{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Loi de Mariotte\n",
"\n",
"\n",
"## Problématique\n",
"Quel est le comportement d’un gaz lorsque sa pression ou son volume varient ?\n",
"\n",
"\n",
"## Objectifs\n",
"Les gaz sont compressibles, c'est-à-dire que le volume d'une quantité de matière de gaz donnée varie quand sa pression varie.\n",
"\n",
"L'objectif du TP consiste à établir la loi qui relie la pression `P` et le volume `V` d'un gaz."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mesures"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Loi de Mariotte\n",
"from web_sciences import WebSciences\n",
"\n",
"my_init = '''\n",
"mode = \"point\";\n",
"var commandes = [{texte_bouton:\"Mesure\", arduino:\"mesure\"}];\n",
"series = [{grandeur: \"P\", unite: \"hPa\"}];\n",
"titre_graphe = \"Loi de Mariotte\";\n",
"axes = [{grandeur: \"V\", unite: \"mL\"}, {grandeur: \"P\", unite: \"hPa\"}];\n",
"'''\n",
"\n",
"interface = WebSciences(my_init)\n",
"interface.affiche()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Exploitation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"# Importation des biblothèques et initialisations\n",
"\n",
"from IPython.display import display, Math\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import linregress\n",
"\n",
"# mesures obtenues\n",
"# copier ci-dessous les tableaux de valeurs donnés par le notebook loi_mariotte_mesures\n",
"V = [60, 55, 50, 45, 40, 35, 30, 25]\n",
"P = [1.02e+3, 1.10e+3, 1.20e+3, 1.31e+3, 1.47e+3, 1.64e+3, 1.89e+3, 2.23e+3]\n",
"\n",
"# V en m3\n",
"V = [v * 1e-6 for v in V]\n",
"# P en Pa\n",
"P = [p * 100 for p in P]\n",
"# calcul de 1/V\n",
"inv_V = [1/v for v in V]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"# calcul des incertitudes de type B\n",
"# u(V) = 1,0 mL\n",
"U_V = [1e-6 for v in V]\n",
"# u(P) = 2,0 % * P\n",
"U_P = [p * 0.02 for p in P]\n",
"# u(1/V) = 1/V**2 * uV \n",
"U_invV = [1/v**2 * uv for v, uv in zip(V, U_V)] "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"slideshow": {
"slide_type": "-"
},
"tags": []
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# paramétrage du graphique\n",
"plt.figure('Loi de Mariotte', figsize=(9,6)) # Initialise la figure\n",
"plt.title('Loi de Mariotte', fontsize = 18) # Titre du graphe\n",
"plt.xlabel('$1/V (m^{-3})$', fontsize = 16) # Label de l’axe des abscisses\n",
"plt.ylabel('P (Pa)', fontsize = 16) # Label de l’axe des ordonnées\n",
"ax=plt.gca()\n",
"ax.spines['right'].set_color('none')\n",
"ax.spines['top'].set_color('none')\n",
"plt.xticks(fontsize=14)\n",
"plt.ticklabel_format(axis='x', style='scientific', scilimits=(-1,2))\n",
"plt.ticklabel_format(axis='y', style='scientific', scilimits=(-1,2))\n",
"plt.yticks(fontsize=14) \n",
"Modele = linregress(inv_V, P)\n",
"m, p = Modele[0], Modele[1] \n",
"plt.plot(inv_V, P, 'r.', ms=14, label='Points expérimentaux') # Points expérimentaux\n",
"plt.plot(inv_V,[m*iv+p for iv in inv_V], 'b--',label='Régression linéaire', lw=1)\n",
"plt.errorbar(inv_V, P, xerr = U_invV, yerr = U_P, fmt = 'none', capsize = 2, ecolor = 'green', zorder = 1)\n",
"plt.grid() \n",
"plt.legend(fontsize=14) \n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Quelle droite a-t-on tracée?\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Votre réponse ici**\n",
"\n",
"On a tracé la droite $P =f(\\dfrac{1}{V})$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"# Compléter pour afficher le coefficient directeur de la droite\n",
"display(Math('m = {:.3f}~Pa.m^3'.format(m)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Quel est le coefficient directeur de cette droite ?\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Votre réponse ici**\n",
"\n",
"Le coefficient directeur de cette droite est $m = 5,062~Pa.m^3$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Sachant que la droite passe par l’origine, donner son équation.\n",
"
\n",
" \n",
"Exprimer le produit $P \\times V$\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {
"tags": []
},
"source": [
"**Votre réponse ici**\n",
"\n",
"Le produit $P \\times V$ a pour expression $P \\times V = 5,062$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"En déduire la loi de Mariotte.\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Votre réponse ici**\n",
"\n",
"D'après la loi de Mariotte, $P \\times V = cte$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Pour aller plus loin\n",
"\n",
"
\n",
" \n",
"- A l’aide de la première cellule du notebook `loi_mariotte_mesures.ipynb` (`Détermination de k`), en gardant le piston de la seringue immobile, poser la paume de la main sur le cylindre pour chauffer l'air qu'il contient.\n",
"\n",
"- En effectuant plusieurs mesures, observer comment évolue la pression.\n",
"
\n",
"\n",
"Cette expérience prouve que la constante dépend d'un paramètre au moins. Lequel ?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Votre réponse ici**\n",
"\n",
"La constante $P \\times V$ dépend de la température."
]
},
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