Add lab session 7 Handed in on Jan 24. Change-Id: I9e804d3f114e175887847cc737ad71d316081a45

commit: 7ca4571785052f797b3e09561a616064ef7699ca [log] [tgz]
author: avm99963 <me@avm99963.com> Sat Jan 30 19:54:32 2021 +0100
committer: avm99963 <me@avm99963.com> Sat Jan 30 19:54:32 2021 +0100
tree: 9ff911e4a1056ff9443cea982d8eee3e17a4cba4
parent: 3358606a80bf5ca3047db49ba7dec04372800d47 [diff]
diff --git a/p7/data/escalfant.dat b/p7/data/escalfant.dat
new file mode 100644
index 0000000..af17686
--- /dev/null
+++ b/p7/data/escalfant.dat

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diff --git a/p7/data/escalfant_deriva.dat b/p7/data/escalfant_deriva.dat
new file mode 100644
index 0000000..4f907c1
--- /dev/null
+++ b/p7/data/escalfant_deriva.dat

@@ -0,0 +1,556 @@
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diff --git a/p7/data/escalfant_integration.dat b/p7/data/escalfant_integration.dat
new file mode 100644
index 0000000..6916f44
--- /dev/null
+++ b/p7/data/escalfant_integration.dat

@@ -0,0 +1,1201 @@
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diff --git a/p7/data/refredant.dat b/p7/data/refredant.dat
new file mode 100644
index 0000000..9fdf897
--- /dev/null
+++ b/p7/data/refredant.dat

@@ -0,0 +1,977 @@
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diff --git a/p7/data/refredant_deriva.dat b/p7/data/refredant_deriva.dat
new file mode 100644
index 0000000..ef8c3b6
--- /dev/null
+++ b/p7/data/refredant_deriva.dat

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diff --git a/p7/data/refredant_integration.dat b/p7/data/refredant_integration.dat
new file mode 100644
index 0000000..5cbf0ef
--- /dev/null
+++ b/p7/data/refredant_integration.dat

@@ -0,0 +1,300 @@
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diff --git a/p7/data/sensibilitat.dat b/p7/data/sensibilitat.dat
new file mode 100644
index 0000000..46c5e18
--- /dev/null
+++ b/p7/data/sensibilitat.dat

@@ -0,0 +1,6 @@
+# T       S
+286.9			111.7
+276.7			112.5
+271.2			111.4
+258.5			86.2
+248.1			84.2

diff --git a/p7/full_laboratori/Practica num 7-SolidificacioAigua.pdf b/p7/full_laboratori/Practica num 7-SolidificacioAigua.pdf
new file mode 100644
index 0000000..5acc517
--- /dev/null
+++ b/p7/full_laboratori/Practica num 7-SolidificacioAigua.pdf
Binary files differ

diff --git a/p7/graphs/generateGraphs.bash b/p7/graphs/generateGraphs.bash
new file mode 100644
index 0000000..778b5be
--- /dev/null
+++ b/p7/graphs/generateGraphs.bash

@@ -0,0 +1,11 @@
+#!/usr/bin/env bash
+mkdir -p ../output
+
+files=('escalfant' 'refredant')
+xtics=('500' '200')
+
+for i in 0 1; do
+  ../../p4/graphs/graph.gnu "../data/${files[i]}.dat" "../data/${files[i]}_deriva.dat" "../output/${files[i]}" "../output/${files[i]}_wd" "${xtics[i]}"
+done
+
+./sensibilitat.gnu

diff --git a/p7/graphs/sensibilitat.gnu b/p7/graphs/sensibilitat.gnu
new file mode 100755
index 0000000..036707c
--- /dev/null
+++ b/p7/graphs/sensibilitat.gnu

@@ -0,0 +1,51 @@
+#!/usr/bin/env gnuplot -c
+outputfile="../output/sensibilitat"
+datafile="../data/sensibilitat.dat"
+
+# == CONFIGURACIÓ DE L'OUTPUT PEL LATEX ==
+set terminal cairolatex size 11cm, 8cm
+set output outputfile.'.tex'
+
+# == CONFIGURACIÓ DEL PLOT ==
+set xlabel '$T \, (\si{\kelvin})$'
+set ylabel '$S \, (\si{\milli\volt\per\watt})$'
+
+# Opcions per la llegenda:
+set key above
+set key spacing 1.5
+
+# == FIT ==
+set fit quiet
+
+# Funció per obtenir els dígits significatius d'una expressió
+f_sd(n, i) = (int(n) == 0 ? f_sd(n*10, i+1) : (int(n) == 1 ? i+1 : i))
+significant_digits(n) = f_sd(n - 10*int(n/10), 0)
+
+significant_digits_r(n) = (n == 1 ? 0 : significant_digits(1 - abs(n)))
+
+f(x) = a*x + b
+fit f(x) datafile u 1:2 via a, b
+stats datafile u 1:2 name "STATS" nooutput
+error_a = STATS_slope_err
+sd_error_a = significant_digits(error_a)
+error_b = STATS_slope_err
+sd_error_b = significant_digits(error_b)
+r = STATS_correlation
+sd_r = significant_digits_r(r)
+title_f(a, b, r) = sprintf('$S(T) = %.'.sd_error_a.'f T + %.'.sd_error_b.'f$, $r = %.'.sd_r.'f$', a, b, r);
+
+print(sprintf('delta(a) = %.'.sd_error_a.'f, sd=%.0f', error_a, sd_error_a))
+print(sprintf('delta(b) = %.'.sd_error_b.'f, sd=%.0f', error_b, sd_error_b))
+print(sprintf('r = %.'.sd_r.'f, sd=%.0f', r, sd_r))
+
+plot datafile u 1:2 t "Dades", \
+     f(x) t title_f(a, b, r)
+
+# == CONFIGURACIÓ DE L'OUTPUT PER SVG ==
+# Això ho uso per generar també una imatge de previsualització que puc carregar
+# a l'ordinador per veure més o menys com a sortit el plot sense haver
+# d'inserir-ho al LaTeX per veure-ho.
+set terminal svg dashed size 600, 600 font "Computer Modern,Tinos,Helvetica,15"
+set output outputfile.'.svg'
+
+replot

diff --git a/p7/informe/p7.pdf b/p7/informe/p7.pdf
new file mode 100644
index 0000000..03c8dc2
--- /dev/null
+++ b/p7/informe/p7.pdf
Binary files differ

diff --git a/p7/informe/p7.tex b/p7/informe/p7.tex
new file mode 100644
index 0000000..3b9c6a8
--- /dev/null
+++ b/p7/informe/p7.tex

@@ -0,0 +1,139 @@
+\documentclass[11pt,a4paper]{article}
+\usepackage[utf8]{inputenc}
+\usepackage[catalan]{babel}
+\usepackage{fancyhdr}
+\usepackage{graphicx}
+\usepackage[labelfont=bf]{caption}
+\usepackage{siunitx}
+\usepackage{geometry}
+\geometry{top=25mm}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{booktabs}
+\usepackage{chemformula}
+\usepackage{multicol}
+\usepackage{hyperref}
+
+\usepackage{biblatex}
+\addbibresource{referencies.bib}
+
+\usepackage{pgfplotstable}
+\pgfplotsset{compat=1.16}
+\pgfplotstableset{
+empty cells with={--}, % replace empty cells with ’--’
+every head row/.style={before row=\toprule,after row=\midrule},
+every last row/.style={after row=\bottomrule},
+set thousands separator={\,}%,
+%every even row/.style={
+%before row={\rowcolor[gray]{0.9}}}, % Add this for stylish tables ;)
+%begin table=\begin{longtable},
+%end table=\end{longtable}
+}
+
+\sisetup{separate-uncertainty=true}
+
+\setlength{\parskip}{1em}
+
+\pagestyle{fancy}
+\fancyhf{}
+\rhead{Adrià Vilanova Martínez}
+\lhead{Pràctica 7}
+\rfoot{\thepage}
+
+%%%% Title %%%%
+\title{\vspace{-2ex}Pràctica 7. Mesura de la calor latent de solidificació de l'\ch{H_2O}\vspace{-2ex}}
+\author{Adrià Vilanova Martínez (T1B)\vspace{-2ex} }
+\date{Tardor 2020}
+
+\begin{document}
+  \maketitle
+
+  \section{Objectiu de la pràctica}
+  L'objectiu d'aquesta pràctica és calcular la calor latent de solidificació de l'aigua, la utilitat de la qual és informar de quanta energia cal per solidificar una certa quantitat d'aigua, o quanta energia es desprén quan es fusiona l'aigua.
+
+  Per fer-ho un tercer utilitzarà un calorímetre diferencial, que amb la calibració que ha fet també aquest tercer permetrà calcular aquest valor. De fet, es calcularà aquesta calor latent 2 vegades: 1 per un procés de solidificació i una altra per la fusió (el canvi d'estat invers).
+
+  \section{Tractament de dades}
+  Per realitzar aquest informe s'han utilitzat les dades recollides al calorímetre 2:
+
+  \begin{center}
+    \begin{minipage}{\textwidth}
+      \begin{multicols}{2}
+        \begin{center}
+          \centering
+          \vspace{-2em}
+          \input{../output/refredant.tex}
+          \captionof{figure}{Mesura del calorímetre refredant l'aigua.}
+        \end{center}
+
+        \begin{center}
+          \centering
+          \vspace{-2em}
+          \input{../output/escalfant.tex}
+          \captionof{figure}{Mesura del calorímetre escalfant l'aigua.}
+        \end{center}
+      \end{multicols}
+    \end{minipage}
+  \end{center}
+
+  \newpage
+
+  Un cop ajustada la línia base amb un polinomi de segon grau, podem obtenir les dades sense deriva:
+
+  \begin{center}
+    \begin{minipage}{\textwidth}
+      \begin{multicols}{2}
+        \begin{center}
+          \centering
+          \vspace{-2em}
+          \input{../output/refredant_wd.tex}
+          \captionof{figure}{Mesura del calorímetre refredant l'aigua.}
+        \end{center}
+
+        \begin{center}
+          \centering
+          \vspace{-2em}
+          \input{../output/escalfant_wd.tex}
+          \captionof{figure}{Mesura del calorímetre escalfant l'aigua.}
+        \end{center}
+      \end{multicols}
+    \end{minipage}
+  \end{center}
+
+  La relació entre el senyal calorimètric i la potència tèrmica és $Y = S(T) \dot{q}$, i per tant per obtenir la potència tèrmica corresponent és necessari saber quin és el valor de la sensibilitat $S(T)$ a la temperatura en què té lloc el canvi de fase. Per això s'utilitza la calibració del calorímetre que ha realitzat el tercer.
+
+  En concret, el tercer ha donat una calibració que consisteix de certes parelles de valors $(T, S(T))$. A partir d'aquests valors s'ha fet una regressió lineal i s'ha obtingut que el valor de la sensibilitat a la temperatura $T$ és: \[ S(T) = \SI{0.9(2)}{\milli\volt\per\watt\per\kelvin} \cdot  T - \SI{132.8(2)}{\milli\volt\per\watt} \]
+
+  \begin{center}
+    \centering
+    \vspace{-2em}
+    \input{../output/sensibilitat.tex}
+    \captionof{figure}{Regressió lineal per trobar una expressió per la sensibilitat del calorímetre.}
+  \end{center}
+
+  Aleshores, es té el següent:
+  \[ Y = S(T) \dot{q} \implies \dot{q} = \frac{Y}{S(T)} \implies Q = \int_{t_0}^{t_1} \dot{q} \, dt = \int_{t_0}^{t_1} \frac{Y}{S(T)} \, dt = \frac{1}{S(T)} \underbrace{\int_{t_0}^{t_1} Y \, dt}_{= I} \]
+
+  Fent aquesta integració numèricament amb l'\texttt{octave} mitjançant el mètode del trapeci s'obtenen els següents valors, tenint en compte que pel refredament $T = \SI{-12.3}{\celsius} = \SI{260.85}{\kelvin}$ i per l'escalfament $T = \SI{3}{\celsius} = \SI{276.15}{\kelvin}$:
+  \[ \begin{cases}
+    |Q_\text{refredant}| = \frac{1}{101.965} \cdot 1395.4 = \SI{13.68(5)}{\joule} \\
+    |Q_\text{escalfant}| = \frac{1}{115.735} \cdot 1300.9 = \SI{11.24(3)}{\joule}
+  \end{cases} \]
+  on la incertesa s'ha calculat com $\delta Q = \delta\frac{1}{S} \cdot I = \frac{I}{S^2} \delta S$, degut al fet que la incertesa del voltatge és insignificant comparada amb la que introdueix el càlcul de la sensibilitat.
+
+  Fent la mitjana podem obtenir un valor que permetrà calcular un valor de $L$ aproximat:
+  \[ Q := \frac{Q_\text{refredant} + Q_\text{escalfant}}{2} = \SI{12.46(122)}{\joule} \]
+  on la incertesa s'ha calculat com $\delta Q = \sqrt{(\delta Q_\text{propagació incerteses})^2 + Q_\text{estadístic}^2}$, on la segona incertesa correspon a la incertesa estadística deguda al fet de fer la mitjana.
+
+  Ara es pot calcular la calor latent de solidificació fàcilment:
+  \[ L_{sl} = \frac{Q}{M} = \frac{\SI{12.46(122)}{\joule}}{\SI{0.04}{\gram}} = \SI{311.5(305)}{\joule\per\gram} \]
+
+  \section{Conclusió}
+  Segons \cite{piequalse} la calor latent de solidificació de l'aigua és de $\SI{334}{\joule\per\gram}$, que està dins del marge d'error del valor calculat experimentalment. Per tant, ambdós valors són compatibles i es pot afirmar que aquest experiment i la teoria que hi ha darrere ens ha permés calcular correctament aquest valor.
+
+  \section{Sobre l'aigua sobrerefredada}
+  L'aigua sobrerefredada és aigua que té una temperatura menor a la temperatura de solidificació, però que tot i així es manté en equilibri en estat líquid. Segons \cite{wikipedia}, el procés de sobrerefredar aigua és important perquè alguns animals puguin sobreviure a temperatures extremes, o pot ser útil per refrigerar begudes comercials a temperatures molt baixes.
+
+  \printbibliography
+
+\end{document}

diff --git a/p7/informe/referencies.bib b/p7/informe/referencies.bib
new file mode 100644
index 0000000..2363b0d
--- /dev/null
+++ b/p7/informe/referencies.bib

@@ -0,0 +1,13 @@
+@online{piequalse,
+    author={The Engineering ToolBox},
+    title={Latent Heat of Melting for some common Materials},
+    url={https://www.engineeringtoolbox.com/latent-heat-melting-solids-d_96.html}
+}
+
+@online{wikipedia,
+    author={},
+    title={Supercooling},
+    year=2021,
+    month=1,
+    url={https://en.wikipedia.org/w/index.php?title=Supercooling&oldid=1000476631}
+}

diff --git a/p7/numericalintegration/main.m b/p7/numericalintegration/main.m
new file mode 100644
index 0000000..cb8aa76
--- /dev/null
+++ b/p7/numericalintegration/main.m

@@ -0,0 +1,12 @@
+M = dlmread('../data/refredant_integration.dat');
+
+d = @(t) (1.370e-06*t^2 + 1.217e-04*t -2.173e+00);
+
+x = M(:, 1);
+y = M(:, 2);
+
+for i = 1:size(y, 1)
+  y(i) = y(i) - d(x(i));
+end
+
+trapz(x, y)

diff --git a/p7/numericalintegration/main2.m b/p7/numericalintegration/main2.m
new file mode 100644
index 0000000..b4ff19f
--- /dev/null
+++ b/p7/numericalintegration/main2.m

@@ -0,0 +1,12 @@
+M = dlmread('../data/escalfant_integration.dat');
+
+d = @(t) (4.053e-08*t^2 + 9.445e-06*t + 5.368e-01);
+
+x = M(:, 1);
+y = M(:, 2);
+
+for i = 1:size(y, 1)
+  y(i) = y(i) - d(x(i));
+end
+
+trapz(x, y)

diff --git a/p7/rawdata/Cal B  Mesura 1 Escalfant.xls b/p7/rawdata/Cal B  Mesura 1 Escalfant.xls
new file mode 100644
index 0000000..a35cc3c
--- /dev/null
+++ b/p7/rawdata/Cal B  Mesura 1 Escalfant.xls
Binary files differ

diff --git a/p7/rawdata/Cal B  Mesura 1 Refredant  M=0_04g T=-12_3.xls b/p7/rawdata/Cal B  Mesura 1 Refredant  M=0_04g T=-12_3.xls
new file mode 100644
index 0000000..ed5834c
--- /dev/null
+++ b/p7/rawdata/Cal B  Mesura 1 Refredant  M=0_04g T=-12_3.xls
Binary files differ

diff --git a/p7/rawdata/IMPORTANT LLEGIR PRIMER.txt b/p7/rawdata/IMPORTANT LLEGIR PRIMER.txt
new file mode 100644
index 0000000..bcd8618
--- /dev/null
+++ b/p7/rawdata/IMPORTANT LLEGIR PRIMER.txt

@@ -0,0 +1,41 @@
+A) SOBRE ELS FITXERS EXCEL: 

+És possible que el vostre ordinador us demani d'instal·lar macros quan obriu els fitxers. Ignoreu el missatge o cancel·leu l'acció. Dels fitxer Excel només voleu les dades, que estan en una pestanya "Dades" a la part inferior-esquerra.

+

+B) SOBRE ELS EXPERIMENTS:

+

+Les mesures corresponen a 3 calorímetres diferents, etiquetats A, B, i C. Escolliu un dels tres per treballar. Les dades, dins de cada calorímetre, corresponen a: 

+

+1) "Refredament" amb nitrogen líquid, i s'indica la temperatura a la que s'observa la transció en el nom del fitxer, aíxí com la massa de la gota d'aigua. Així "Cal A  Mesura 1 M=0_05g T=-15.7.xls" vol dir que a -15.7ºC s'ha observat el pic calorimètric de la transició de fase pel calorímetre A, que conté una gota d'aigua de 0.05g. 

+

+B) "Escalfament", on s'estudia el canvi de fase quan augmenta la temperatura gradualment de -10ºC a 10ºC. En totes les mesures el canvi de fase té lloc gradualment, començant cap a 2ºC i acabant a uns 5ºC. Podeu prendre com a aproximació que la transició té lloc a 3ºC. 

+ 

+Heu de fer l'anàlsi tant de l'escalfament com del refradament, treient la calor latent L per a cada un d'ells, i donant com a valor final la mitjana dels dos.

+

+Cada calorímetre es calibra en la pràctica 4, i aquí (pràctica 7) es fa servir el calibratge per trobar la calor latent de solidificació.

+

+Els calibratges que podeu fer servir són:

+

+CALORÍMETRE A

+Temperatura T (K)	Sensibilitat S (mV/W)

+293.2			98.8

+251.0			89.5

+256.7			90.7

+267.4			106.9

+

+CALORÍMETRE B

+Temperatura T (K)	Sensibilitat S (mV/W)

+286.9			111.7

+276.7			112.5

+271.2			111.4

+258.5			86.2

+248.1			84.2

+

+CALORÍMETRE C

+Temperatura T (K)	Sensibilitat S (mV/W)

+296.7			219.2

+285.9			221.3

+263.2			205.2

+261.3			189.8

+

+Per a trobar la S que us interessa, feu un ajust lineal S(T) dels punts i agafeu la S que correspon a la temperatura de transció observada (on hi ha el pic calorimètric). De cara a l'informe, no cal que poseu aquestes dades, simplement dieu que heu fet un ajust lineal i que heu agafat la S de l'ajut que correspon a la temperatura de transició.

+
commit	7ca4571785052f797b3e09561a616064ef7699ca	[log] [tgz]
author	avm99963 <me@avm99963.com>	Sat Jan 30 19:54:32 2021 +0100
committer	avm99963 <me@avm99963.com>	Sat Jan 30 19:54:32 2021 +0100
tree	9ff911e4a1056ff9443cea982d8eee3e17a4cba4
parent	3358606a80bf5ca3047db49ba7dec04372800d47 [diff]