diff --git a/HPLthermo/Ex1_Physics.ipynb b/HPLthermo/Ex1_Physics.ipynb index 983927c..f71f465 100644 --- a/HPLthermo/Ex1_Physics.ipynb +++ b/HPLthermo/Ex1_Physics.ipynb @@ -1,1444 +1,788 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Physique Générale II : Cycles et Machines thermiques
\n", " Notebook 1
\n", " F.Hartmann, L.Gervaise, K.Sheth, X.Fang

\n", " Intructions afin d'utiliser ce notebook :\n", " \n", "
  • Vous pouvez effacer toutes les aides et réponses en allant dans Kernel > Restart Kernel and clear all outputs
    • \n", "
    " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Executez la prochaine cellule afin d'importer toutes les librairies nécessaires au bon fonctionnement de ce notebook :" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "%matplotlib inline\n", "#import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import ipywidgets as widgets\n", "import matplotlib.image as mpimg\n", "from IPython.display import HTML\n", "from IPython.display import display, Math, Latex\n", "import random\n", "\n", "def hide_toggle(for_next=False):\n", " this_cell = \"\"\"$('div.cell.code_cell.rendered.selected')\"\"\"\n", " next_cell = this_cell + '.next()'\n", "\n", " toggle_text = 'Toggle show/hide' # text shown on toggle link\n", " target_cell = this_cell # target cell to control with toggle\n", " js_hide_current = '' # bit of JS to permanently hide code in current cell (only when toggling next cell)\n", "\n", " if for_next:\n", " target_cell = next_cell\n", " toggle_text += ' next cell'\n", " js_hide_current = this_cell + '.find(\"div.input\").hide();'\n", "\n", " js_f_name = 'code_toggle_{}'.format(str(random.randint(1,2**64)))\n", "\n", " html = \"\"\"\n", " \n", "\n", " {toggle_text}\n", " \"\"\".format(\n", " f_name=js_f_name,\n", " cell_selector=target_cell,\n", " js_hide_current=js_hide_current, \n", " toggle_text=toggle_text\n", " )\n", "\n", " return HTML(html)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Exercice Thermodynamique
    \n", "\n", "Cet exercice est insipiré d'un des exercices présent dans l'une des séries d'exercice. Cette version digitale et détaillée de l'exercice a pour but de vous guider afin de trouver les réponses et de vous inculquer une certaine méthodologie.\n", "\n", "\n", "
    \n", " \"Cycle\n", "\n", "###### Cycle de Carnot - Récepteur (Credit: Cours 16 slide 12)\n", "\n", "
    " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", " 1) Exécutez la cellule suivante afin de faire apparaître la première question : " ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "1) Veuillez cocher les réponses correctes concernant un cycle de Carnot inverse (récepteur) :" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "2b1b0fefea564ac9b6f2932e51977323", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "Box(children=(Label(value=''), RadioButtons(layout=Layout(width='max-content'), options=('A. Le gaz reçoit de …" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('1) Veuillez cocher les réponses correctes concernant un cycle de Carnot inverse (récepteur) :'))\n", "widgets.Box(\n", " [\n", " widgets.Label(value=''),\n", " widgets.RadioButtons(\n", " options=[\n", " 'A. Le gaz reçoit de la chaleur de la source chaude et en cède à la source froide',\n", " 'B. Le gaz reçoit de la chaleur de la source froide et en cède à la source chaude',\n", " ],\n", " layout={'width': 'max-content'}\n", " ),\n", " widgets.RadioButtons(\n", " options=[\n", " 'C. Il faut fournir du travail au système',\n", " 'D. Le système fournit du travail, il n’est pas nécessaire de lui en fournir'\n", " ],\n", " layout={'width': 'max-content'}\n", " )\n", " \n", " ]\n", ")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Exécutez la cellule suivante afin d'obtenir un indice concernant la première question :" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "Aide : Le transfert de chaleur va de la source froide à la source chaude (Slide 12 Cours 16)" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('Aide : Le transfert de chaleur va de la source froide à la source chaude (Slide 12 Cours 16)'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Réponse (exécutez la prochaine cellule): " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "display(Latex('Les réponses correctes sont les réponses B et C'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "On considère une pompe à chaleur utilisée afin de chauffer une piscine et de refroidir une chambre froide, le gaz de cette pompe à chaleur est considéré comme parfait de coefficient γ et de chaleur spécifique $C_v$.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", " Principe général de la pompe à chaleur

    \n", "Grâce à la question précédente vous savez maintenant que le transfert de chaleur va de la source froide vers la source chaude. Cependant la chaleur passe toujours du corps le plus chaud vers le corps le plus froid.

    \n", "Si l'on veut prélever de la chaleur à la source froide pour en donner à la source chaude, il va falloir un liquide encore plus froid que la température de la chambre froide. Dans le cas d'une pompe à chaleur ce liquide est le liquide friorigène. Au cours du circuit il va être compressé pour être liquide et évaporé afin de refroidir et de capter la chaleur de l'environnement froid.

    \n", " \n", " ![CarnotUrl](http://cooltec.ch/wpimages/animation-pompe-a-chaleur.gif)\n", "\n", "(Crédit : CoolTec : les pompes à chaleur)

    \n", "On a donc un circuit fermé avec un liquide qui a la capacité de s'evaporer et de se condenser rapidement. Le circuit se compose d'un compresseur (joue le rôle de pompe), un condenseur (ici le gaz se transforme en liquide et transmet sa chaleur) et un évaporateur (pour retransformer le liquide en gaz). Ce circuit est une pompe à chaleur.

    \n", "En mettant le compresseur en route, le gaz friorigène est attiré depuis l'évaporateur vers le compresseur, il se liquédie et transmet la chaleur acquise dans l'évaporateur. On prend donc la chaleur de l'environnement et on la transfère au circuit de chauffage (ici pour la piscine). Pour le réfigérateur, la chaleur est extraite de l'intérieur du réfrigérateur vers l'extérieur (la pièce dans laquelle il se trouve)

    \n", " \n", "Après cette brève explication, place aux questions :" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "2) Commencez par donner la relation des gaz parfaits ainsi que l’expression de l’énergie interne en fonction de la chaleur spécifique :

    \n", "Réponse (exécutez la prochaine cellule): " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "\n", "display(Latex('Relation des gaz parfaits : $pV = nRT$'))\n", "display(Latex('Expression de l énergie interne : $ΔU = C_v ΔT$'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "On considère le cycle thermodynamique suivant ne comprenant que des transformations réversibles :

    \n", "
  • Une détente isobare de la température T1, de la pression p1 et du volume V1 au volume V2
    \n", "
  • Une compression isochore jusqu’à la pression p3
    \n", "
  • Une compression isotherme
    \n", "
  • Une détente adiabatique jusqu’au volume V1

    \n", "3) Dessinez le cycle en question et indiquez si il est moteur ou récepteur:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", " \n", "Aide : le cycle est l'un des 4 cycles présents ci-dessous (exécutez la cellule), pensez bien au sens des transformations, si cela implique une augmentation de volume (détente) ou une réduction du volume (compression). Réfléchissez de la même manière pour la pression. Chaque transformation a sa forme particulière, veillez à utiliser la forme appropriée.\n" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
    " - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "\n", "\n", "plt.figure(1)\n", "img=mpimg.imread('Figs/Cycle2.png')\n", + "plt.figure(figsize=(10,10))\n", "imgplot = plt.imshow(img)\n", "plt.axis('off')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Réponse (exécutez la prochaine cellule): " ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'Cycle de Carnot récepteur car le sens est anti horaire')" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
    " - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "plt.figure(2)\n", "img1=mpimg.imread('Figs/Cycle3.png')\n", + "plt.figure(figsize=(6,6))\n", "imgplot = plt.imshow(img1)\n", "plt.axis('off')\n", "plt.title('Cycle de Carnot récepteur car le sens est anti horaire')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "4) Pour chacune des transformations, indiquez une relation entre l’état initial et l’état final :
    Pensez au paramètre qui est constant et à l'implication dans la loi des gaz parfaits ou à la relation impliquée par une certaine transformation.
    \n", " Réponse (exécutez la prochaine cellule):" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "Isobare : $V/T$ = cst" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Isochore : $P/T$ = cst" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Isotherme : $PV$ = cst" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Adiabatique : $PV^γ$ = cst" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('Isobare : $V/T$ = cst'))\n", "display(Latex('Isochore : $P/T$ = cst'))\n", "display(Latex('Isotherme : $PV$ = cst'))\n", "display(Latex('Adiabatique : $PV^γ$ = cst'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "5) Calculez les variables d’état pour chacun des quatre coins du cycle en fonction de ($C_v$, γ, $p_1$, $V_1$, $T_1$, $V_2$ et $p_3$) et en vous aidant de vos réponses à la question précédente :

    \n", "Servez vous des relations précédemments trouvées afin de trouver les variables d'état.

    \n", "Les réponses sont données transformation par transformation :" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Les réponses pour la première transformation sont : " ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "On rappelle que pour une transformation isobare : $V/T$ = cst" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$p_2$ = $p_1$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\dfrac{V_1}{T_1}$ = $\\dfrac{V_2}{T_2}$ et on obtient $T_2$ = $\\dfrac{V_2T_1}{V_1}$ " - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('On rappelle que pour une transformation isobare : $V/T$ = cst'))\n", "display(Latex('$p_2$ = $p_1$'))\n", "display(Latex('$\\dfrac{V_1}{T_1}$ = $\\dfrac{V_2}{T_2}$ et on obtient $T_2$ = $\\dfrac{V_2T_1}{V_1}$ '))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Les réponses pour la deuxième transformation sont : " ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "On rappelle que pour une transformation isochore : $P/T$ = cst" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$V_3$ = $V_2$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\dfrac{p_3}{T_3}$ = $\\dfrac{p_2}{T_2}$ et on obtient $T_3$ = $\\dfrac{p_3T_2}{p_2}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Or $p_2$ = $p_1$ et $T_2$ = $\\dfrac{V_2T_1}{V_1}$ donc $T_3$ = $\\dfrac{p_3V_2T_1}{p_1V_1}$ " - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('On rappelle que pour une transformation isochore : $P/T$ = cst'))\n", "display(Latex('$V_3$ = $V_2$'))\n", "display(Latex('$\\dfrac{p_3}{T_3}$ = $\\dfrac{p_2}{T_2}$ et on obtient $T_3$ = $\\dfrac{p_3T_2}{p_2}$'))\n", "display(Latex('Or $p_2$ = $p_1$ et $T_2$ = $\\dfrac{V_2T_1}{V_1}$ donc $T_3$ = $\\dfrac{p_3V_2T_1}{p_1V_1}$ '))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Exprimez les variables grâce à la troisième transformation
    (Aide : vous aurez besoin de la quatrième transformation pour exprimer les variables en fonction de celles indiquées au début de la question).

    \n", "Les réponses pour la troisième transformation sont: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "display(Latex('On rappelle que pour une transformation isotherme : $pV$ = cst'))\n", "display(Latex('$T_4$ = $T_3$'))\n", "display(Latex('$p_4V_4$ = $p_3V_3$ et on obtient $p_4$ = $\\dfrac{p_3V_3}{V_4}$'))\n", "display(Latex('Or $V_3$ = $V_2$ donc $p_4$ = $\\dfrac{p_3V_2}{V_4}$ '))\n", "display(Latex('Cependant ni $p_4$, ni $V_4$ ne font partie des paramètres à utiliser pour exprimer les différentes variables d état, on va donc utiliser les relations de la dernière transformation'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Les réponses pour la quatrième transformation sont: " ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "On rappelle que pour une transformation adiabatique : $pV^γ$ = cst" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$p_4V^γ_4$ = $p_1V^γ_1$ donc $p_4$ = $p_1(\\dfrac{V_1}{V_4})^γ$ " - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "En egalisant l expression de $p_4$ de la troisième et quatrième transformation on obtient:" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\dfrac{p_3V_2}{V_4}$ = $p_1(\\dfrac{V_1}{V_4})^γ$ et donc $V_4$ = $V^{γ/(γ-1)}_1(\\dfrac{p_1}{V_2p_3})^{1/(γ-1)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "En remplacant $V_4$ dans l expression$p_4$ on obtient : $p_4$=$\\dfrac{p_3V_2}{V_4}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$p_4$=$\\dfrac{p_3V_2}{V_4}$=$\\dfrac{(p_3V_2)^{γ/(γ-1)}}{(p_1V_1^γ)^{1/(γ-1)}}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Ainsi voici l ensemble des variables d état obtenues" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Point 1 : $p_1$, $V_1$ et $T_1$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Point 2 : $p_2$ = $p_1$, $V_2$ et $T_2$ = $\\dfrac{V_2T_1}{V_1}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Point 3 : $p_3$, $V_3$ = $V_2$ et $T_3$ = $\\dfrac{p_3V_2T_1}{p_1V_1}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Point 4 : $p_4$= $\\dfrac{(p_3V_2)^{γ/(γ-1)}}{(p_1V_1^γ)^{1/(γ-1)}}$, $V_4$=$V^{γ/(γ-1)}_1(\\dfrac{p_1}{V_2p_3})^{1/(γ-1)}$ et $T_4$ = $T_3$ = $\\dfrac{p_3V_2T_1}{p_1V_1}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('On rappelle que pour une transformation adiabatique : $pV^γ$ = cst'))\n", "display(Latex('$p_4V^γ_4$ = $p_1V^γ_1$ donc $p_4$ = $p_1(\\dfrac{V_1}{V_4})^γ$ '))\n", "display(Latex('En egalisant l expression de $p_4$ de la troisième et quatrième transformation on obtient:'))\n", "display(Latex('$\\dfrac{p_3V_2}{V_4}$ = $p_1(\\dfrac{V_1}{V_4})^γ$ et donc $V_4$ = $V^{γ/(γ-1)}_1(\\dfrac{p_1}{V_2p_3})^{1/(γ-1)}$'))\n", "display(Latex('En remplacant $V_4$ dans l expression$p_4$ on obtient : $p_4$=$\\dfrac{p_3V_2}{V_4}$'))\n", "display(Latex('$p_4$=$\\dfrac{p_3V_2}{V_4}$=$\\dfrac{(p_3V_2)^{γ/(γ-1)}}{(p_1V_1^γ)^{1/(γ-1)}}$'))\n", "display(Latex(''))\n", "display(Latex('Ainsi voici l ensemble des variables d état obtenues'))\n", "display(Latex('Point 1 : $p_1$, $V_1$ et $T_1$'))\n", "display(Latex('Point 2 : $p_2$ = $p_1$, $V_2$ et $T_2$ = $\\dfrac{V_2T_1}{V_1}$'))\n", "display(Latex('Point 3 : $p_3$, $V_3$ = $V_2$ et $T_3$ = $\\dfrac{p_3V_2T_1}{p_1V_1}$'))\n", "display(Latex('Point 4 : $p_4$= $\\dfrac{(p_3V_2)^{γ/(γ-1)}}{(p_1V_1^γ)^{1/(γ-1)}}$, $V_4$=$V^{γ/(γ-1)}_1(\\dfrac{p_1}{V_2p_3})^{1/(γ-1)}$ et $T_4$ = $T_3$ = $\\dfrac{p_3V_2T_1}{p_1V_1}$'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "5) Calculez la variation d’énergie interne ΔU et d’entropie ΔS sur le cycle entier :
    \n", "Exécutez la prochaine cellule afin d'afficher une aide" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "Aide : la machine fait des cycles réversibles" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('Aide : la machine fait des cycles réversibles'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Réponse (exécutez la prochaine cellule): " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "display(Latex('ΔU=0 et ΔS=0 sur un cycle'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "6) Donnez la relation reliant le travail, l’énergie interne ainsi que la chaleur ainsi que les formules permettant de calculer l’énergie interne et le travail :" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "display(Latex('$ΔU_{1->2}$ = $W_{1->2}$ + $Q_{1->2}$'))\n", "display(Latex('Expression de l énergie interne : $ΔU_{1->2}$ = $C_vΔT$'))\n", "display(Latex('Expression du travail : $W_{1->2}$ = $-\\int_{V_1}^{V_2} P dV$'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "7) Calculez le travail W sur un cycle, ainsi que les quantités de chaleur échangées avec la source froide (Qf) et la source chaude (Qc). Précisez lors de quelle(s) transformation(s) ont lieu ces échanges de chaleur.

    \n", " \n", "
    \n", " \"\"/\n", "\n", - "(Credit: Cours 16 slide 13)\n", + "###### (Credit: Cours 16 slide 13)\n", "\n", - "
    \n", + "
    \n", " \n", "Les réponses sont données transformation par transformation :" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Aide (exécutez la prochaine cellule): " ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "Utilisez les formules précédemment trouvées pour calculer $W$, $ΔU$ et $Q$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "La machine fonctionnant en cycle récepteur, elle donne de la chaleur à la source chaude ($Q_c<0$) et en prend à la source froide ($Q_f>0$)" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('Utilisez les formules précédemment trouvées pour calculer $W$, $ΔU$ et $Q$'))\n", "display(Latex('La machine fonctionnant en cycle récepteur, elle donne de la chaleur à la source chaude ($Q_c<0$) et en prend à la source froide ($Q_f>0$)'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Les réponses pour la première transformation sont : " ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "Transformation isobare :" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$ΔU_{1->2}$ = $W_{1->2}$ + $Q_{1->2}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$ΔU_{1->2}$ = $C_vΔT$ = $C_v(T_2 - T_1)$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Or $T_2$ = $\\dfrac{V_2T_1}{V_1}$ donc $ΔU_{1->2}$ = $C_vT_1(\\dfrac{V_2}{V_1} - 1)$ qui est $>0$ car $V_2>V_1$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$W_{1->2}$ = $-\\int_{V_1}^{V_2} P dV$ =$-P_1(V_2 - V_1)$=$P_1(V_1 - V_2)$ qui est $>0$ car $V_2>V_1$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$Q_{1->2}$ = $ΔU_{1->2}$ - $W_{1->2}$ qui est >0 " - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('Transformation isobare :'))\n", "display(Latex('$ΔU_{1->2}$ = $W_{1->2}$ + $Q_{1->2}$'))\n", "display(Latex('$ΔU_{1->2}$ = $C_vΔT$ = $C_v(T_2 - T_1)$'))\n", "display(Latex('Or $T_2$ = $\\dfrac{V_2T_1}{V_1}$ donc $ΔU_{1->2}$ = $C_vT_1(\\dfrac{V_2}{V_1} - 1)$ qui est $>0$ car $V_2>V_1$'))\n", "display(Latex(''))\n", "display(Latex('$W_{1->2}$ = $-\\int_{V_1}^{V_2} P dV$ =$-P_1(V_2 - V_1)$=$P_1(V_1 - V_2)$ qui est $>0$ car $V_2>V_1$'))\n", "display(Latex(''))\n", "display(Latex('$Q_{1->2}$ = $ΔU_{1->2}$ - $W_{1->2}$ qui est >0 '))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Les réponses pour la deuxième transformation sont : " ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "Transformation isochore :" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$dV$ = $0$ donc $W_{2->3}$ = $0$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$Q_{2->3}$ = $ΔU_{2->3}$ = $C_vΔT$ = $C_v(T_3 - T_2)$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Or $T_3$ = $\\dfrac{p_3V_2T_1}{p_1V_1}$ et $T_2$ = $\\dfrac{V_2T_1}{V_1}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "Donc $Q_{2->3}$ = $\\dfrac{C_vV_2T_1}{V_1}(\\dfrac{P_3}{P_1} - 1)$ qui est $>0$ car $P_3>P_1$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('Transformation isochore :'))\n", "display(Latex('$dV$ = $0$ donc $W_{2->3}$ = $0$'))\n", "display(Latex(''))\n", "display(Latex('$Q_{2->3}$ = $ΔU_{2->3}$ = $C_vΔT$ = $C_v(T_3 - T_2)$'))\n", "display(Latex('Or $T_3$ = $\\dfrac{p_3V_2T_1}{p_1V_1}$ et $T_2$ = $\\dfrac{V_2T_1}{V_1}$'))\n", "display(Latex('Donc $Q_{2->3}$ = $\\dfrac{C_vV_2T_1}{V_1}(\\dfrac{P_3}{P_1} - 1)$ qui est $>0$ car $P_3>P_1$' ))\n", "display(Latex(''))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Les réponses pour la troisième transformation sont : " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "display(Latex('Transformation isotherme :'))\n", "display(Latex('$ΔT$ = $0$ donc $ΔU_{3->4}$ = $0$'))\n", "display(Latex(''))\n", "display(Latex('$W_{3->4}$ = $- Q_{3->4}$ = $-\\int_{V_3}^{V_4} P dV$ = $-\\int_{V_2}^{V_4} P dV$ = $-P_4V_4\\int_{V_2}^{V_4} \\dfrac{dV}{V}$ = $-P_4V_4 ln(\\dfrac{V_4}{V_2})$ = $P_4V_4 ln(\\dfrac{V_2}{V_4})$'))\n", "display(Latex('$W_{3->4}$ = $P_4V_4 ln(\\dfrac{V_2}{V_4})$ qui est $>0$ car $V_2>V_4$'))\n", "display(Latex(''))\n", "display(Latex('$Q_{3->4}$ est donc $<0$'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Les réponses pour la quatrième transformation sont : " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "display(Latex('Transformation adiabatique :'))\n", "display(Latex('$Q_{4->1}$ = $0$ car il n y a pas d échange de chaleur'))\n", "display(Latex(''))\n", "display(Latex('$W_{4->1}$ = $ΔU_{4->1}$ = $C_vΔT$ = $C_v(T_4 - T_1)$ '))\n", "display(Latex('Or $T_4$ = $T_3$ = $\\dfrac{p_3V_2T_1}{p_1V_1}$ donc $W_{4->1}$ = $C_vT_1(\\dfrac{p_3V_2}{p_1V_1} - 1)$ qui est $>0$ car $P_3 > P_1$ et $V_2 > V_1$'))\n", "display(Latex(''))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Les quantités de chaleur échangées avec la source froide (Qf) et la source chaude (Qc) sont : " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [], "source": [ "display(Latex('La machine fonctionnant en cycle récepteur, elle donne de la chaleur à la source chaude ($Q_c<0$) et en prend à la source froide ($Q_f>0$), ce qui donne :'))\n", "display(Latex('$Q_c$ = $Q_{3->4}$ '))\n", "display(Latex(''))\n", "display(Latex('$Q_f$ = $Q_{1->2}$ + $Q_{2->3}$'))\n", "display(Latex(''))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "8) Donnez les relations de rendement pour un cycle de type « pompe à chaleur » et un cycle de type « réfrigérateur » ainsi que l’expression du travail en fonction des quantités de chaleur :" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Réponse (exécutez la prochaine cellule): " ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "$η_{pompe}$ = $\\dfrac{|Q_c|}{|W|}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$η_{réfrigérateur}$ = $\\dfrac{|Q_f|}{|W|}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$W = -(Q_c + Q_f)$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('$η_{pompe}$ = $\\dfrac{|Q_c|}{|W|}$'))\n", "display(Latex(''))\n", "display(Latex('$η_{réfrigérateur}$ = $\\dfrac{|Q_f|}{|W|}$'))\n", "display(Latex(''))\n", "display(Latex('$W = -(Q_c + Q_f)$'))\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "9) Déterminez le rendement de la pompe à chaleur pour la piscine ($η_{piscine}$) et pour la patinoire ($η_{patinoire}$) :\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "Réponse (exécutez la prochaine cellule): " ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": { "jupyter": { "source_hidden": true } }, - "outputs": [ - { - "data": { - "text/latex": [ - "$η_{pompe}$ = $\\dfrac{-Q_c}{W}$ = $\\dfrac{Q_c}{Q_c + Q_f}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$η_{réfrigérateur}$ = $\\dfrac{Q_f}{W}$ = $\\dfrac{-Q_f}{Q_c + Q_f}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(Latex('$η_{pompe}$ = $\\dfrac{-Q_c}{W}$ = $\\dfrac{Q_c}{Q_c + Q_f}$'))\n", "display(Latex(''))\n", "display(Latex('$η_{réfrigérateur}$ = $\\dfrac{Q_f}{W}$ = $\\dfrac{-Q_f}{Q_c + Q_f}$'))\n" ] }, { "cell_type": "markdown", - "metadata": { - "jupyter": { - "source_hidden": true - } - }, + "metadata": {}, "source": [ "
    \n", "Le Jupyter Notebook t'as plu? Nous t'invitons à remplir ce formulaire anonyme afin de nous donner tes impressions et tes remarques qui nous seront très utiles afin de construire un meilleur second Notebook pour tes révisions. Tu le recevras la semaine prochaine. Merci !

    \n", " \n", "https://docs.google.com/forms/d/e/1FAIpQLSfkqiL1Z4L_OIsyy16AfhY1UYa4_4inbnuPO4mrhRPsEBDG1Q/viewform?usp=sf_link\n", " \n", " " ] }, { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "jupyter": { + "source_hidden": true + } + }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.1" + "version": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 }