \\ \hline
+		323 & 238,9 & 0,3 & 353,6 & 0,6 & 1,349 & 0,005 \\ \hline
+		328 & 240,1 & 0,3 & 355,4 & 0,6 & 1,342 & 0,005 \\ \hline
+	\end{tabular}
+	\caption{Результаты вычислений при различных температурах}
+	\label{tab:resConstL}
+\end{table}
+
+Также, согласно формуле \eqref{5}, коэффициент наклона $ \displaystyle a = \frac{c}{2L}$. Тогда вычислим скорость звука $ c $ при фиксированной температуре и её погрешность, результаты вычислений занесём в таблицу \ref{tab:resConstL}.
+
+Кроме того, по формуле \eqref{gamma} вычислим $ \gamma $ при фиксированной температуре и погрешность этого вычисления. Результаты занесём в таблицу $ \ref{tab:resConstL} $. 
+
+Согласно полученным данным, можно утверждать, что $ \gamma $ остаётся постоянной в исследуемом диапазоне температур. Поэтому усредним результаты, полученные при различных значениях температуры и получим для воздуха:
+
+\[ \boxed{\gamma = 1,350 \pm 0,004}\quad (\varepsilon=0,3\%) \]
+
+\section{Обсуждение результатов и выводы}
+
+В ходе выполнения работы мы измерили частоту колебаний и длину волны при резонансе звуковых колебаний в газе, заполняющем экспериментальную установку.
+
+Измерения проводились на установке, на которой длина трубы оставалась постоянной на протяжении всего опыта, а резонанса мы добивались при помощи изменения частоты звукового сигнала. В ходе этих измерений также исследовалась зависимость коэффициента адиабаты $ \gamma $ от температуры газа. Было получено, что показатель адиабаты не зависит от температуры в диапазоне температур $ 20-60 $ $ ^\circ C $ и равняется:
+
+\[ \boxed{\gamma_L = 1,350 \pm 0,004}\quad (\varepsilon=0,5\%) \]
+
+Сравним полученные данные с табличными. Согласно справочнику, показатель адиабаты для воздуха при нормальных условиях равен \underline{$ \gamma = 1,4 $}. Таким образом, можно утверждать, что результаты измерения незначительно отличаются от табличных. Это может быть связано с большой неточностью определения резонансных частот. Чтобы этого избежать, необходимо использовать генератор частоты с возможностью более точной настройки для возможности чёткого отслеживания резонансов.
+
+\end{document}
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diff --git a/2.4.1/lab.pdf b/2.4.1/lab.pdf
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diff --git a/2.4.1/lab.tex b/2.4.1/lab.tex
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+++ b/2.4.1/lab.tex
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+\documentclass[a4paper,12pt]{article}
+\usepackage{cmap}
+\usepackage[utf8]{inputenc}
+\usepackage[warn]{mathtext}
+\usepackage{epsf,amsmath,amsfonts,amssymb,amsbsy}
+\usepackage[mathscr]{eucal}
+\usepackage[english, russian]{babel}
+\usepackage{gnuplottex}
+
+\author{Гришаев Григорий С01-119}
+\title{Отчёт о выполнении лабораторной работы 2.4.1}
+\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
+\usepackage{graphicx}
+\usepackage{indentfirst}
+\graphicspath{{images/}}
+\DeclareGraphicsExtensions{.pdf,.png,.jpg}
+\usepackage{pgfplots}
+\begin{document}
+	\maketitle
+	\begin{center}
+		{\Large Определение теплоты испарения жидкости}
+	\end{center}
+	\paragraph*{Цель работы:}) измерение давления насыщенного пара жидкости при разной температуре;
+	2) вычисление по полученным данным теплоты испарения с помощью уравнения Клапейрона–Клаузиуса.
+	\paragraph*{В работе используются:}термостат; герметический сосуд, заполненный исследуемой жидкостью; отсчетный микроскоп.
+
+\section{Теоретические сведения}
+Теплоту парообразования жидкостей можно измерить непосредственно при помощи калориметра. Такой метод, однако, не позволяет получить точных результатов из-за неконтролируемых потерь тепла,
+которые трудно сделать малыми. В настоящей работе для определения теплоты испарения применен косвенный метод, основанный на формуле Клапейрона–Клаузиуса: 
+$$\frac{dP}{dT} = \frac{L}{T(V_2 - V_1)}\;(1).$$
+
+Здесь $P$ — давление насыщенного пара жидкости при температуре $T$, $T$ — абсолютная температура
+жидкости и пара, $L$ — теплота испарения жидкости, $V_2$ — объем пара, $V_1$ — объем жидкости. Найдя
+из опыта $\frac{dP}{dT},\; T,\; V_2$ и $V_1$, можно определить $L$ путем расчета. Величины $L, \;V2$
+и $V1$ в формуле (1) должны относиться к одному и тому же количеству вещества; мы будем относить
+их к одному молю.
+В нашем приборе измерения производятся при давлениях ниже атмосферного. В этом случае задача
+существенно упрощается.
+
+С помощью урав
+
+\end{document}
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new file mode 100644
index 0000000..f6f2fe7
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+++ b/2.4.1/lab2.4.1-gnuplottex-fig1.gnuplot
@@ -0,0 +1,27 @@
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+# 4.6*x smooth csplines title "$ q_{2} $" linestyle 2
diff --git a/2.4.1/lab2.4.1-gnuplottex-fig1.tex b/2.4.1/lab2.4.1-gnuplottex-fig1.tex
new file mode 100644
index 0000000..782cc4a
--- /dev/null
+++ b/2.4.1/lab2.4.1-gnuplottex-fig1.tex
@@ -0,0 +1,160 @@
+% GNUPLOT: LaTeX picture with Postscript
+\begingroup
+  \makeatletter
+  \providecommand\color[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package color not loaded in conjunction with
+      terminal option `colourtext'%
+    }{See the gnuplot documentation for explanation.%
+    }{Either use 'blacktext' in gnuplot or load the package
+      color.sty in LaTeX.}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\includegraphics[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package graphicx or graphics not loaded%
+    }{See the gnuplot documentation for explanation.%
+    }{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
+    \renewcommand\includegraphics[2][]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \@ifundefined{ifGPcolor}{%
+    \newif\ifGPcolor
+    \GPcolorfalse
+  }{}%
+  \@ifundefined{ifGPblacktext}{%
+    \newif\ifGPblacktext
+    \GPblacktexttrue
+  }{}%
+  % define a \g@addto@macro without @ in the name:
+  \let\gplgaddtomacro\g@addto@macro
+  % define empty templates for all commands taking text:
+  \gdef\gplbacktext{}%
+  \gdef\gplfronttext{}%
+  \makeatother
+  \ifGPblacktext
+    % no textcolor at all
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+  \else
+    % gray or color?
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+      \expandafter\def\csname LTw\endcsname{\color{white}}%
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+      \expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
+      \expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
+      \expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
+      \expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
+      \expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
+      \expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
+    \else
+      % gray
+      \def\colorrgb#1{\color{black}}%
+      \def\colorgray#1{\color[gray]{#1}}%
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+      \expandafter\def\csname LTb\endcsname{\color{black}}%
+      \expandafter\def\csname LTa\endcsname{\color{black}}%
+      \expandafter\def\csname LT0\endcsname{\color{black}}%
+      \expandafter\def\csname LT1\endcsname{\color{black}}%
+      \expandafter\def\csname LT2\endcsname{\color{black}}%
+      \expandafter\def\csname LT3\endcsname{\color{black}}%
+      \expandafter\def\csname LT4\endcsname{\color{black}}%
+      \expandafter\def\csname LT5\endcsname{\color{black}}%
+      \expandafter\def\csname LT6\endcsname{\color{black}}%
+      \expandafter\def\csname LT7\endcsname{\color{black}}%
+      \expandafter\def\csname LT8\endcsname{\color{black}}%
+    \fi
+  \fi
+    \setlength{\unitlength}{0.0500bp}%
+    \ifx\gptboxheight\undefined%
+      \newlength{\gptboxheight}%
+      \newlength{\gptboxwidth}%
+      \newsavebox{\gptboxtext}%
+    \fi%
+    \setlength{\fboxrule}{0.5pt}%
+    \setlength{\fboxsep}{1pt}%
+    \definecolor{tbcol}{rgb}{1,1,1}%
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+    \gplgaddtomacro\gplbacktext{%
+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
+      \put(462,1900){\makebox(0,0)[r]{\strut{}$35$}}%
+      \csname LTb\endcsname%%
+      \put(462,2386){\makebox(0,0)[r]{\strut{}$40$}}%
+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
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+      \csname LTb\endcsname%%
+      \put(6803,220){\makebox(0,0){\strut{}$50$}}%
+    }%
+    \gplgaddtomacro\gplfronttext{%
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+      \put(3477,220){\makebox(0,0){\strut{}$35$}}%
+      \csname LTb\endcsname%%
+      \put(4586,220){\makebox(0,0){\strut{}$40$}}%
+      \csname LTb\endcsname%%
+      \put(5694,220){\makebox(0,0){\strut{}$45$}}%
+      \csname LTb\endcsname%%
+      \put(6803,220){\makebox(0,0){\strut{}$50$}}%
+    }%
+    \gplgaddtomacro\gplfronttext{%
+    }%
+    \gplbacktext
+    \put(0,0){\includegraphics[width={360.00bp},height={252.00bp}]{./lab2.4.1-gnuplottex-fig1}}%
+    \gplfronttext
+  \end{picture}%
+\endgroup
diff --git a/2.4.1/lab2.4.1.aux b/2.4.1/lab2.4.1.aux
new file mode 100644
index 0000000..e020924
--- /dev/null
+++ b/2.4.1/lab2.4.1.aux
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diff --git a/2.4.1/lab2.4.1.gnuploterrors b/2.4.1/lab2.4.1.gnuploterrors
new file mode 100644
index 0000000..e69de29
diff --git a/2.4.1/lab2.4.1.log b/2.4.1/lab2.4.1.log
new file mode 100644
index 0000000..3cf4b92
--- /dev/null
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+\documentclass[a4paper,12pt]{article}
+\usepackage{cmap}
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+\usepackage[warn]{mathtext}
+\usepackage{epsf,amsmath,amsfonts,amssymb,amsbsy}
+\usepackage[mathscr]{eucal}
+\usepackage[english, russian]{babel}
+\author{Гришаев Григорий С01-119}
+\title{Отчёт о выполнении лабораторной работы 2.4.1}
+\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
+\usepackage{graphicx}
+\usepackage{indentfirst}
+\graphicspath{{images/}}
+\DeclareGraphicsExtensions{.pdf,.png,.jpg}
+\usepackage{pgfplots}
+\usepackage{gnuplottex}
+\begin{document}
+	\maketitle
+	\begin{center}
+		{\Large Определение теплоты испарения жидкости}
+	\end{center}
+
+\paragraph*{Цель работы:} 1) измерение давления насыщенного пара жидкости при разной температуре; 2) вычисление по полученным данным теплоты испарения с помощью уравнения Клапейрона–Клаузиуса.
+\paragraph*{В работе используются:} термостат; герметический сосуд, заполненный исследуемой жидкостью; отсчетный микроскоп.
+
+\section{Теоретические сведения}
+Теплоту парообразования жидкостей можно измерить непосредственно при помощи калориметра. Такой метод, однако, не позволяет получить точных результатов из-за неконтролируемых потерь тепла, которые трудно сделать малыми. В настоящей работе для определения теплоты испарения применен
+косвенный метод, основанный на формуле Клапейрона–Клаузиуса: 
+
+$$\frac{dP}{dT} = \frac{L}{T(V_2 - V_1)}\;(1).$$
+
+Здесь $P$ — давление насыщенного пара жидкости при температуре $T$, $T$ — абсолютная температура жидкости и пара, $L$ — теплота испарения жидкости, $V_2$ — объем пара, $V_1$ — объем жидкости.
+Найдя из опыта $\frac{dP}{dT},\; T,\; V_2$ и $V_1$, можно определить $L$ путем расчета. Величины $L, \;V_2$ и $V_1$ в формуле (1) должны относиться к одному и тому же количеству вещества; мы будем относить их к одному молю.
+
+В нашем приборе измерения производятся при давлениях ниже атмосферного. В этом случае задача существенно упрощается.
+
+С помощью уравнения Ван-дер-Ваальса можно получить зависимость $P(T)$, с помощью которой определить искомую величину:
+
+$$(P+\frac{a}{V^2})(V-b)=RT \; (2)$$
+В таблице ниже приведены все значения параметров различных жидкостей уранения Ван-дер-Ваальса в условиях данного опыта.
+\begin{figure}[h]
+	\center{\includegraphics[scale=1]{tabl}}
+\end{figure}
+Откуда видно, что $\frac{V_1}{V_2} < 0.005$, a $\frac{a}{PV^2}<0.03$, ошибка метода измерений равна 4\%, тогда записав уравнение Клапейрона-Менделеева для насыщенного пара, получим:
+$V=\frac{RT}{P}\;.$
+Пренебрегая $V_1$ (который не превосходит $0,5\%$ от $V_2$), запишем:
+$$L=\frac{RT^2}{P} \frac{dP}{dT} = -R\frac{d(lnP)}{d(1/T)}\;(3).$$
+Эта формула является окончательной.
+
+\section{Экспериментальная установка:}
+
+Схема установки изображена на рисунке 1. Установка включает термостат  
+\begin{figure}[h]
+	\center{\includegraphics[scale=0.5]{2}}
+	\caption{Схема установки для определения теплоты испарения}
+\end{figure}
+
+\section{Ход работы}
+
+\begin{enumerate}
+\item Измерим разность уровней в ртутном U-образном манометре с помощью микроскопа и температуру по термометру. $H$ - высота высокого колена, $h$ -низкого. При этом будем настраивать микроскоп, так, чтобы каждый раз основание мениска было у метки прибора (в дальнейшем считаем, что высота мениска не меняется, не смотря на то что поверхностное натяжение ртути на самом деле зависит от температуры и высота немного должна меняется). Результаты представлены в таблицах 1 и 2. Под $P_0$ подразумевается давление 1 мм рт.ст.
+
+Погрешность определения температуры возьмём учитывая точность прибора и тот факт, что во время измерений уровней температура могла немного изменяться $$\sigma_{T} = 0.2 \; K.$$ Соответсвенно $$\sigma_{\frac{1}{T}} = \frac{\sigma_T}{T^2} \; K^{-1}.$$
+
+Исследуемая жидкость - вода. 
+
+\begin{center}
+	\begin{table}[h]
+	\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
+	\hline 
+		$h ,\; {мм}$  & 83.3  & 83.05 & 82.75 & 81.95 &  81.25 & 80.5 & 79.9  & 78.7 &  78.05 &  77.2 & 76.55 & 76.00 & 74.7 & 73.75 & 72.45 & 71.15& 70 & 68.7 & 67.85 \\
+	\hline 
+		$H, \; {мм}$ & 109.1 & 109.35 & 110.2 & 110.8  & 111.65 & 112.4 & 113.5  &  114.2 & 115.3 & 116.0 & 117.1 & 117.7 & 118.8 & 120 & 121.35 & 122.45 & 123.7 & 125.15 & 126.4 \\
+	\hline 
+		$t,\; ^\circ С$ & 22.04 & 23.01 & 24.00 & 25.04 & 26.00  & 27.03 & 28.02 & 29.05  & 30.03 &  31.04 & 32.00 & 33.04 & 34.03 & 35.03 & 36.05 & 37.04 & 38.03 & 39.04 & 40.02 \\
+	\hline 
+%	$P, {кПа}$ &  & & & & &  & &  &  &  &  \\ 
+%	\hline 
+%	$\sigma_{P}, {Па}$  & \multicolumn{11}{|c|}{}  \\
+%	\hline 
+%	$\ln(\frac {P}{P_0})$  &  &  &   &  & &  &  &  &  & &  \\ 
+%	\hline 
+%	$\sigma_{\ln(\frac {P}{P_0})}$ &  &  &  & &  &  &  &  &  &  &  \\ 
+%	\hline
+%	$T,\; {K}$ & &  &   &  & &  &  &  &  & &  \\ 
+%	\hline
+%	$\sigma_{T},\; {K}$ &\multicolumn{11}{|c|}{} \\
+%	\hline 
+%	$\frac{1}{T}$ $\cdot 10^{-3},{K}^{-1}$ & &  &   &  & &  &  &  &  & &  \\
+%	\hline
+%	$\sigma_{\frac{1}{T}} \cdot 10^{-6},\; {K}^{-1}$ & &  &   &  & &  &  &  &  & &  \\
+%	\hline
+\end{tabular}
+	\caption{При нагреве}
+\end{table}
+\end{center}
+
+\begin{center}
+\begin{table}[h]
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
+	\hline 
+	$h ,\; {мм}$ & 67.85  & 69.6  &  71.45 & 73.15 & 73.15 & 76.05 & 78 &  &  &  & \\ 
+	\hline 
+	$H, \; {мм}$ &  126.4 &  124.5 & 122.3& 119.9 & 119.9 & 117.8  & 115.45  &   &  &  &  \\ 
+	\hline 
+	$t,\; ^\circ С$ & 40.02 & 38.04 & 36.05  & 34.04  & 32.03  & 30.03  & 28. &  &  &  &  \\
+	\hline 
+%	$P, {кПа}$ &  & & & & &  & &  &  &  &  \\ 
+%	\hline 
+%	$\sigma_{P}, {Па}$  & \multicolumn{11}{|c|}{}  \\
+%	\hline 
+%	$\ln(\frac {P}{P_0})$  &  &  &   &  & &  &  &  &  & &  \\ 
+%	\hline 
+%	$\sigma_{\ln(\frac {P}{P_0})}$ &  &  &  & &  &  &  &  &  &  &  \\ 
+%	\hline
+%	$T,\; {K}$ & &  &   &  & &  &  &  &  & &  \\ 
+%	\hline
+%	$\sigma_{T},\; {K}$ &\multicolumn{11}{|c|}{} \\
+%	\hline 
+%	$\frac{1}{T}$ $\cdot 10^{-3},{K}^{-1}$ & &  &   &  & &  &  &  &  & &  \\
+%	\hline
+%	$\sigma_{\frac{1}{T}} \cdot 10^{-6},\; {K}^{-1}$ & &  &   &  & &  &  &  &  & &  \\
+%	\hline
+\end{tabular}
+	\caption{При остывании}
+\end{table}
+\end{center}
+
+\begin{figure}[h!]
+	\centering
+	\begin{gnuplot}[terminal=epslatex]
+		set grid
+		#set xlabel '$ N $, Вт'
+		#set ylabel '$ \Delta T $, C'
+
+		set multiplot
+		set yrange [20:65]
+		set xrange [22:50]
+set key spacing 2
+set key bottom right
+set key off
+
+set style line 1 lt 1 pt 7 ps 0.5 lc rgb "red" 
+set style line 2 lt 1 pt 7 ps 0.5 lc rgb "blue"
+set style line 4 lc black 
+
+set key box linestyle 4
+set key opaque Left
+
+plot "PT.txt" using 1:2  notitle linestyle 1
+plot "PT2.txt" using 1:2  notitle linestyle 2
+
+		#plot "2.1.1(q2).txt" using 1:2  notitle linestyle 2 
+
+		#plot	3.68*x smooth csplines title "$ q_{1} $" linestyle 1, \
+		#	4.6*x smooth csplines title "$ q_{2} $" linestyle 2
+	\end{gnuplot}
+\end{figure}
+
+\end{enumerate}
+
+
+\end{document}
diff --git a/2.5.1/data.txt b/2.5.1/data.txt
new file mode 100644
index 0000000..707de4d
--- /dev/null
+++ b/2.5.1/data.txt
@@ -0,0 +1,61 @@
+l = 0.05 мм - цена деления микроскопа
+19 делений - игла
+
+Спирт
+_____
+51 Дел 
+49
+48
+49
+49
+
+K = 0.2
+9,80665 Па
+______
+Анилин
+22 мм - h1
+23 С
+
+117 Дел
+116 
+118
+116
+117
+
+5 мм - h2
+23 С
+211 Дел
+212
+212
+211
+210
+
+28 С
+210 Дел
+209
+209
+208
+208
+
+33 C
+207 Дел
+207
+207
+207
+206
+
+38 С
+205 Дел
+206
+205
+205
+204
+
+43 С
+
+
+48 С
+
+53 С
+
+58 С
diff --git a/2.5.1/images/1.jpg b/2.5.1/images/1.jpg
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index 0000000..b7759de
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+\documentclass[a4paper,12pt]{article}
+\usepackage{cmap}
+\usepackage[utf8]{inputenc}
+\usepackage[warn]{mathtext}
+\usepackage{epsf,amsmath,amsfonts,amssymb,amsbsy}
+\usepackage[mathscr]{eucal}
+\usepackage[english, russian]{babel}
+\usepackage{gnuplottex}
+
+\author{Гришаев Григорий С01-119}
+\title{Отчёт о выполнении лабораторной работы 2.5.1}
+\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
+\usepackage{graphicx}
+\usepackage{indentfirst}
+\graphicspath{{images/}}
+\DeclareGraphicsExtensions{.pdf,.png,.jpg}
+\usepackage{pgfplots}
+\begin{document}
+	\maketitle
+	\begin{center}
+		{\Large Измерение коэффициента поверхностного натяжения жидкости}
+	\end{center}
+	\paragraph*{Цель работы:}1) измерение температурной зависимости коэффициента поверхностного натяжения дистиллированной воды с использованием известного коэффициента поверхностного натяжения спирта; 2) определение полной поверхностной энергии и теплоты, необходимой для изотермического образования единицы поверхности жидкости при различной температуре.
+	\paragraph*{В работе используются:}прибор Ребиндера с термостатом и микроманометром; исследуемые жидкости; стаканы.
+
+
+\section{Теоретические сведения}
+	Наличие поверхностного слоя приводит к различию давлений по разные стороны от искривленной границы раздела двух сред.  Для сферического пузырька с воздухом  внутри жидкости избыточное давление даётся формулой Лапласа:
+	\begin{equation}
+		\label{eq1}
+		\Delta P = P_{внутри} - P_{снаружи} = \frac{2 \sigma}{r};
+	\end{equation}
+	где $ \sigma $ – коэффициент поверхностного натяжения, $ P_{внутри} $ и $ Р_{снаружи} $ – давление внутри пузырька и снаружи, $ r $ – радиус кривизны поверхности раздела двух фаз. Эта формула лежит в основе предлагаемого метода определения коэффициента поверхностного натяжения жидкости. Измеряется давление $ \Delta $, необходимое для выталкивания в жидкость пузырька воздуха.
+
+\section{Экспериментальная установка}
+\begin{figure}[h]
+	\center{\includegraphics{1}}
+	\caption{Схема установки для измерения температурной зависимости коэффициента поверхностного натяжения.}
+\end{figure}
+Исследуемая жидкость (дистиллированная вода) наливается в сосуд (колбу) В (рис.1). Тестовая жидкость (этиловый спирт) наливается в сосуд Е. При измерениях колбы герметично закрываются пробками.  Через одну из двух пробок проходит полая металлическая игла С. Этой пробкой закрывается сосуд, в котором проводятся измерения. Верхний конец иглы открыт в атмосферу, а нижний погружен в жидкость. Другой сосуд герметично закрывается второй пробкой. При создании достаточного разряжения воздуха в колбе с иглой пузырьки воздуха начинают пробулькивать через жидкость. Поверхностное натяжение можно определить по величине разряжения $ \Delta P $ (1), необходимого для прохождения пузырьков (при известном радиусе иглы).
+
+Разряжение в системе создается с помощью аспиратора А. Кран К2 разделяет две полости аспиратора. Верхняя полость при закрытом кране К2  заполняется водой. Затем кран К2 открывают и заполняют водой  нижнюю полость  аспиратора.  Разряжение воздуха создается в нижней полости  при открывании крана К1, когда  вода вытекает из неё по каплям. В колбах В и С, соединённых трубками с нижней полостью аспиратора,  создается такое же пониженное давление. Разность давлений в полостях с разряженным воздухом и атмосферой измеряется спиртовым микроманометром.
+
+Для стабилизации температуры исследуемой жидкости через рубашку D колбы В непрерывно прогоняется вода из термостата.
+
+Обычно кончик иглы лишь касается поверхности жидкости, чтобы исключить влияние гидростатического давления столба жидкости. Однако при измерении температурной зависимости коэффициента поверхностного натяжения возникает ряд сложностей. Во-первых, большая теплопроводность металлической трубки приводит к тому, что температура на конце трубки заметно ниже, чем в глубине жидкости. Во-вторых, тепловое расширение поднимает уровень жидкости при увеличении температуры.
+
+Обе погрешности можно устранить, погрузив кончик трубки до самого дна. Полное давление, измеренное при этом микроманометром, $ P = \Delta P + \rho g h $. 
+Заметим, что $ \rho g h $ от температуры практически не зависит, так как подъём уровня жидкости компенсируется уменьшением её плотности (произведение $ \rho h $ определяется массой всей жидкости и поэтому постоянно).
+Величину  $ \rho g h $ следует измерить двумя способами. Во-первых, замерить величину $ Р_{1} = \Delta P' $, когда кончик трубки только касается поверхности жидкости. 
+Затем при этой же температуре опустить иглу до дна и замерить $ Р_{2}= \rho g h + \Delta P" $ ($ \Delta P' $, $ \Delta P" $ – давление Лапласа). Из-за  несжимаемости  жидкости можно положить $ \Delta P'= \Delta P'' $ и тогда $ \rho g h = Р_{2} - Р_{1} $. Во-вторых, при измерениях $ Р_{1} $ и $ Р_{2} $ замерить линейкой  глубину погружения иглы $ h $. Это можно сделать, замеряя расстояние между верхним концом иглы и любой неподвижной частью прибора при положении иглы на поверхности и в глубине колбы.)
+
+\section{Ход работы}
+\begin{enumerate}
+	\item Измерение диаметра иглы
+		Измерим максимальное давление при пробулькивании пузырьков воздуха через спирт.
+	\begin{table}[h]
+	\begin{center}
+	\begin{tabular}{|c|c|}
+				\hline
+				$ P' $, дел & $ P $, Па \\
+				\hline
+				39 & 76.5  \\
+				\hline
+				39 & 76.5 \\
+				\hline
+				39 & 76.5 \\
+				\hline
+				39 & 76.5 \\
+				\hline
+	\end{tabular}
+	\end{center}
+	\end{table}
+
+		$$ P = P' * 0.2 * 9.81 $$
+	Среднее значение: $ \overline P = 76.5\; Па$
+
+		Систематическую погрешность берем из расчета, что она составила половину цены деления микроманометра: $ \sigma_{P} = 0.98\; Па $ ($ \epsilon = 1.28\% $)
+
+		Коэффициент поверхностного натяжения этилового спирта при комнатной температуре (табличное значение): $ \sigma_{эт.спирта} = 22.4\; \frac{мН}{м} $
+
+		С учетом формулы (1):
+
+
+		$$ d = \frac{4 \sigma_{эт.спирта}}{\Delta P} \approx 1.17\; мм $$
+
+		Вычисляем погрешность полученного результата:
+
+		$$ \sigma_{d} = d * \epsilon_{\Delta P} \approx 0.03\; мм $$
+		
+		Т.е. $ d = (1.17 \pm 0.03) \; мм$ ($ \epsilon_{d} \approx 3 \% $)
+
+		С помощью прямого измерения с использованием микроскопа получаем $ d = (1.15 \pm 0.05)\; мм $
+
+		Значение, измеренное косвенно, совпадает со значение, измеренным непосредственно, в пределах погрешности.
+	\item Поправка для погруженной в воду иглы
+	\begin{table}[h]
+	\begin{center}
+	\begin{tabular}{|c|c|}
+				\hline
+				$ P_{1} $, дел & $ P_{1} $, Па \\
+				\hline
+				105 & 206.01 \\
+				\hline
+				106 & 207.97 \\
+				\hline
+				106 & 207.97 \\
+				\hline
+				106 & 207.97 \\
+				\hline
+	\end{tabular}
+	\end{center}
+	\end{table}
+	\begin{table}[h]
+	\begin{center}
+	\begin{tabular}{|c|c|}
+				\hline
+				$ P_{2} $, дел & $ P_{2} $, Па \\
+				\hline
+				155 & 304.11 \\
+				\hline
+				155 & 304.11 \\
+				\hline
+				155 & 304.11 \\
+				\hline
+				155 & 304.11 \\
+				\hline
+	\end{tabular}
+	\end{center}
+	\end{table}
+
+	$$ h_{1} = 17\; мм $$
+	$$ h_{2} = 7\; мм $$
+	$$ \sigma_{h} = 0.5\; мм$$
+	$$ \overline P_{1} = 207.65\; Па $$
+	$$ \overline P_{2} = 304.11\; Па $$
+	По полученным данным вычисляем $ P_{2} - P_{1} = 96.47\; Па $
+	$$ \sigma_{P}^{случ} = \sqrt{\frac{1}{n(n-1)}\sum_{i=1}^{n}(P_{i}-\overline P)^{2}} $$
+	$$ \sigma_{P} = \sqrt{(\sigma_{P}^{сист})^{2}+(\sigma_{P}^{случ})^{2}} $$
+
+	$$ \sigma_{P_{1}} = 1.99\; Па $$
+	$$ \sigma_{P_{2}} = 1.96\; Па $$
+
+\end{enumerate}
+
+\end{document}
diff --git a/2.5.1/q.txt b/2.5.1/q.txt
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+почему работаем у дна?
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+\documentclass[a4paper,12pt]{article} 
+\usepackage[T2A]{fontenc}			
+\usepackage[utf8]{inputenc}			
+\usepackage[english,russian]{babel}	
+\usepackage{amsmath,amsfonts,amssymb,amsthm,mathtools} 
+\usepackage[colorlinks, linkcolor = blue]{hyperref}
+\usepackage{upgreek}\usepackage[left=2cm,right=2cm,top=2cm,bottom=3cm,bindingoffset=0cm]{geometry}
+\usepackage{graphicx}
+\usepackage{xcolor}
+\author{Гришаев Г.П.}
+\title{3.3.4. Эффект Холла в полупроводниках.}
+\date{\today}
+\begin{document}
+\maketitle
+\newpage
+\textbf{Цель работы}: измерение подвижности и концентрации носителей заряда в полупроводниках.
+
+
+\textbf{В работе используются}: электромагнит с источником питания, амперметр, милливеберметр, реостат, источник питания, цифровой вольтметр, образцы легированного германия.\\
+\section*{Описание работы}
+\begin{center}
+\includegraphics[scale=0.5]{1.png}
+\end{center}
+Схема для измерения ЭДС Холла представлена на рисунке. В зазоре электромагнита создаётся постоянное магнитное поле, величину которого можно менять регуляторами источника питания электромагнита. Градуировка магнита проводится при помощи милливеберметра.\\
+Образец из легированного германия, смонтированный в специальном держателе, подключается к источнику питания. При замыкании К$_2$ вдоль длинной стороны образца течёт ток, величина которого регулируется реостатом $R$ и измеряется миллиамперметром. В образце, помещённом в зазор, возникает разность потенциалов $U_{34}$, которая измеряется с помощью цифрового вольтметра.\\
+Влияние омического падения напряжения исключается измерением напряжения $U_0$ между 3 и 4 в отсутствие магнитного поля. По знаку $\mathcal{E} = U_{34} \pm U_0$ можно определить характер проводимости -- электронный или дырочный, зная напрявление тока в образце и напрвление магнитного поля.\\
+Померив ток $I_{35}$ в образце и напряжение $U_{35}$ между контактами 3 и 5 в отсутствие магнитного поля можно рассчитать проводимость материала по формуле
+$$
+\sigma = \frac{IL_{35}}{U_{35}al},
+$$
+где $L_{35}$ -- расстояние между контактами 3 и 5, а $a$ и $l$ -- толщина и ширина образца.
+\section*{Ход работы}
+\begin{enumerate}
+\item Подготовим установку к работе.
+\item Проградуируем электромагнит. Определим связь между индукцией $B$ магнитного поля в зазоре электромагнита и током $I_M$ через обмотку сняв зависимость потока $\text{Ф} = BSN$, пронизывающего пробную катушку, находящуюся в зазоре, от тока $I_M$.
+\begin{table}[h]
+\centering
+\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
+\hline
+$I$, А  &  &  &  &  &  &  &  &  \\ \hline
+$B$, Вб &  &  &  &  &  &  &  &  \\ \hline
+\end{tabular}
+\end{table}
+\end{enumerate}
+\end{document} 
diff --git a/3.4.2/mls.py b/3.4.2/mls.py
new file mode 100644
index 0000000..2c00a73
--- /dev/null
+++ b/3.4.2/mls.py
@@ -0,0 +1,16 @@
+import matplotlib.pyplot as plt
+
+tau0 = 6.9092
+k = 24 * 10 ** (-3)
+
+taus = [7.982, 7.967, 7.949, 7.929, 7.908, 7.880, 7.848, 7.818, 7.782, 7.735, 7.687, 7.634, 7.583, 7.512, 7.478, 7.423, 7.318, 7.266, 7.177, 7.136, 7.109, 7.092] 
+T = [14.2, 15.05, 15.51, 16.03, 16.52, 17.03, 17.54, 18.03, 18.52, 19.04, 19.53, 20.04, 20.53, 21.05, 21.51, 22.04, 23.02, 24.03, 26.09, 28.09, 30.1, 32.04]
+delta_u = [-6, -16, -16, -16, -16, -14, -14, -15, -15, -14, -14, -13, -14, -9, -11, -14, -12, -20, -15, -15, -12, -13]
+
+y = [1 / (tau ** 2 - tau0 ** 2) for tau in taus]
+
+for i in range(len(T)):
+    T[i] += k * delta_u[i]
+plt.scatter(T,y)
+
+plt.show()
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+\documentclass[a4paper, 12pt]{article}%тип документа
+
+%отступы
+\usepackage[left=2cm,right=2cm,top=2cm,bottom=3cm,bindingoffset=0cm]{geometry}
+
+%Русский язык
+\usepackage[T2A]{fontenc} %кодировка
+\usepackage[utf8]{inputenc} %кодировка исходного кода
+\usepackage[english,russian]{babel} %локализация и переносы
+
+%Вставка картинок
+\usepackage{wrapfig}
+\usepackage{graphicx}
+\graphicspath{{pictures/}}
+\DeclareGraphicsExtensions{.pdf,.png,.jpg}
+
+%оглавление
+\usepackage{titlesec}
+\titlespacing{\chapter}{0pt}{-30pt}{12pt}
+\titlespacing{\section}{\parindent}{5mm}{5mm}
+\titlespacing{\subsection}{\parindent}{5mm}{5mm}
+\usepackage{setspace}
+
+%Графики
+\usepackage{multirow}
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.9}
+
+%Математика
+\usepackage{amsmath, amsfonts, amssymb, amsthm, mathtools}
+
+%Заголовок
+\author{Гришаев Григорий Павлович \\
+группа С01-119}
+\title{\textbf{Работа 3.4.5\\
+Петля гистерезиса (динамический метод)}}
+\newtheorem{task}{Задача}
+\begin{document}
+\maketitle
+\newpage
+\section*{Цель работы}
+Исследование предельных петель гистерезиса и начальных кривых намагничивания для нескольких ферромагнитных образцов; определение магнитных характеристик материалов, чувствительность каналов $X$ и $Y$ осциллографа и постоянную времени $\tau$ интегрирующей цепочки.
+\section*{В работе используются}
+автотрансформатор, понижающий трансформатор, амперметр и вольтметр, резистор, делитель напряжения, интегрирующая цепочка, электронный осциллограф, тороидальные образцы с двумя обмотками.
+\section*{Экспериментальная установка}
+\includegraphics[width = \textwidth]{1.png}
+
+Действующее значение переменного тока в обмотке $N_0$ измеряется амперметром $A$. Последовательно с амперметром включено сопротивление $R_0$, напряжение с которого подается на вход $X$ электронного осциллографа. Это напряжение пропорционально току в обмотке $N_0$, а следовательно и напряженности $H$ магнитного поля в образце.
+
+Для измерения магнитной индукции $B$ с измерительной обмотки $N_{\text{и}}$ на вход интегрирующей $RC$-цепочки подается напряжение $U_{\text{и}}(U_{\text{вх}})$, пропорциональное $\dot{B}$, а, с выхода снимается напряжение $U_{\text{с}}(U_{\text{вых}})$, пропорциональное величине $B$, а подается на вход $Y$.
+
+\section*{Теория}
+\subsection*{Измерение напряжения с помощью осциллографа}
+Исследуемый сигнал подается на вход $X$; длина $2x$ горизонтальной черты, наблюдаемой на экране, характеризует удвоенную амплитуду сигнала. 
+
+Если известна чувствительность усилителя $K_x$ в вольтах на деление шкалы экрана, то удвоенная амплитуда напряжения определяется произведением
+\[2U_{X, 0} = 2x \cdot K_x\]
+Напряжение, подаваемое на вход $Y$ определяется аналогично. 
+
+Калибровку осей осциллографа можно использовать для построения кривой гистерезиса в координатах $B$ и $H$:
+
+Зная величину сопротивления $R_0$, с которого снимается сигнал, можно определить чувствительность канала по току $K_{XI} = \dfrac{K_x}{R_0}$ [A/дел]; затем, используя формулу 
+\begin{equation}
+H = \dfrac{IN_0}{2\pi R}
+\end{equation}
+определить цену деления шкалы в A/м.
+
+Используя формулу 
+\begin{equation}
+B = \dfrac{R_{\text{и}}C_{\text{и}}U_{\text{вых}}}{SN_{\text{и}}}
+\end{equation}
+можно рассчитать цену деления вертикальной шкалы в теслах.
+\subsection*{Проверка калибровки горизонтальной оси ЭО с помощью амперметра}
+проводится при закороченной обмотке $N_0$. Эта обмотка с помещенным в нее ферромагнитным образцом является нелинейным элементом, так что ток в ней не имеет синусоидальной формы, и это не позволяет связать амплитуду тока с показаниями амперметра.
+\begin{equation}
+m_X = \dfrac{2 \sqrt{2} R_0 I_{\text{эф}}}{2x} \text{[B/дел]}
+\end{equation}
+\subsection*{Проверка калибровки вертикальной оси ЭО с помощью вольтметра}
+Сигнал с обмотки 12,6 В понижающего трансформатора подается на делитель напряжения. Часть этого напряжения снимается с делителя с коэффициентом деления $K_{\text{Д}}$ (1/10 или 1/100) и подается на вход $Y$. Мультиметр $V$ измеряет напряжение $U_{\text{эф}}$ на этих же клеммах делителя.
+
+Далее по формуле 
+\begin{equation}
+m_Y = \dfrac{2\sqrt{2}U_{\text{эф}}}{2y} \text{[B/дел]}
+\end{equation}
+можно рассчитать чувствительность канала $Y$.
+\subsection*{Постоянная времени $RC$-цепочки}
+Рассчитывается по формуле 
+\begin{equation}
+RC = \dfrac{U_{\text{вх}}}{\Omega U_{\text{вых}}}
+\end{equation}
+\end{document}
+
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diff --git a/Malinovskii_V2.5.1/head.tex b/Malinovskii_V2.5.1/head.tex
new file mode 100644
index 0000000..962873b
--- /dev/null
+++ b/Malinovskii_V2.5.1/head.tex
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diff --git a/Malinovskii_V2.5.1/main.aux b/Malinovskii_V2.5.1/main.aux
new file mode 100644
index 0000000..a1e2302
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diff --git a/Malinovskii_V2.5.1/main.log b/Malinovskii_V2.5.1/main.log
new file mode 100644
index 0000000..0f64d1a
--- /dev/null
+++ b/Malinovskii_V2.5.1/main.log
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diff --git a/Malinovskii_V2.5.1/main.pdf b/Malinovskii_V2.5.1/main.pdf
new file mode 100644
index 0000000..a482fcf
Binary files /dev/null and b/Malinovskii_V2.5.1/main.pdf differ
diff --git a/Malinovskii_V2.5.1/main.py b/Malinovskii_V2.5.1/main.py
new file mode 100644
index 0000000..6468a93
--- /dev/null
+++ b/Malinovskii_V2.5.1/main.py
@@ -0,0 +1,42 @@
+from math import *
+
+s = [[float(k) for k in x.split('\t') if k != '--'] for x in '23	176	176	176	176	175	--	--	--	--	--	--	--	--	--	--\n\
+30	174	174	175	175	174	175	--	--	--	--	--	--	--	--	--\n\
+35	174	174	174	174	174	174	173	173	174	174	174	174	174	173	174\n\
+40	172	172	172	172	172	172	172	172	172	172	172	172	172	172	172\n\
+45	171	171	171	171	171	171	171	171	171	171	171	171	171	171	171\n\
+50	170	170	169	169	170	170	170	169	169	170	170	169	170	170	170\n\
+55	169	169	169	169	169	169	169	170	170	169	169	170	170	169	169\n\
+60	168	169	168	168	168	168	168	168	169	169	168	168	168	168	168'.split('\n')]
+
+
+def avg(list_):
+	m = 0
+	ms = 0
+	for v in list_:
+		m += v
+		ms += v ** 2
+	n = len(list_)
+
+	m /= n
+	ms /= n
+	return (m, ((ms - m ** 2) / (n * (n - 1))) ** 0.5)
+
+dsdt = 112 / 10**6
+ddsdt = 8 / 10 ** 6
+for line in s:
+	T = line[0]
+	p, dp = avg(line[1:])
+	#print(p, sqrt(dp ** 2 + 0.5 ** 2))
+	#print(T, '{0:.1f}'.format(p), '{0:.2f}'.format(p * 1.05 / 1000 * 0.2 / 4 * 1000), sep='$&$', end='$\\\\ \\hline\n$')
+	#print(T, 0.1, p * 9.8 * 1.05 / 1000 * 0.2 / 4 * 1000, p * 9.8 * 1.05 / 1000 * 0.2 / 4 * 1000 * (0.025 / 1.05 + 0.5 / p))
+	#print(T, 0.1, - T * dsdt * 1000, 1000 * T * dsdt * (ddsdt / dsdt + 0.1 / T))
+	#print(T, 0.1, )
+	f =  - T * dsdt * 1000
+	s = p * 9.8 * 1.05 / 1000 * 0.2 / 4 * 1000
+	df = 1000 * T * dsdt * (ddsdt / dsdt + 0.1 / T)
+	ds = p * 9.8 * 1.05 / 1000 * 0.2 / 4 * 1000 * (0.025 / 1.05 + 0.5 / p)
+	#print(T, '{0:.1f}'.format(p), '{0:.0f}'.format(s), sep='$&$', end='$\\\\ \\hline\n$')
+	#print(T, 0.1, '{0:.1f}'.format(f), '{0:.1f}'.format(df), '{0:.0f}'.format(f + s), '{0:.0f}'.format(df + ds), sep='$&$', end='$\\\\ \\hline\n$')
+	print(T, 0.1, s - f, ds + df)
+	#print(T, 0.1, p * 9.8 * 1.05 / 1000 * 0.2 / 4 * 1000 - T * dsdt * 1000, 1000 * T * dsdt * (ddsdt / dsdt + 0.1 / T) + p * 9.8 * 1.05 / 1000 * 0.2 / 4 * 1000 * (0.025 / 1.05 + 0.5 / p))
\ No newline at end of file
diff --git a/Malinovskii_V2.5.1/main.tex b/Malinovskii_V2.5.1/main.tex
new file mode 100644
index 0000000..44ef57c
--- /dev/null
+++ b/Malinovskii_V2.5.1/main.tex
@@ -0,0 +1,182 @@
+\include{head}
+\usepackage{booktabs}
+
+\begin{document}
+
+\begin{center}
+  \LARGE{Работа 2.5.1}\\[0.2cm]
+  \LARGE{Измерение коэффициента поверхностного натяжения жидкости}\\[0.2cm]
+  \large{Гришаев Григорий С01-119}\\[0.2cm]
+
+\end{center}
+
+\textbf{Цель работы:} 1) измерение коэффициента поверхностного натяжения исследуемой жидкости при разной температуре с использованием известного коэффициента поверхностного натяжениядругой жидкости 2) определение полной поверхностной энергиии теплоты, необходимой для изотермического образования единицы поверхности жидкости.
+
+\textbf{В работе используются:} прибор Ребиндера с термостатом, исследуемые жидкости, стаканы.
+
+\section*{Описание работы}
+
+Наличие поверхностного слоя приводит к различию давлений поразные стороны от искривленной границы раздела двух сред. Для сферического пузырька внутри жидкости избыточное давление дается формулой Лапласа
+$$\Delta P = P_\text{внутри}-P_\text{снаружи}=2\sigma/r.$$
+Эта формула лежит в основе предлагаемого метода определения коэффициента поверхностного натяжения жидкости. Измеряется давление, необходимое для выталкивания в жидкость пузырька газа.\\
+
+Наличие поверхностного слоя приводит к различию давлений по разные стороны от искривленной границы раздела двух сред. Для сферического пузырька внутри жидкости избыточное давление дается формулой Лапласа $\Delta P = P_\text{внутри}-P_\text{снаружи}=2\sigma/r$. Эта формула лежит в основе предлагаемого метода определения коэффициента поверхностного натяжения жидкости. Измеряется давление, необходимое для выталкивания в жидкость пузырька газа.
+
+Исследуемая жидкость наливается в сосуд $B$. Дистиллированная вода наливается в сосуд $E$. Сосуды закрыты пробками. Через пробку сосуда, в котором проводятся измерения, проходит полая металлическая игла $С$, нижний конец которой погружен в жидкость, а верхний открыт в атмосферу. Если другой сосуд герметично закрыт, то в сосуде с иглой создается разрежение, и пузырьки воздуха начинают пробулькивать через жидкость. Поверхностное натяжение можно найти по величине разрежения, необходимого для прохождения пузырьков. При приоткрытом кране $\text{К}_1$ из аспиратора $A$ по каплям вытекает вода, создавая разрежение, которое измеряется наклонным спиртовым манометром $М$. Показания манометра, умноженные на зависящий от наклона коэффициент ($0.2$), дают давление в $\text{кгс}/\text{м}^2$. Чтобы пополнить запас воды, достаточно при помощи крана $\text{К}_2$ соединить нижнюю часть аспиратора с атмосферой и предварительно заполненной водой верхней частью. Через рубашку $D$ непрерывно прогоняется вода из термостата для стабилизации температуры исследуемой жидкости.
+
+\newpage
+Схема установки представлена на рис. 1:
+\begin{center}
+\includegraphics[width=0.95\textwidth]{equip.png}.
+\end{center}
+\newpage
+
+В начале эксперимента зальем аспиратор $A$ водой, и поместим чистую иглу в сосуд со спиртом $B$ так, чтобы кончик иглы лишь касался поверхности.\\
+Откроем кран $K_1$, в следствие этому давление в установке упадет, из-за чего показания манометра вырастут. Проверим установку на наличие утечки, закрыв кран $K_1$. Если показания манометра не меняются со временем, то все в порядке.\\
+При открытом кране так, что период падения капель равна $\approx 5 \text{с}$, давление прекращает расти при значении, равном $2\sigma/(r\,\sin(\alpha))$, поскольку при нем образуется пузырек газа в шприце, и давление падает. На манометре получаются давления:\\
+
+\begin{center}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
+\hline
+$p,\,\text{кгс}/\text{м}^2$&$55$&$54$&$55$&$54$&$55$&$55$&$55$&$54$&$55$&$54$&$55$&$55$&$54$&$54$&$54$&$54$\\
+\hline
+\end{tabular},
+\end{center}
+$$\Delta p = 0.5\,\text{кгс}/\text{м}^2, \sin(\alpha) = 0.2.$$
+Из измерений следует, что
+$$p = (54.5 \pm 0.6) \text{кгс}/\text{м}^2.$$
+Взяв табличное значение вязкости спитра $\sigma = (22\pm2) \text{мН}/\text{м}$, получим диаметр, равный
+$$d_\text{косв} = \frac{4\sigma}{p\sin(\alpha)} = (0.82\pm0.08) \text{мм}.$$
+Измерив диаметр иголки под микроскопом, получаем значение диаметра, равное
+$$d_\text{прям} = (1.05\pm0.03) \text{мм}.$$
+Промыв и просушив иглоку, переставим ее в сосуд с водой. Сначала измерим давления появления пузырьков при касании иголкой воды (при высоте иголки над дном сосуда $h_1$), а потом измерим то же самое, но при максимальном погружении иглы -- $h_2$.
+\begin{center}
+	\begin{tabular}{|c|c|c|c|c|c|c|c|}
+	\hline
+	$h,\,\text{мм}$ & \multicolumn{5}{c|}{$p,\,\text{кгс}/\text{м}^2$} & $<p>,\,\text{кгс}/\text{м}^2$ & $\Delta<p>,\,\text{кгс}/\text{м}^2$\\
+	\hline
+	$37.5$&$134$&$133$&$133$&$133$&$133$&$133.2$&$0.5$\\
+	\hline
+	$30.5$&$176$&$176$&$176$&$176$&$175$&$175.8$&$0.5$\\
+	\hline
+	\end{tabular}
+\end{center}
+$$\Delta h = 0.25\,\text{мм},\,\Delta p = 0.5\,\text{кгс}/\text{м}^2, \sin(\alpha) = 0.2.$$
+Прямое измерение $h_1 - h_2$ дает результат:
+$$h_1 - h_2 = 7 \pm 1 \text{мм}.$$
+Из давлений следует, что разница высот:
+$$\frac{p_2 - p_1}{\rho\,g}sin(\alpha)=8.5\pm0.2\text{мм}.$$
+Далее проведем опыт при самой большой глубине погружения иглы и разной температуте. Для того, чтобы достичь равномерного прогрева воды в установке, после смены температуры термостата, подождем $5$ минут перед измерениями давления.
+Результаты представлены ниже:
+\begin{center}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
+\hline
+$T,\,^\circ C$&\multicolumn{15}{c|}{$p,\,\text{кгс}/\text{м}^2$}\\
+\hline
+$23$&$176$&$176$&$176$&$176$&$175$&$--$&$--$&$--$&$--$&$--$&$--$&$--$&$--$&$--$&$--$\\
+\hline
+$30$&$174$&$174$&$175$&$175$&$174$&$175$&$--$&$--$&$--$&$--$&$--$&$--$&$--$&$--$&$--$\\
+\hline
+$35$&$174$&$174$&$174$&$174$&$174$&$174$&$173$&$173$&$174$&$174$&$174$&$174$&$174$&$173$&$174$\\
+\hline
+$40$&$172$&$172$&$172$&$172$&$172$&$172$&$172$&$172$&$172$&$172$&$172$&$172$&$172$&$172$&$172$\\
+\hline
+$45$&$171$&$171$&$171$&$171$&$171$&$171$&$171$&$171$&$171$&$171$&$171$&$171$&$171$&$171$&$171$\\
+\hline
+$50$&$170$&$170$&$169$&$169$&$170$&$170$&$170$&$169$&$169$&$170$&$170$&$169$&$170$&$170$&$170$\\
+\hline
+$55$&$169$&$169$&$169$&$169$&$169$&$169$&$169$&$170$&$170$&$169$&$169$&$170$&$170$&$169$&$169$\\
+\hline
+$60$&$168$&$169$&$168$&$168$&$168$&$168$&$168$&$168$&$169$&$169$&$168$&$168$&$168$&$168$&$168$\\
+\hline
+\end{tabular}
+\end{center}
+Из данных выше можно найти $<p>$ и $\sigma = \frac{pr}{2} \sin(\alpha)$.
+\begin{center}
+\begin{tabular}{|c|c|c|}
+\hline
+$T,\,^\circ C$&$<p>,\,\text{кгс}/\text{м}^2$&$\sigma, \text{мН}/\text{м}$\\\hline
+$23.0$&$175.8$&$90$\\ \hline
+$30.0$&$174.5$&$90$\\ \hline
+$35.0$&$173.8$&$89$\\ \hline
+$40.0$&$172.0$&$88$\\ \hline
+$45.0$&$171.0$&$88$\\ \hline
+$50.0$&$169.7$&$87$\\ \hline
+$55.0$&$169.3$&$87$\\ \hline
+$60.0$&$168.2$&$87$\\ \hline
+\end{tabular}
+\end{center}
+$$\Delta p = \Delta <p> = 0.5\,\text{кгс}/\text{м}^2, \Delta T = 0.1\,^\circ C, \Delta \sigma = \sigma (\frac{\Delta p}{p} + \frac{\Delta d}{d}) = 2 \text{мН}/\text{м}.$$
+Статистическая погрешность $p$ получилась сильно меньше приборной.
+\begin{center}
+\includegraphics[width=0.90\textwidth]{plot0.png}
+\end{center}
+Из МНК получаются коэффициенты:
+$$\sigma = (93.0\pm0.2) \text{мН}/\text{м}^2 - (110 \pm 5) \text{$\mu$Н}/(\text{м}^2\,^\circ C).$$
+Понятно, что погрешности этих величин неправильные. Намного удобнее считать МНК графика температуры от давления:
+\begin{center}
+\includegraphics[width=0.90\textwidth]{plot1.png}
+\end{center}
+Так происходит из-за относительно высокого значения погрешности диаметра иголки.
+Параметры этого графика:
+$$T = (8.4\pm 0.4)\cdot10^2\,^\circ C - (4.6 \pm 0.2)\,\frac{^\circ C}{\text{кгс}}\cdot p.$$
+Этой погрешности уже можно верить. Из нее получим
+$$\frac{\delta \sigma}{\delta T} = \frac{d\sin(\alpha)}{4}\frac{\delta p}{\delta T} = (112\pm8)\frac{\text{$\mu$Н}}{\text{м}\,^\circ C}.$$
+Также мы можем найти графики теплоты образования единицы поверхности жидкости $q$ и поверхнострую энергию $U$ площади $F$.
+$$q = - T \frac{\delta \sigma}{\delta T}$$
+$$U/F = \sigma - T \frac{\delta \sigma}{\delta T}$$
+\begin{center}
+\begin{tabular}{cc}
+\includegraphics[width=0.48\textwidth]{plot2.png}&
+\includegraphics[width=0.48\textwidth]{plot3.png}\\
+\end{tabular}
+\end{center}
+
+В этих графиках я брал полученное значение $\frac{\delta \sigma}{\delta T}$. Пересчет значений:
+\begin{center}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+$T\,^\circ C$&$\Delta T\,^\circ C$&$q,\,\frac{\text{мН}}{\text{м}}$&$\Delta q,\,\frac{\text{мН}}{\text{м}}$&$U/F,\,\frac{\text{мН}}{\text{м}}$&$\Delta (U/F),\,\frac{\text{мН}}{\text{м}}$\\
+\hline
+$23.0$&$0.1$&$-2.6$&$0.2$&$93$&$3$\\ \hline
+$30.0$&$0.1$&$-3.4$&$0.3$&$93$&$3$\\ \hline
+$35.0$&$0.1$&$-3.9$&$0.3$&$93$&$3$\\ \hline
+$40.0$&$0.1$&$-4.5$&$0.3$&$93$&$3$\\ \hline
+$45.0$&$0.1$&$-5.0$&$0.4$&$93$&$3$\\ \hline
+$50.0$&$0.1$&$-5.6$&$0.4$&$93$&$3$\\ \hline
+$55.0$&$0.1$&$-6.2$&$0.5$&$93$&$3$\\ \hline
+$60.0$&$0.1$&$-6.7$&$0.5$&$93$&$3$\\ \hline
+\end{tabular}.
+\end{center}
+
+\section*{Вывод}
+Поверхностное натяжение линейно меняется от температуры, и мы смогли это пронаблюдать. Характеристики этой зависимости не совпали с табличными значениями, но не сильно (для задач на поверхностное натяжение) -- меньше, чем на 1 порядок. Главным источником погрешности в этом эксперименте являлась неточность измерения диаметра. Если бы я улучшал этот эксперимент, я бы двигался в направлении уменьшения этой погрешности -- например, давал бы табличную. Я научился измерять поверхностное натяжение границы жидкость-газ при помощи иглы и того факта, что пузырьки воздуха выходят из этой иглы только при определенном давлении, зависящем от $\sigma$.
+\end{document}
+
+
+
+
+
+
+
+
+\lipsum[1-4]
+\begin{wrapfigure}{R}{5cm}
+\centering
+\includegraphics[width=0.20\textwidth]{rd.png}
+\caption{1}
+\end{wrapfigure}
+\lipsum[1-6]
+
+
+\begin{figure}[h]
+\begin{center}$
+\begin{array}{cccc}
+\includegraphics[width=0.20\textwidth]{rd.png}&
+\includegraphics[width=0.20\textwidth]{rd.png}&
+\includegraphics[width=0.20\textwidth]{rd.png}&
+\includegraphics[width=0.20\textwidth]{rd.png}\\
+(1) & (2) & (3) & (4)
+\end{array}$
+\end{center}
+\end{figure}
diff --git a/Malinovskii_V2.5.1/main2.py b/Malinovskii_V2.5.1/main2.py
new file mode 100644
index 0000000..3d4ddb7
--- /dev/null
+++ b/Malinovskii_V2.5.1/main2.py
@@ -0,0 +1,18 @@
+from math import *
+
+s = [float(x) for x in '176	176	176	176	175'.split('\t')]
+
+
+def avg(list_):
+	m = 0
+	ms = 0
+	for v in list_:
+		m += v
+		ms += v ** 2
+	n = len(list_)
+
+	m /= n
+	ms /= n
+	return (m, ((ms - m ** 2) / (n * (n - 1))) ** 0.5)
+
+print(avg(s))
\ No newline at end of file
diff --git a/Malinovskii_V2.5.1/makefile b/Malinovskii_V2.5.1/makefile
new file mode 100644
index 0000000..6bcfceb
--- /dev/null
+++ b/Malinovskii_V2.5.1/makefile
@@ -0,0 +1,8 @@
+all:
+	pdflatex main.tex interaction=batchmode
+	
+clear:
+	rm *.log *.aux *.out
+
+read:
+	xreader main.pdf
\ No newline at end of file
diff --git a/Malinovskii_V2.5.1/out b/Malinovskii_V2.5.1/out
new file mode 100644
index 0000000..4b53793
--- /dev/null
+++ b/Malinovskii_V2.5.1/out
@@ -0,0 +1,9 @@
+23.0$&$175.8$&$90$\\ \hline
+$30.0$&$174.5$&$90$\\ \hline
+$35.0$&$173.8$&$89$\\ \hline
+$40.0$&$172.0$&$88$\\ \hline
+$45.0$&$171.0$&$88$\\ \hline
+$50.0$&$169.7$&$87$\\ \hline
+$55.0$&$169.3$&$87$\\ \hline
+$60.0$&$168.2$&$87$\\ \hline
+$
\ No newline at end of file
diff --git a/Malinovskii_V2.5.1/out.png b/Malinovskii_V2.5.1/out.png
new file mode 100644
index 0000000..694e832
Binary files /dev/null and b/Malinovskii_V2.5.1/out.png differ
diff --git a/Malinovskii_V2.5.1/plot0 b/Malinovskii_V2.5.1/plot0
new file mode 100644
index 0000000..22ef85d
--- /dev/null
+++ b/Malinovskii_V2.5.1/plot0
@@ -0,0 +1,11 @@
+set terminal pngcairo size 500, 500 enhanced font 'Verdana, 10'
+
+f(x) = a + b * x
+
+fit f(x) 'data' u 1:3 via a, b
+
+set xlabel 'T, deg'
+set ylabel 'sigma, мН/м^2'
+plot 'data' using 1:3:2:4 w xyerrorbars title 'sigma-plot', f(x) title 'fitting line'
+
+pause -1
\ No newline at end of file
diff --git a/Malinovskii_V2.5.1/plot0.png b/Malinovskii_V2.5.1/plot0.png
new file mode 100644
index 0000000..c1bcc14
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diff --git a/Malinovskii_V2.5.1/plot1 b/Malinovskii_V2.5.1/plot1
new file mode 100644
index 0000000..9eda391
--- /dev/null
+++ b/Malinovskii_V2.5.1/plot1
@@ -0,0 +1,11 @@
+set terminal pngcairo size 500, 500 enhanced font 'Verdana, 10'
+
+f(x) = a + b * x
+
+fit f(x) 'data2' u 3:1 via a, b
+
+set ylabel 'T, deg'
+set xlabel 'p, кгс'
+plot 'data2' using 3:1:4:2 w xyerrorbars title 'pressure-plot', f(x) title 'fitting line'
+
+pause -1
\ No newline at end of file
diff --git a/Malinovskii_V2.5.1/plot1.png b/Malinovskii_V2.5.1/plot1.png
new file mode 100644
index 0000000..311ddbd
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diff --git a/Malinovskii_V2.5.1/plot2 b/Malinovskii_V2.5.1/plot2
new file mode 100644
index 0000000..1619f29
--- /dev/null
+++ b/Malinovskii_V2.5.1/plot2
@@ -0,0 +1,11 @@
+set terminal pngcairo size 500, 500 enhanced font 'Verdana, 10'
+
+f(x) = -b * x
+
+fit f(x) 'data2' u 1:3 via b
+
+set xlabel 'T, deg'
+set ylabel 'q, мН/м'
+plot 'data2' using 1:3:2:4 w xyerrorbars title 'q-plot', f(x) title 'fitting line'
+
+pause -1
\ No newline at end of file
diff --git a/Malinovskii_V2.5.1/plot2.png b/Malinovskii_V2.5.1/plot2.png
new file mode 100644
index 0000000..69eea33
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diff --git a/Malinovskii_V2.5.1/plot3 b/Malinovskii_V2.5.1/plot3
new file mode 100644
index 0000000..3ccaaf2
--- /dev/null
+++ b/Malinovskii_V2.5.1/plot3
@@ -0,0 +1,11 @@
+set terminal pngcairo size 500, 500 enhanced font 'Verdana, 10'
+
+f(x) = a - b * x
+
+fit f(x) 'data3' u 1:3 via b, a
+
+set xlabel 'T, deg'
+set ylabel 'U/F, мН/м'
+plot 'data3' using 1:3:2:4 w xyerrorbars title 'uf-plot', f(x) title 'fitting line'
+
+pause -1
\ No newline at end of file
diff --git a/Malinovskii_V2.5.1/plot3.png b/Malinovskii_V2.5.1/plot3.png
new file mode 100644
index 0000000..2efd270
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diff --git a/Malinovskii_V2.5.1/texput.log b/Malinovskii_V2.5.1/texput.log
new file mode 100644
index 0000000..040c8fa
--- /dev/null
+++ b/Malinovskii_V2.5.1/texput.log
@@ -0,0 +1,21 @@
+This is pdfTeX, Version 3.141592653-2.6-1.40.23 (TeX Live 2021/Arch Linux) (preloaded format=pdflatex 2022.3.24)  17 APR 2022 16:06
+entering extended mode
+ restricted \write18 enabled.
+ %&-line parsing enabled.
+**lab.tex
+
+! Emergency stop.
+<*> lab.tex
+           
+End of file on the terminal!
+
+ 
+Here is how much of TeX's memory you used:
+ 3 strings out of 478276
+ 110 string characters out of 5853013
+ 289381 words of memory out of 5000000
+ 18313 multiletter control sequences out of 15000+600000
+ 469259 words of font info for 28 fonts, out of 8000000 for 9000
+ 1141 hyphenation exceptions out of 8191
+ 0i,0n,0p,1b,6s stack positions out of 5000i,500n,10000p,200000b,80000s
+!  ==> Fatal error occurred, no output PDF file produced!
diff --git a/Senokosov_A/2.5.1.aux b/Senokosov_A/2.5.1.aux
new file mode 100644
index 0000000..3c2926e
--- /dev/null
+++ b/Senokosov_A/2.5.1.aux
@@ -0,0 +1,61 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\babel@aux[2]{}
+\@nameuse{bbl@beforestart}
+\catcode `"\active 
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\contentsline\oldcontentsline
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax 
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\babel@aux{russian}{}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Введение}{1}{section.1}\protected@file@percent }
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+\newlabel{key}{{1}{1}{Теоретические сведения}{equation.2.1}{}}
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+\MT@newlabel{key}
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+\usepackage{tabularx}
+
+\usepackage{hyperref}
+\usepackage[rgb]{xcolor}
+\hypersetup{
+	colorlinks=true,urlcolor=blue
+}
+
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.9}
+
+%%% Дополнительная работа с математикой
+\usepackage{amsmath,amsfonts,amssymb,amsthm,mathtools} % AMS
+\usepackage{icomma} % "Умная" запятая: $0,2$ --- число, $0, 2$ --- перечисление
+
+%% Номера формул
+\mathtoolsset{showonlyrefs=true} % Показывать номера только у тех формул, на которые есть \eqref{} в тексте.
+
+%% Шрифты
+\usepackage{euscript}	 % Шрифт Евклид
+\usepackage{mathrsfs} % Красивый матшрифт
+
+%% Свои команды
+\DeclareMathOperator{\sgn}{\mathop{sgn}}
+
+%% Перенос знаков в формулах (по Львовскому)
+\newcommand*{\hm}[1]{#1\nobreak\discretionary{}
+	{\hbox{$\mathsurround=0pt #1$}}{}}
+
+\date{\today}
+
+\usepackage{gensymb}
+
+\author{Гришаев Григорий С01-119}
+\title{Лабораторная работа 2.5.1}
+\date{\today}
+
+\begin{document}
+	
+\maketitle 
+
+\section{Введение}
+\textbf{Цель работы:}  \begin{enumerate}
+	\item измерение температурной зависимости  коэффициента поверхностного натяжения дистиллированной воды с использованием известного коэффициента поверхностного натяжения спирта;
+	\item определение полной поверхностной энергии  и теплоты, необходимой для изотермического образования единицы  поверхности жидкости  при различной температуре.
+\end{enumerate}
+
+\textbf{В работе используются:} прибор  Ребиндера  с термостатом и микроманометром; исследуемые жидкости; стаканы; микроскоп.
+\section{Теоретические сведения}
+
+Наличие поверхностного слоя приводит к различию давлений по разные стороны от искривленной границы раздела двух сред.  Для сферического пузырька с воздухом  внутри жидкости избыточное давление даётся формулой Лапласа:
+
+\begin{equation}\label{key}
+\Delta P = P_{int} - P_{ext} = \frac{2\sigma}{r},
+\end{equation}
+где $ \sigma $ -- коэффициент поверхностного натяжения, $ P_{int} $ и $ P_{ext} $ -- давление внутри пузырька и снаружи, $ r $ -- радиус кривизны поверхности раздела двух фаз. Эта формула лежит в основе предлагаемого метода определения коэффициента поверхностного натяжения жидкости. Измеряется давление $ \Delta P $, необходимое для выталкивания в жидкость пузырька воздуха.
+
+\section{Экспериментальная установка}
+
+\begin{figure}[H]
+	\begin{center}
+		\includegraphics[width=15cm]{ust.jpg}
+		\caption{Рисунок экспериментальной установки}\label{img:ust}
+	\end{center}
+\end{figure}
+
+Исследуемая жидкость (дистиллированная вода) наливается в сосуд (колбу) $ B $ (рис. \ref{img:ust}). Тестовая жидкость  (этиловый спирт) наливается  в сосуд $ E $.  При измерениях  колбы герметично закрываются  пробками. Через одну из двух пробок  проходит полая металлическая игла $ С $. Этой пробкой закрывается сосуд, в котором  проводятся измерения. Верхний конец иглы открыт в атмосферу, а нижний погружен в жидкость. Другой сосуд герметично закрывается второй пробкой. При создании достаточного  разряжения воздуха в колбе с иглой пузырьки воздуха начинают пробулькивать через жидкость. Поверхностное натяжение можно определить по величине разряжения $ \Delta P $ \eqref{key}, необходимого для прохождения пузырьков (при известном радиусе иглы).
+
+Разряжение в системе создается с помощью аспиратора $ A $. Кран $ K_2 $ разделяет две полости аспиратора. Верхняя полость при закрытом кране $ K_2 $ заполняется водой. Затем кран $ K_2 $ открывают и заполняют водой  нижнюю полость  аспиратора.  Разряжение воздуха создается в нижней полости  при открывании крана $ K_1 $, когда  вода вытекает из неё по каплям. В колбах $ В $ и $ С $, соединённых трубками с нижней полостью аспиратора, создается такое же пониженное давление. Разность давлений в полостях с разряженным воздухом и атмосферой измеряется спиртовым микроманометром. 
+
+Для стабилизации температуры исследуемой жидкости через рубашку $ D $ колбы $ В $ непрерывно прогоняется вода из термостата.
+
+Обычно кончик иглы лишь касается поверхности жидкости, чтобы исключить влияние гидростатического давления столба жидкости. Однако при измерении температурной зависимости коэффициента поверхностного натяжения возникает ряд сложностей. Во-первых, большая теплопроводность металлической трубки приводит к тому, что температура на конце трубки заметно ниже, чем в глубине жидкости. Во-вторых, тепловое расширение поднимает уровень жидкости при увеличении температуры.
+
+Обе погрешности можно устранить, погрузив кончик трубки до самого дна. Полное давление, измеренное при этом микроманометром, равно \[ P = \Delta P + \rho g h.\] Заметим, что $ \rho gh $ от температуры практически не зависит, так как подъём уровня жидкости компенсируется уменьшением её плотности (произведение $ \rho g $ определяется массой всей жидкости и поэтому постоянно). Величину  $ \rho g h $ следует измерить двумя способами.
+
+Во-первых, замерить величину $ P_1= \Delta P' $, когда кончик трубки только касается поверхности жидкости. Затем при этой же температуре опустить иглу до дна и замерить $ P_2= \rho gh + \Delta P'' $ ($ \Delta P' $, $ \Delta P'' $ -- давление Лапласа). Из-за  несжимаемости  жидкости можно положить $ \Delta P' = \Delta P'' $ и тогда \[ \rho gh= P_2 - P_1. \]
+ 
+Во-вторых, при измерениях $ P_1 $ и $ P_2 $ замерить линейкой  глубину погружения иглы $ h $. Это можно сделать, замеряя расстояние между верхним концом иглы и любой неподвижной частью прибора при положении иглы на поверхности и в глубине колбы.
+\newpage
+\section{Ход работы}
+
+\subsection{Измерение диаметра иглы}
+
+Измерим максимальное давление $ \Delta P_{alc} $  при  пробулькивании пузырьков воздуха через спирт. Результаты измерений занесём в таблицу \ref{tab:alcohol}.
+
+\begin{table}[H]
+	\centering
+	\begin{tabular}{|c|c|c|c|c|}
+		\hline
+		№ & $ P' $, дел. &  $ P $, Па  & $ \langle P \rangle $, Па   & $ \sigma_{P} $, Па             \\ \hline
+		1 & 47  & 92,2 & \multirow{5}{*}{93,1} & \multirow{5}{*}{2,0} \\ \cline{1-3}
+		2 & 48  & 94,2 &                       &                      \\ \cline{1-3}
+		3 & 48  & 94,2 &                       &                      \\ \cline{1-3}
+		4 & 47  & 92,2 &                       &                      \\ \cline{1-3}
+		5 & 47  & 92,2 &                       &                      \\ \hline
+	\end{tabular}
+	\caption{Результаты измерений в спирте}
+	\label{tab:alcohol}
+\end{table}
+
+Учтём, что показания микроманометра связаны с давлением следующим соотношением: \[ P=P' \cdot 0,2 \cdot 9,81, \] где $ P' $ -- колличество делений шкалы, а константы остаются постоянными во время всей работы и определяются исходя из паспорта устройства.
+
+Вычислим среднее значение измеренного давления. Для этого воспользуемся следующей формулой:
+
+\begin{equation}\label{mid}
+\langle P \rangle = \frac{\sum\limits_{k=1}^{N} P_k}{N} \approx 93,1 \text{ Па},
+\end{equation}
+где $ N $ -- число проведённых измерений.
+
+Также вычислим случайную погрешность измерений по формуле
+
+\begin{equation}\label{occasion}
+\sigma_{P}^{\text{случ}} = \sqrt{\frac{1}{N(N-1)}\sum\limits_{k=1}^N\left(P_k-\langle P \rangle\right)^2} \approx 0,5 \text{ Па}.
+\end{equation}
+
+Систематическую погрешность определим из расчёта, что погрешность измерения составила $ 1 $ деление прибора, или же \underline{$ \sigma_{P}^\text{сист} \approx 1,9 $ Па}.
+
+Полная погрешность измерений определяется по формуле:
+
+\begin{equation}\label{full_pogr}
+\sigma_{P}=\sqrt{(\sigma_{P}^\text{сист})^2 + (\sigma_{P}^\text{случ})^2} \approx 2,0 \text{ Па}.
+\end{equation}
+
+Итого получаем \underline{ $ \Delta P_{alc} = (93,1 \pm 2,0) \text{ Па},$} \quad $(\varepsilon = 2,2 \%) $.
+
+\medskip
+
+Согласно ГОСТ 8.428-81 коэффициент поверхностного натяжения этилового спирта при комнатной температуре равен $ \sigma_{alc} = 22,4 $ мН/м. По полученным результатам измерения и при помощи \eqref{key} вычисляем диаметр иглы по формуле:
+
+\label{diametr}
+
+\begin{equation}\label{igla}
+d=\frac{4\sigma_{alc}}{\Delta P_{alc}} \approx 0,96 \text{ мм}.
+\end{equation}
+
+Также вычисляем погрешность полученного результата:
+
+\begin{equation}\label{igla_pogr}
+\sigma_d=d\cdot\varepsilon_{\Delta P_{alc}} \approx 0,02 \text{ мм}.
+\end{equation}
+
+Таким образом, получаем окончательный результат измерения диаметра иглы косвенным способом:
+\begin{itemize}
+	\item $\underline{ d = (0,96 \pm 0,02) \text{ мм},} \: (\varepsilon = 2,2\%). $
+\end{itemize}
+
+Также проведём измерение диаметра иглы при помощи оптического микроскопа.
+
+По результатам прямого измерения получаем $ \underline{d = (1,00 \pm 0,05) \text{ мм}}, \: (\varepsilon = 5\%) $.
+
+\medskip
+
+Таким образом, диаметр иглы, измеренный двумя различными способами, совпадает в пределах погрешности, что может говорить о справедливости формулы, представленной в теоретических сведениях, а также об исправной работе экспериментальной установки.
+
+\subsection{Определения поправки при измерении давления для погруженной в воду иглы}
+
+Перенесём предварительно промытую и просушенную от спирта иглу в колбу с дистиллированной водой. Измерим максимальное давление $ P_1 $ при пробулькивании пузырьков, когда игла лишь касается поверхности воды. Измерите расстояние между верхним концом иглы и любой неподвижной часть прибора $ h_1 $.
+
+Утопим иглу в воду. Измерим $ h_2 $. Также измерим максимальное давление в пузырьках $ P_2 $. Полученные результаты заносим в таблицу \ref{tab:popravka}.
+
+% Please add the following required packages to your document preamble:
+% \usepackage{multirow}
+\begin{table}[H]
+	\centering
+	\begin{tabular}{ccccccc}
+		\hline
+		\multicolumn{1}{|c|}{№} &
+		\multicolumn{1}{c|}{$ P_1 $, дел.} &
+		\multicolumn{1}{c|}{$ P_1 $, Па} &
+		\multicolumn{1}{c|}{$ \langle P_1 \rangle $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_{P_1} $, Па} &
+		\multicolumn{1}{c|}{$ h_1 $, мм} &
+		\multicolumn{1}{c|}{$ \sigma_{h_1} $, мм} \\ \hline
+		\multicolumn{1}{|c|}{1} &
+		\multicolumn{1}{c|}{131} &
+		\multicolumn{1}{c|}{257,0} &
+		\multicolumn{1}{c|}{\multirow{6}{*}{257,0}} &
+		\multicolumn{1}{c|}{\multirow{6}{*}{1,9}} &
+		\multicolumn{1}{c|}{\multirow{6}{*}{54,0}} &
+		\multicolumn{1}{c|}{\multirow{6}{*}{0,5}} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{2} &
+		\multicolumn{1}{c|}{131} &
+		\multicolumn{1}{c|}{257,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{3} &
+		\multicolumn{1}{c|}{131} &
+		\multicolumn{1}{c|}{257,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{4} &
+		\multicolumn{1}{c|}{131} &
+		\multicolumn{1}{c|}{257,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{5} &
+		\multicolumn{1}{c|}{131} &
+		\multicolumn{1}{c|}{257,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{6} &
+		\multicolumn{1}{c|}{131} &
+		\multicolumn{1}{c|}{257,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \hline
+		&
+		&
+		&
+		&
+		&
+		&
+		\\ \hline
+		\multicolumn{1}{|c|}{№} &
+		\multicolumn{1}{c|}{$ P_2 $, дел.} &
+		\multicolumn{1}{c|}{$ P_2 $, Па} &
+		\multicolumn{1}{c|}{$ \langle P_2 \rangle $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_{P_2} $, Па} &
+		\multicolumn{1}{c|}{$ h_2 $, мм} &
+		\multicolumn{1}{c|}{$ \sigma_{h_2} $, мм} \\ \hline
+		\multicolumn{1}{|c|}{1} &
+		\multicolumn{1}{c|}{190} &
+		\multicolumn{1}{c|}{372,2} &
+		\multicolumn{1}{c|}{\multirow{6}{*}{374,4}} &
+		\multicolumn{1}{c|}{\multirow{6}{*}{1,9}} &
+		\multicolumn{1}{c|}{\multirow{6}{*}{42,0}} &
+		\multicolumn{1}{c|}{\multirow{6}{*}{0,5}} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{2} &
+		\multicolumn{1}{c|}{191} &
+		\multicolumn{1}{c|}{374,7} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{3} &
+		\multicolumn{1}{c|}{191} &
+		\multicolumn{1}{c|}{374,7} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{4} &
+		\multicolumn{1}{c|}{191} &
+		\multicolumn{1}{c|}{374,7} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{5} &
+		\multicolumn{1}{c|}{191} &
+		\multicolumn{1}{c|}{374,7} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{1-3}
+		\multicolumn{1}{|c|}{6} &
+		\multicolumn{1}{c|}{191} &
+		\multicolumn{1}{c|}{374,7} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \hline
+	\end{tabular}
+	\caption{Определение поправки к давлению}
+	\label{tab:popravka}
+\end{table}
+
+Исходя из экспериментальных данных, определяем среднее значение давления $ \langle P \rangle $ и погрешность измерения $ \sigma_{P} $ по формулам \eqref{mid}, \eqref{occasion} и \eqref{full_pogr}.
+
+По полученным данным определяем \[ P_2-P_1 = 117,4 \text{ Па}. \]
+
+Также вычисляем погрешность:  \begin{equation}\label{pogr_sum}
+\sigma_{\Delta P} = \sqrt{\sigma^2_{P_1}+\sigma^2_{P_2}} \approx 2,8 \text{ Па}.
+\end{equation}
+
+Таким образом, получаем $ \underline{\Delta P = (117,4 \pm 2,8) \text{ Па},} \: (\varepsilon = 2,4\%).$
+
+По полученному значению $ \Delta P $ можем рассчитать $ \Delta h $ по следующей формуле: \[ \Delta h = \frac{\Delta P}{\rho g} \approx 11,9 \text{ мм}, \] где $ \rho = 1000 $ кг/$ \text{м}^3 $ -- плотность воды и $ g = 9,81 $ м/$ \text{с}^2 $ -- ускорение свободного падения.
+
+\medskip
+
+При этом погрешность нашего измерения равна \[ \sigma_{\Delta h} = \Delta h \cdot \varepsilon_{\Delta P} \approx 0,3 \text{ мм}. \]
+
+Таким образом, получаем $ \underline{\Delta h = (11,9 \pm 0,3) \text{ мм}}, \: (\varepsilon = 2,4\%). $
+
+\medskip
+
+Заметим, что полученный результат в пределах погрешности совпадает с результатом, полученном прямым измерением $ \underline{\Delta h' = (12,0 \pm 0,7) \text{ мм},} \: (\varepsilon = 5,9\%). $
+
+Значит, в ходе дальнейших измерений мы будем делать поправку \label{popravka} $  \underline{\Delta P = (117,4 \pm 2,8) \text{ Па},}$ на~добавочное давление со стороны столба жидкости.
+
+\subsection{Измерение температурной зависимости коэффициента поверхностного натяжения}
+
+Снимем температурную зависимость $ \sigma(T) $ дистиллированной воды. Для этого включим термостат и подождём, пока нужная нам температура не стабилизируется. После этого проведём измерение давления. Для уменьшения погрешности опыта замер давления  при фиксированной температуре проведём несколько раз. Результаты измерений занесём в таблицу \ref{tab:pov}.
+
+% Please add the following required packages to your document preamble:
+% \usepackage{multirow}
+\begin{table}[H]
+	\centering
+	\begin{tabular}{ccccccc}
+		\hline
+		\multicolumn{1}{|c|}{$ T $, К} &
+		\multicolumn{1}{c|}{$ P' $, дел} &
+		\multicolumn{1}{c|}{$ P' $, Па} &
+		\multicolumn{1}{c|}{$ \langle P' \rangle $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_{P'} $, Па} &
+		\multicolumn{1}{c|}{$ P $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_P $, Па} \\ \hline
+		\multicolumn{1}{|c|}{\multirow{5}{*}{302}} &
+		\multicolumn{1}{c|}{190} &
+		\multicolumn{1}{c|}{372,8} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{374,3}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{2,0}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{257,0}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{3,4}} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{191} &
+		\multicolumn{1}{c|}{374,7} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{191} &
+		\multicolumn{1}{c|}{374,7} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{191} &
+		\multicolumn{1}{c|}{374,7} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{191} &
+		\multicolumn{1}{c|}{374,7} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \hline
+		&
+		&
+		&
+		&
+		&
+		&
+		\\ \hline
+		\multicolumn{1}{|c|}{$ T $, К} &
+		\multicolumn{1}{c|}{$ P' $, дел} &
+		\multicolumn{1}{c|}{$ P' $, Па} &
+		\multicolumn{1}{c|}{$ \langle P' \rangle $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_{P'} $, Па} &
+		\multicolumn{1}{c|}{$ P $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_P $, Па} \\ \hline
+		\multicolumn{1}{|c|}{\multirow{5}{*}{307}} &
+		\multicolumn{1}{c|}{189} &
+		\multicolumn{1}{c|}{370,8} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{370,8}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{2,0}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{253,4}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{3,4}} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{189} &
+		\multicolumn{1}{c|}{370,8} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{189} &
+		\multicolumn{1}{c|}{370,8} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{189} &
+		\multicolumn{1}{c|}{370,8} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{189} &
+		\multicolumn{1}{c|}{370,8} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \hline
+		&
+		&
+		&
+		&
+		&
+		&
+		\\ \hline
+		\multicolumn{1}{|c|}{$ T $, К} &
+		\multicolumn{1}{c|}{$ P' $, дел} &
+		\multicolumn{1}{c|}{$ P' $, Па} &
+		\multicolumn{1}{c|}{$ \langle P' \rangle $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_{P'} $, Па} &
+		\multicolumn{1}{c|}{$ P $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_P $, Па} \\ \hline
+		\multicolumn{1}{|c|}{\multirow{5}{*}{312}} &
+		\multicolumn{1}{c|}{187} &
+		\multicolumn{1}{c|}{366,9} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{366,9}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{2,0}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{249,5}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{3,4}} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{187} &
+		\multicolumn{1}{c|}{366,9} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{187} &
+		\multicolumn{1}{c|}{366,9} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{187} &
+		\multicolumn{1}{c|}{366,9} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{187} &
+		\multicolumn{1}{c|}{366,9} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \hline
+		&
+		&
+		&
+		&
+		&
+		&
+		\\ \hline
+		\multicolumn{1}{|c|}{$ T $, К} &
+		\multicolumn{1}{c|}{$ P' $, дел} &
+		\multicolumn{1}{c|}{$ P' $, Па} &
+		\multicolumn{1}{c|}{$ \langle P' \rangle $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_{P'} $, Па} &
+		\multicolumn{1}{c|}{$ P $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_P $, Па} \\ \hline
+		\multicolumn{1}{|c|}{\multirow{5}{*}{317}} &
+		\multicolumn{1}{c|}{185} &
+		\multicolumn{1}{c|}{363,0} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{363,4}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{2,0}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{246,0}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{3,4}} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{185} &
+		\multicolumn{1}{c|}{363,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{186} &
+		\multicolumn{1}{c|}{364,9} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{185} &
+		\multicolumn{1}{c|}{363,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{185} &
+		\multicolumn{1}{c|}{363,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \hline
+		&
+		&
+		&
+		&
+		&
+		&
+		\\ \hline
+		\multicolumn{1}{|c|}{$ T $, К} &
+		\multicolumn{1}{c|}{$ P' $, дел} &
+		\multicolumn{1}{c|}{$ P' $, Па} &
+		\multicolumn{1}{c|}{$ \langle P' \rangle $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_{P'} $, Па} &
+		\multicolumn{1}{c|}{$ P $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_P $, Па} \\ \hline
+		\multicolumn{1}{|c|}{\multirow{5}{*}{322}} &
+		\multicolumn{1}{c|}{184} &
+		\multicolumn{1}{c|}{361,0} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{360,6}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{2,0}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{243,2}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{3,4}} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{184} &
+		\multicolumn{1}{c|}{361,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{183} &
+		\multicolumn{1}{c|}{359,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{184} &
+		\multicolumn{1}{c|}{361,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{184} &
+		\multicolumn{1}{c|}{361,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \hline
+		&
+		&
+		&
+		&
+		&
+		&
+		\\ \hline
+		\multicolumn{1}{|c|}{$ T $, К} &
+		\multicolumn{1}{c|}{$ P' $, дел} &
+		\multicolumn{1}{c|}{$ P' $, Па} &
+		\multicolumn{1}{c|}{$ \langle P' \rangle $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_{P'} $, Па} &
+		\multicolumn{1}{c|}{$ P $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_P $, Па} \\ \hline
+		\multicolumn{1}{|c|}{\multirow{5}{*}{327}} &
+		\multicolumn{1}{c|}{183} &
+		\multicolumn{1}{c|}{359,0} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{358,3}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{2,0}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{240,9}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{3,4}} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{182} &
+		\multicolumn{1}{c|}{357,1} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{183} &
+		\multicolumn{1}{c|}{359,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{183} &
+		\multicolumn{1}{c|}{359,0} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{182} &
+		\multicolumn{1}{c|}{357,1} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \hline
+		&
+		&
+		&
+		&
+		&
+		&
+		\\ \hline
+		\multicolumn{1}{|c|}{$ T $, К} &
+		\multicolumn{1}{c|}{$ P' $, дел} &
+		\multicolumn{1}{c|}{$ P' $, Па} &
+		\multicolumn{1}{c|}{$ \langle P' \rangle $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_{P'} $, Па} &
+		\multicolumn{1}{c|}{$ P $, Па} &
+		\multicolumn{1}{c|}{$ \sigma_P $, Па} \\ \hline
+		\multicolumn{1}{|c|}{\multirow{5}{*}{332}} &
+		\multicolumn{1}{c|}{181} &
+		\multicolumn{1}{c|}{355,1} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{354,7}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{2,0}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{237,3}} &
+		\multicolumn{1}{c|}{\multirow{5}{*}{3,4}} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{181} &
+		\multicolumn{1}{c|}{355,1} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{181} &
+		\multicolumn{1}{c|}{355,1} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{181} &
+		\multicolumn{1}{c|}{355,1} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \cline{2-3}
+		\multicolumn{1}{|c|}{} &
+		\multicolumn{1}{c|}{180} &
+		\multicolumn{1}{c|}{353,2} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} &
+		\multicolumn{1}{c|}{} \\ \hline
+	\end{tabular}
+	\caption{Измерение температурной зависимости коэффициента поверхностного натяжения}
+	\label{tab:pov}
+\end{table}
+\newpage
+Исходя из экспериментальных данных, определяем среднее значение давления $ \langle P' \rangle $ и погрешность измерения $ \sigma_{P'} $ (для давления без учёта поправки) по формулам \eqref{mid}, \eqref{occasion} и \eqref{full_pogr}.
+
+Также учитываем поправку к измеренному давлению, которая была вычислена в \ref{popravka}. Погрешность после её учёта вычисляем по формуле \eqref{pogr_sum}. Полученные результаты также заносим в таблицу \ref{tab:pov}.
+
+По полученным данным вычислим коэффициент поверхностного натяжения для каждой из температур по формуле
+
+\begin{equation}\label{sigma}
+\sigma = \frac{Pd}{4},
+\end{equation}
+где $ d $ -- диаметр иглы, вычисленный в \ref{diametr}. Погрешность такого результата вычисляется по следующей формуле:
+
+\begin{equation}\label{otn_pogr}
+\sigma_\sigma = \sigma\sqrt{\varepsilon^2_P + \varepsilon^2_d}.
+\end{equation}
+
+Полученные результаты заносим в таблицу \ref{tab:temp}.
+
+\begin{table}[H]
+	\centering
+	\begin{tabular}{|c|c|c|c|c|}
+		\hline
+		№ & $ T $, К   & $ \sigma_T, К $   & $ \sigma $, мН/м & $ \sigma_\sigma $, мН/м \\ \hline
+		1 & 302,0 & 0,1 & 61,9  & 1,6   \\ \hline
+		2 & 307,0 & 0,1 & 61,0  & 1,6   \\ \hline
+		3 & 312,0 & 0,1 & 60,1  & 1,5   \\ \hline
+		4 & 317,0 & 0,1 & 59,2  & 1,5   \\ \hline
+		5 & 322,0 & 0,1 & 58,6  & 1,5   \\ \hline
+		6 & 327,0 & 0,1 & 58,0  & 1,5   \\ \hline
+		7 & 332,0 & 0,1 & 57,2  & 1,5   \\ \hline
+	\end{tabular}
+	\caption{Зависимость коэффициента пов. натяжения от $T$}
+	\label{tab:temp}
+\end{table}
+
+Полученную зависимость наносим на график (рис. ). Вычислим коэффициенты аппроксимирующей прямой $ \sigma = kT + b $, где $ \displaystyle k = \frac{d\sigma}{dT} $, используя метод наименьших квадратов:
+
+\[ k = \frac{\langle T\sigma \rangle - \langle T \rangle \langle \sigma \rangle}{\langle T^2 \rangle - \langle T \rangle ^2} \approx -0,155\text{ } \frac{\text{мН}}{\text{м}\cdot\text{К}},\]
+
+\[ b = \langle \sigma \rangle - k\langle T \rangle \approx 108,6\text{ } \frac{\text{мН}}{\text{м}}. \]
+
+Случайные погрешности определения этих коэффициентов вычислим по следующим формулам:
+
+\[ \sigma^\text{случ}_k = \sqrt{\frac{1}{N-2} \left(\frac{\left\langle\left(\sigma - \langle \sigma\right\rangle\right)^2 \rangle}{\left\langle\left(T - \langle T\right\rangle\right)^2 \rangle}\right)-k^2} \approx 0,005 \text{ } \frac{\text{мН}}{\text{м}\cdot\text{К}},\]
+
+\[ \sigma^\text{случ}_b=\sigma^\text{случ}_k\sqrt{\left\langle x^2 \right\rangle} \approx 1,7\text{ } \frac{\text{мН}}{\text{м}}. \]
+
+Систематические погрешности оценим по следующим формулам:
+
+\[ \sigma^\text{сист}_k = |k|\sqrt{\varepsilon^2_T+\varepsilon^2_\sigma} \approx 0,004 \text{ } \frac{\text{мН}}{\text{м}\cdot\text{К}}, \]
+\[ \sigma^\text{сист}_b = |b|\sqrt{\varepsilon^2_T+\varepsilon^2_\sigma} \approx 2,8 \text{ } \frac{\text{мН}}{\text{м}}. \]
+
+\newpage
+
+Таким образом, полные погрешности измерений определяются следующими соотношениями:
+\[ \sigma_k = \sqrt{(\sigma_k^\text{сист})^2 + (\sigma_k^\text{случ})^2} \approx 0,006 \text{ } \frac{\text{мН}}{\text{м}\cdot\text{К}},\]
+\[ \sigma_b = \sqrt{(\sigma_b^\text{сист})^2 + (\sigma_b^\text{случ})^2} \approx 3,3 \text{ } \frac{\text{мН}}{\text{м}}. \]
+
+Таким образом, окончательно получаем:
+\begin{itemize}
+	\item $ \displaystyle \underline{k = \frac{d\sigma}{dT} = (-0,155 \pm 0,006) \text{ } \frac{\text{мН}}{\text{м}\cdot\text{К}}, \: (\varepsilon = 4,2\%);} $
+	\item $ \displaystyle \underline{b = (108,6 \pm 3,3) \text{ } \frac{\text{мН}}{\text{м}}, \: (\varepsilon = 2,9\%).}$
+\end{itemize}
+
+\begin{center}
+	\begin{tikzpicture}
+	\begin{axis}[
+	title={Графики зависимостей},
+	xlabel={$ T $, \textdegree К},
+	ylabel={$\sigma$, мН/м},
+	legend pos=north east,
+	xmajorgrids=true,
+	ymajorgrids=true,
+	grid style=dashed,
+	width = 520,
+	height = 350,
+	xmin = 300,
+	xmax = 335,
+	ymin =40,
+	ymax =135,
+	]
+	\legend{ 
+		,,,
+		$ \sigma(T) $,
+		$ q = - T \frac{d\sigma}{dT} $,
+		$ \frac{U}{F} = (\sigma - T\frac{d\sigma}{dT}) $
+	};
+	\addplot+ [blue, only marks, mark size = 4pt,
+	error bars/.cd,
+	x dir=both, x explicit,
+	y dir=both, y explicit, 
+	] table [x = T, y = sigma, x error = dT, y error = ds,] {
+		T	sigma	dT	ds                  
+		302	61.89142053	0.1	1.578711731
+		307	61.04078762	0.1	1.560148221
+		312	60.09563994	0.1	1.542739875
+		317	59.24500703	0.1	1.530060624
+		322	58.58340366	0.1	1.517994324
+		327	58.01631505	0.1	1.509164465
+		332	57.16568214	0.1	1.492275431
+	};
+	\addplot+ [blue, only marks, mark size = 4pt,
+	] table [x = T, y = sigma,] {
+		T	sigma                
+		302	46.892827
+		307	47.66919831
+		312	48.44556962
+		317	49.22194093
+		322	49.99831224
+		327	50.77468354
+		332	51.55105485
+	};
+	\addplot+ [blue, only marks, mark size = 4pt,
+	] table [x = T, y = sigma,] {
+		T	sigma                
+		302	108.7842475
+		307	108.7099859
+		312	108.5412096
+		317	108.466948
+		322	108.5817159
+		327	108.7909986
+		332	108.716737
+	};
+	\addplot [red, domain=297:350, line width =3.2pt] {108.6  -0.155*x};
+	\addplot [pink, domain=297:350, line width =3.2pt] {x * 0.155};
+	\addplot [black, domain=297:350, line width =3.2pt] {108.6};
+	\end{axis}
+	\end{tikzpicture}
+\end{center}
+
+По полученным данным можно нанести на график зависимость от температуры коэффициента поверхностного натяжения $ \underline{\sigma(T)} $, теплоты образования единицы поверхности жидкости $ \displaystyle \underline{q = -T\frac{d\sigma}{dT}} $ и поверхностной энергии $ U $ единицы площади $ F $: $ \displaystyle \underline{\frac{U}{F} = \left(\sigma - T \frac{d\sigma}{dT}\right).} $
+
+\section{Обсуждение результатов и выводы}
+
+В ходе работы были выполнены следующие задачи:
+
+\begin{itemize}
+	\item Был измерен диаметр иглы при помощи известного коэффициента поверхностного натяжения спирта. Полученный результат $\underline{ d = (0,96 \pm 0,02) \text{ мм},} \: (\varepsilon = 2,2\%)$ с хорошей точностью совпадает с диаметром, измеренным при помощи светового микроскопа.
+	
+	\item Было определено добавочное давление $ \underline{\Delta P = (117,4 \pm 2,8) \text{ Па},} \: (\varepsilon = 2,4\%)$, создаваемое столбом жидкости при опускании иглы на $ \underline{\Delta h' = (12,0 \pm 0,7) \text{ мм},} \: (\varepsilon = 5,9\%). $ Полученное экспериментально значение $ \Delta h $ в пределах погрешности совпало с прямым измерением $ \Delta h' $. Полученная поправка к давлению была использована в дальнейшем в основной части работы.
+	
+	\item Был экспериментально получен коэффициент поверхностного натяжения воды при различных её температурах. Так, например, при температуре $ 29 ^\circ C $ коэффициент $ \sigma \approx (61,9 \pm 1,6) $ мН/м. А при $ 59 ^\circ C $ -- $ \sigma \approx (57,2 \pm 1,5) $ мН/м.
+	
+	\item Была экспериментально получена зависимость коэффициента поверхностного натяжения дистиллированной воды от температуры. Был вычислен коэффициент пропорциональности $ \displaystyle \underline{k = \frac{d\sigma}{dT} = (-0,155 \pm 0,006) \text{ } \frac{\text{мН}}{\text{м}\cdot\text{К}},} \: (\varepsilon = 4,2\%). $ 
+	
+	\item Были построены графики зависимости от температуры теплоты образования единицы поверхности жидкости и поверхностной энергии единицы площади.
+\end{itemize}
+
+Полученные результаты дают основание полагать, что теоретические данные довольно точно описывают наблюдаемые зависимости. При этом численные результаты значительно отличаются от табличных данных, что может говорить о низкой точности метода измерений, которая, вероятно, связана с необходимостью учёта сложных не квазистатических процессов, происходящих при пробулькивании пузырька. Также большую погрешность мог внести тот факт, что <<дистиллированная>> вода, используемая в ходе эксперимента имела примеси спирта, которые попали туда в результате некачественной очистки иглы от остатков этанола после первой части работы. Более того, в колбе с водой были обнаружены волокна тряпки, которая использовалась для протирки иглы от спирта, что тоже могло повлиять на точность полученных результатов.  
+
+
+
+
+
+
+
+
+
+
+
+\end{document}
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diff --git a/mls.py b/mls.py
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+++ b/mls.py
@@ -0,0 +1,46 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+#x = [146.66, 293.33, 439.99, 573.33, 693.33, 773.33, 839.99, 879.99]
+x = [0.3, 0.4, 0.5, 0.6, 0.8, 1.0] 
+
+#y = [-37, -79, -122, -161, -194, -218, -234, -245]
+#y=[-53, -110, -165, -214, -261, -292, -314, -327]
+#y = [-67, -137, -209, -274, -328, -368, -395, -411]
+#y = [-83, -166, -249, -327, -393, -441, -474, -496]
+#y = [-113, -229, -336, -442, -531, -595, -638, -664]
+#y = [-142, -286, -424, -553, -663, -745, -800, -831]
+#y=[135, 277, 417, 547, 660, 736,  791, 821]
+y = [-0.28, -0.38, -0.47, -0.56, -0.75, -0.94]
+u0 = 0
+
+if len(x) != len(y):
+    print("size mismatch")
+    exit()
+
+y = [i - u0 for i in y]
+
+n = len(x)
+
+mean_xy = 0
+mean_x_sq = 0
+
+for i in range(n):
+    mean_xy += x[i] * y[i]
+    mean_x_sq += x[i] ** 2
+
+mean_xy /= n
+mean_x_sq /= n
+
+k = mean_xy / mean_x_sq
+
+print("k = ", k)
+
+plt.scatter(x,y)
+#plt.show()
+x_axis = np.array(range(0, 1000))
+y_axis = k * x_axis 
+
+plt.plot(x_axis, y_axis)
+plt.show()
+#`plot(x, y))