Add lab session 1
Handed in on 24 Nov 2020.
Change-Id: I3e575d6a149be83142809ad2c41b3adca5212009
diff --git a/p1/data/data.ods b/p1/data/data.ods
new file mode 100644
index 0000000..905c6e9
--- /dev/null
+++ b/p1/data/data.ods
Binary files differ
diff --git a/p1/data/epsilons.dat b/p1/data/epsilons.dat
new file mode 100644
index 0000000..b53dae1
--- /dev/null
+++ b/p1/data/epsilons.dat
@@ -0,0 +1,3 @@
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diff --git a/p1/data/epsilons2.dat b/p1/data/epsilons2.dat
new file mode 100644
index 0000000..f9a9f92
--- /dev/null
+++ b/p1/data/epsilons2.dat
@@ -0,0 +1,9 @@
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diff --git a/p1/data/m3.dat b/p1/data/m3.dat
new file mode 100644
index 0000000..3cfb77b
--- /dev/null
+++ b/p1/data/m3.dat
@@ -0,0 +1,557 @@
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diff --git a/p1/data/m3_100.dat b/p1/data/m3_100.dat
new file mode 100644
index 0000000..50f4dce
--- /dev/null
+++ b/p1/data/m3_100.dat
@@ -0,0 +1,10 @@
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diff --git a/p1/data/m3_53.dat b/p1/data/m3_53.dat
new file mode 100644
index 0000000..07e9bc9
--- /dev/null
+++ b/p1/data/m3_53.dat
@@ -0,0 +1,28 @@
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diff --git a/p1/data/m3_deriva.dat b/p1/data/m3_deriva.dat
new file mode 100644
index 0000000..d6942b2
--- /dev/null
+++ b/p1/data/m3_deriva.dat
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diff --git a/p1/data/m5.dat b/p1/data/m5.dat
new file mode 100644
index 0000000..656cc35
--- /dev/null
+++ b/p1/data/m5.dat
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new file mode 100644
index 0000000..408b543
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diff --git a/p1/data/m9.dat b/p1/data/m9.dat
new file mode 100644
index 0000000..9b1dcbb
--- /dev/null
+++ b/p1/data/m9.dat
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+687.00 -1.128E-02
+688.00 -1.769E-02
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+696.00 -2.617E-02
diff --git a/p1/data/m9_100.dat b/p1/data/m9_100.dat
new file mode 100644
index 0000000..8061d00
--- /dev/null
+++ b/p1/data/m9_100.dat
@@ -0,0 +1,12 @@
+43.00 4.021E+00
+44.00 4.018E+00
+45.00 4.014E+00
+46.00 4.010E+00
+47.00 4.008E+00
+48.00 4.005E+00
+49.00 4.003E+00
+50.00 4.001E+00
+51.00 3.996E+00
+52.00 3.994E+00
+53.00 3.992E+00
+54.00 3.990E+00
diff --git a/p1/data/m9_53.dat b/p1/data/m9_53.dat
new file mode 100644
index 0000000..37909c1
--- /dev/null
+++ b/p1/data/m9_53.dat
@@ -0,0 +1,59 @@
+621.00 2.047E+00
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+678.00 2.048E+00
+679.00 2.048E+00
diff --git a/p1/data/m9_deriva.dat b/p1/data/m9_deriva.dat
new file mode 100644
index 0000000..25eef2b
--- /dev/null
+++ b/p1/data/m9_deriva.dat
@@ -0,0 +1,62 @@
+0.00 -2.392E-02
+1.00 -2.379E-02
+2.00 -2.422E-02
+3.00 -2.332E-02
+4.00 -2.371E-02
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diff --git a/p1/full_laboratori/Practica num 1-Termoparell.pdf b/p1/full_laboratori/Practica num 1-Termoparell.pdf
new file mode 100644
index 0000000..02cd9a2
--- /dev/null
+++ b/p1/full_laboratori/Practica num 1-Termoparell.pdf
Binary files differ
diff --git a/p1/graphs/generate.bash b/p1/graphs/generate.bash
new file mode 100644
index 0000000..83c840e
--- /dev/null
+++ b/p1/graphs/generate.bash
@@ -0,0 +1,11 @@
+#!/usr/bin/env bash
+mkdir -p ../output
+
+data="../data"
+output="../output"
+
+for i in 3 5 9; do
+ ./graph.gnu "$data/m${i}.dat" "$data/m${i}_deriva.dat" "$data/m${i}_100.dat" "$data/m${i}_53.dat" "$output/m${i}"
+done
+
+./graph2.gnu "$data/epsilons2.dat" "$output/epsilons"
diff --git a/p1/graphs/graph.gnu b/p1/graphs/graph.gnu
new file mode 100755
index 0000000..e38dfea
--- /dev/null
+++ b/p1/graphs/graph.gnu
@@ -0,0 +1,88 @@
+#!/usr/bin/env gnuplot -c
+# == DEFINICIONS ==
+outputfile = ARG5 # Nom de la imatge resultant (sense extensió)
+datafile = ARG1 # Nom del fitxer de dades que es vol usar
+filederiva = ARG2
+fileahundred = ARG3
+filefiftythree = ARG4
+error_sist_b = 0.001 # Error sistemàtic en l'eix y
+
+# Set to 1 for linear fitting.
+# Set to 2 for no fitting.
+linear = 2
+
+# == CONFIGURACIÓ DE L'OUTPUT PEL LATEX ==
+set terminal cairolatex size 7.4cm, 6cm
+set output outputfile.'.tex'
+
+# == CONFIGURACIÓ DEL PLOT ==
+set xlabel "$t \\, (\\si{\\second})$"
+set ylabel "$\\varepsilon \\, (\\si{\\milli\\volt})$"
+
+set autoscale yfixmin
+set autoscale xfixmax
+
+# Opcions per la llegenda:
+set key above
+set key spacing 1.5
+
+# == CONFIGURACIÓ DEL 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 - n))
+
+if (linear == 1) {
+ f(x) = a*x + b # Funció a fitar
+ fit f(x) filederiva u 1:2 via a, b # Fem el fit de les dades
+
+ # Això s'usa per obtenir el valor del coeficient de correlació "r", que estarà
+ # guardat a la var. "STATS_correlation"
+ stats filederiva u 1:2 name "STATS" nooutput
+
+ error_a = STATS_slope_err
+ sd_error_a = significant_digits(error_a)
+ error_b = sqrt(STATS_slope_err + error_sist_b)
+ sd_error_b = significant_digits(error_b)
+ r = STATS_correlation
+ sd_r = significant_digits_r(r)
+
+ print("=== ".filederiva." ===")
+ print("* Línia base: fit lineal")
+}
+
+if (linear == 2) {
+ print("=== ".filederiva." ===")
+ print("* Línia base: no es fa fit")
+
+ f(x) = 0 # Cap fit
+}
+
+print("* t = 0 ºC")
+stats filederiva u (column(2) - f(column(1))) name "STATS_ZERO" nooutput
+sign_dig_epsilon_100 = significant_digits(STATS_ZERO_stddev)
+print(sprintf(" - epsilon = %.".sign_dig_epsilon_100."f +- %.".sign_dig_epsilon_100."f", STATS_ZERO_mean, STATS_ZERO_stddev))
+
+print("* t = 100 ºC")
+stats fileahundred u (column(2) - f(column(1))) name "STATS_AHUNDRED" nooutput
+sign_dig_epsilon_100 = significant_digits(STATS_AHUNDRED_stddev)
+print(sprintf(" - epsilon = %.".sign_dig_epsilon_100."f +- %.".sign_dig_epsilon_100."f", STATS_AHUNDRED_mean, STATS_AHUNDRED_stddev))
+
+print("* t = 53 ºC")
+stats filefiftythree u (column(2) - f(column(1))) name "STATS_FIFTYTHREE" nooutput
+sign_dig_epsilon_100 = significant_digits(STATS_FIFTYTHREE_stddev)
+print(sprintf(" - epsilon = %.".sign_dig_epsilon_100."f +- %.".sign_dig_epsilon_100."f", STATS_FIFTYTHREE_mean, STATS_FIFTYTHREE_stddev))
+
+plot [0:] datafile u 1:(column(2) - f(column(1))) t "Força electromotriu mesurada" w l, STATS_AHUNDRED_mean t "$\\varepsilon(\\SI{100}{\\celsius})$", STATS_FIFTYTHREE_mean t "$\\varepsilon(\\SI{53}{\\celsius})$"
+
+# == 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/p1/graphs/graph2.gnu b/p1/graphs/graph2.gnu
new file mode 100755
index 0000000..5ee1cdb
--- /dev/null
+++ b/p1/graphs/graph2.gnu
@@ -0,0 +1,42 @@
+#!/usr/bin/env gnuplot -c
+# == DEFINICIONS ==
+outputfile = ARG2 # Nom de la imatge resultant (sense extensió)
+datafile = ARG1 # Nom del fitxer de dades que es vol usar
+
+# == CONFIGURACIÓ DE L'OUTPUT PEL LATEX ==
+set terminal cairolatex size 10cm, 10cm
+set output outputfile.'.tex'
+
+# == CONFIGURACIÓ DEL PLOT ==
+set xlabel "$t \\, (\\si{\\second})$"
+set ylabel "$\\varepsilon \\, (\\si{\\milli\\volt})$"
+
+set autoscale yfixmin
+set autoscale xfixmax
+
+# Opcions per la llegenda:
+set key above
+set key spacing 1.5
+
+# == CONFIGURACIÓ DEL 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 - n))
+
+p(x) = a*x + b*x*x # Funció a fitar
+fit p(x) datafile u 1:2 via a, b # Fem el fit de les dades
+
+plot [-50:150] datafile u 1:2:(0):3 w xyerr t "Dades", p(x) t "$\\varepsilon(t)$"
+
+# == 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/p1/informe/p1.pdf b/p1/informe/p1.pdf
new file mode 100644
index 0000000..1b25014
--- /dev/null
+++ b/p1/informe/p1.pdf
Binary files differ
diff --git a/p1/informe/p1.tex b/p1/informe/p1.tex
new file mode 100644
index 0000000..c61ed45
--- /dev/null
+++ b/p1/informe/p1.tex
@@ -0,0 +1,157 @@
+\documentclass[11pt,a4paper]{article}
+\usepackage[utf8x]{inputenc}
+\usepackage[catalan]{babel}
+\usepackage{fancyhdr}
+\usepackage{graphicx}
+\usepackage[labelfont=bf]{caption}
+\usepackage{siunitx}
+\usepackage{geometry}
+\geometry{top=25mm}
+\usepackage{amsmath}
+\usepackage{booktabs}
+\usepackage{chemformula}
+\usepackage{multicol}
+%\usepackage{hyperref} % @TODO: Remove when generating the PDF
+
+\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}%,
+%every even row/.style={
+%before row={\rowcolor[gray]{0.9}}}, % Add this for stylish tables ;)
+%begin table=\begin{longtable},
+%end table=\end{longtable}
+}
+
+\setlength{\parskip}{1em}
+
+\pagestyle{fancy}
+\fancyhf{}
+\rhead{Adrià Vilanova Martínez}
+\lhead{Pràctica 1}
+\rfoot{\thepage}
+
+%%%% Title %%%%
+\title{\vspace{-2ex}Pràctica 1. Calibratge d'un termoparell\vspace{-2ex}}
+\author{Adrià Vilanova Martínez (T1B)\vspace{-2ex} }
+\date{Tardor 2020}
+
+\begin{document}
+ \maketitle
+
+ \section{Objectiu de la pràctica}
+
+ L'objectiu de la pràctica és calibrar el termoparell C del laboratori de la facultat, a partir del fet que la força electromotriu $\varepsilon$ generada a causa de l'efecte Seebeck (explicat al guió de pràctiques) depèn de la temperatura de la sonda $T$ si la temperatura de la sonda de referència $T_0$ es manté constant a $\SI{0}{\celsius}$ i de la suposició que aquesta relació ve donada per un polinomi de segon grau amb terme independent nul: $\varepsilon(t) = a_1 t + a_2 t^2$ on $t = T - T_0$.
+
+ Així doncs, a partir de les dades experimentals recollides per un tercer al laboratori s'aproximarà el polinomi anterior per mínims quadrats. Les dades consisteixen de parelles $(\varepsilon, T)$, que es recullen posant la sonda del termoparell en fonts de les quals es coneix a priori la seva temperatura teòrica.
+
+ \section{Desenvolupament}
+
+ \begin{center}
+ \begin{minipage}{\textwidth}
+ \begin{multicols}{2}
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/m3.tex}
+ \captionof{figure}{Mesura C3.}
+ \end{center}
+
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/m5.tex}
+ \captionof{figure}{Mesura C5.}
+ \end{center}
+ \end{multicols}
+ \end{minipage}
+ \end{center}
+
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/m9.tex}
+ \captionof{figure}{Mesura C9.}
+ \end{center}
+
+ A partir de les mesures anteriors, podem obtenir les següents parelles $(T, \varepsilon)$:
+
+ \begin{center}
+ \centering
+ % \pgfplotstabletypeset[
+ % columns/0/.style={column name=$T \, (\si{\celsius})$},
+ % columns/1/.style={column name=$\varepsilon_1 \, (\si{\milli\volt})$, fixed, fixed zerofill, precision=4},
+ % columns/2/.style={column name=$\delta(\varepsilon_1) \, (\si{\milli\volt})$, fixed, fixed zerofill, precision=4},
+ % columns/3/.style={column name=$\varepsilon_2 \, (\si{\milli\volt})$, fixed, fixed zerofill, precision=4},
+ % columns/4/.style={column name=$\delta(\varepsilon_2) \, (\si{\milli\volt})$, fixed, fixed zerofill, precision=4},
+ % columns/5/.style={column name=$\varepsilon_3 \, (\si{\milli\volt})$, fixed, fixed zerofill, precision=4},
+ % columns/6/.style={column name=$\delta(\varepsilon_3) \, (\si{\milli\volt})$, fixed, fixed zerofill, precision=4}
+ % ]
+ % {../data/epsilons.dat}
+
+ \begin{tabular}{ccccccc}
+ \specialrule{.1em}{.05em}{.05em}
+ $T \, (\si{\celsius})$ & $\varepsilon_1 \, (\si{\milli\volt})$ & $\delta(\varepsilon_1) \, (\si{\milli\volt})$ & $\varepsilon_2 \, (\si{\milli\volt})$ & $\delta(\varepsilon_2) \, (\si{\milli\volt})$ & $\varepsilon_3 \, (\si{\milli\volt})$ & $\delta(\varepsilon_3) \, (\si{\milli\volt})$ \\
+ \hline
+ 0 & 0.012 & 0.006 & -0.012 & 0.003 & -0.031 & 0.008 \\
+ 100 & 4.019 & 0.004 & 4.014 & 0.002 & 4.004 & 0.010 \\
+ 53 & 2.0739 & 0.0008 & 2.0825 & 0.0005 & 2.0465 & 0.0008 \\
+ \specialrule{.1em}{.05em}{.05em}
+ \end{tabular}
+
+ \captionof{table}{Dades experimentals.}
+ \end{center}
+
+ On les $\varepsilon_i$ han estat calculades com la mitjana dels valors de $\epsilon_i(t)$ que s'ha considerat que estaven a regions estables, i $\delta(\varepsilon_i)$ s'ha calculat com la desviació típica dels valors considerats per calcular la mitjana. La incertesa s'ha pres així perquè la incertesa de la mesura de l'aparell és menyspreable davant de l'altra incertesa, que és la que domina.
+
+ \begin{center}
+ \centering
+ \begin{tabular}{ccccccc}
+ \specialrule{.1em}{.05em}{.05em}
+ $T \, (\si{\celsius})$ & $\bar{\varepsilon} \, (\si{\milli\volt})$ & $\delta(\bar{\varepsilon}) \, (\si{\milli\volt})$ \\
+ \hline
+ 0 & 0.010 & 0.006 \\
+ 100 & 4.012 & 0.005 \\
+ 53 & 2.0676 & 0.0007 \\
+ \specialrule{.1em}{.05em}{.05em}
+ \end{tabular}
+
+ \captionof{table}{Valors mitjos de les forces electromotrius depenent de la temperatura.}
+ \end{center}
+
+ S'ha calculat l'error de les mitjanes mitjançant la teoria de propagació d'errors: $\delta(\bar{\varepsilon}) = \delta\left(\frac{\sum \varepsilon_i}{n}\right) = \frac{\sum \delta(\varepsilon_i)}{n}$.
+
+ A continuació s'ajustarà la funció $\varepsilon(t) = a_1t + a_2t^2$ als darrers valors obtinguts mitjançant mínims quadrats, i recordant que $T_0 = \SI{0}{\celsius} \implies T = t$.
+
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/epsilons.tex}
+ \captionof{figure}{Gràfica de l'ajust de $\varepsilon(t)$. S'ha graficat amb un domini més gran que $[0, 100] \, (\si{\celsius})$ per poder mostrar la convexitat de l'ajust.}
+ \end{center}
+
+ Els valors dels paràmetres que s'han obtingut són els següents: \[ \begin{cases}
+ a_1 = 0.038 \\
+ a_2 = 2.4 \cdot 10^{-5}
+ \end{cases} \]
+
+ on les incerteses estadístiques donades pel gnuplot són: \[ \begin{cases}
+ \delta(a_1)_{est} = 0.0004 \\
+ \delta(a_2)_{est} = 6 \cdot 10^{-6}
+ \end{cases} \]
+
+ Com $a_1 \gg a_2$, es calcula la incertesa total de $a_1$ com \[ \delta(a_1) = \sqrt{\delta(a_1)_{est}^2 + \delta(a_1)_{sist}^2} = 0.008 \]
+
+ \section{Conclusió}
+
+ Els coeficients de calibració del termoparell amb les seves corresponents incerteses (tenint en compte que per $a_2$ no s'ha tingut en compte la incertesa sistemàtica) són: \[ \begin{cases}
+ a_1 = 0.038 \pm 0.008 \\
+ a_2 = (24 \pm 6) \cdot 10^{-6}
+ \end{cases} \]
+
+ A partir de les dades recollides s'ha comprovat que l'ajust és bó (la variància dels residus del procediment de mínims quadrats és de $3 \cdot 10^{-4}$), però això només es pot assegurar pels valors de temperatura dins del rang $[0, 100] \, (\si{\celsius})$, ja que fora d'aquest rang s'estarien extrapolant els resultats, i pot ser que allà el comportament sigui diferent.
+
+ Com a observació, els termoparells són aparells útils en quant al fet que es poden utilitzar en entorns molt diversos i permeten mesurar rangs grans de temperatura en oposició a dispositius que mesuren la temperatura a partir de propietats termomètriques com la dilatació d'un material.
+\end{document}
diff --git a/p1/rawdata/LLEGIR PRIMER.txt b/p1/rawdata/LLEGIR PRIMER.txt
new file mode 100644
index 0000000..85aa5d5
--- /dev/null
+++ b/p1/rawdata/LLEGIR PRIMER.txt
@@ -0,0 +1,4 @@
+Cada carpeta correspon a mesures en un termoparell concret. El que heu de fer és escollir un termoparell qualsevol i, després, agafar tres fitxers qualsevols dels disponibles per fer l'anàlisi de dades.
+
+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. Del fitxer Excel només voleu les dades, que estan en una pestanya "Dades" a la part inferior-esquerra.
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diff --git a/p1/rawdata/detectors_20201116.pdf b/p1/rawdata/detectors_20201116.pdf
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