{"id":29134,"date":"2021-03-09T13:00:26","date_gmt":"2021-03-09T13:00:26","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29134"},"modified":"2024-12-30T07:47:05","modified_gmt":"2024-12-30T07:47:05","slug":"limite-thermodynamique-pression-et-variables","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/fr\/limite-thermodynamique-pression-et-variables\/","title":{"rendered":"Limite Thermodynamique, Pression et Variables"},"content":{"rendered":"<p><center><\/p>\n<h1>Limite Thermodynamique, Pression et Variables Extensives et Intensives<\/h1>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><em><strong>R\u00e9sum\u00e9 :<\/strong><br \/>\nCe cours introduit le concept de Limite Thermodynamique pour expliquer comment certains syst\u00e8mes physiques sont trait\u00e9s statistiquement. Une analogie avec des particules heurtant un mur est utilis\u00e9e, o\u00f9 la pression est d\u00e9finie comme la force totale par unit\u00e9 de surface. En consid\u00e9rant une surface infinie, la pression dans un conteneur est calcul\u00e9e \u00e0 partir de l&#8217;impulsion exerc\u00e9e par les mol\u00e9cules sur ses parois.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Objectifs d&#8217;Apprentissage :<\/strong><br \/> \u00c0 la fin de ce cours, l&#8217;\u00e9tudiant sera capable de :<\/p>\n<ol>\n<li><strong>Expliquer<\/strong> comment la limite thermodynamique s&#8217;applique \u00e0 la d\u00e9finition de la pression en termes de force totale et de surface<\/li>\n<li><strong>Comprendre<\/strong> comment la limite thermodynamique est appliqu\u00e9e en physique statistique et dans la th\u00e9orie cin\u00e9tique des gaz.<\/li>\n<li><strong>Comprendre<\/strong> la diff\u00e9rence entre les variables intensives et extensives.<\/li>\n<li><strong>Comprendre<\/strong> les id\u00e9es de base derri\u00e8re les diff\u00e9rentes approches de l&#8217;\u00e9tude de la thermodynamique.<\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n<strong><u>TABLE DES MATI\u00c8RES<\/u>:<\/strong><br \/>\n<a href=\"#1\">INTRODUCTION DE LA PRESSION DANS LA LIMITE THERMODYNAMIQUE<\/a><br \/>\n<a href=\"#2\">LA LIMITE THERMODYNAMIQUE<\/a><br \/>\n<a href=\"#3\">VARIABLES EXTENSIVES ET INTENSIVES<\/a><br \/>\n<a href=\"#4\">APPROCHES DE LA THERMODYNAMIQUE<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/aFNvauKaF4o\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Introduction de la Pression dans la Limite Thermodynamique<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=aFNvauKaF4o&amp;t=95s\" rel=\"noopener\" target=\"_blank\"><strong>Le concept de Limite Thermodynamique<\/strong><\/a> aide \u00e0 comprendre pourquoi certains syst\u00e8mes physiques peuvent \u00eatre trait\u00e9s \u00e0 l&#8217;aide de consid\u00e9rations statistiques. Cela est d\u00fb au <a href=\"https:\/\/toposuranos.com\/mol-y-masa-molar\/\" rel=\"noopener\" target=\"_blank\"><strong>grand nombre de particules qui les composent.<\/strong><\/a> Une mani\u00e8re simple de le d\u00e9montrer est \u00e0 travers une analogie. Imaginez que vous ayez un canon \u00e0 particules qui les tire \u00e0 une certaine vitesse contre un mur\u00a0; comme les particules ont une masse, en heurtant le mur, elles transf\u00e8rent une partie de leur quantit\u00e9 de mouvement, et donc exercent une impulsion.<\/p>\n<p style=\"text-align: justify;\">Ainsi, en connaissant la vitesse et la masse, on peut calculer la force exerc\u00e9e par chaque particule. Maintenant, imaginez qu&#8217;il ne s&#8217;agisse pas d&#8217;un canon, mais d&#8217;une pluie uniform\u00e9ment concentr\u00e9e de particules innombrables frappant une r\u00e9gion du sol, qui peut \u00eatre aussi grande que nous le souhaitons. Qu&#8217;obtiendrions-nous en cons\u00e9quence\u00a0?<\/p>\n<ol style=\"text-align: justify;\">\n<li>La force moyenne exerc\u00e9e augmente \u00e0 mesure que l&#8217;on consid\u00e8re une surface plus grande. Cela a du sens car plus la surface est grande, plus de particules sont re\u00e7ues.<\/li>\n<li>Bien que la force exerc\u00e9e par chaque particule fluctue, cela est \u00ab\u00a0liss\u00e9\u00a0\u00bb et tend vers une valeur moyenne. En fait, les fluctuations peuvent \u00eatre importantes, mais si nous augmentons la surface, la force totale sera si \u00e9norme que cette fluctuation sera insignifiante.<\/li>\n<\/ol>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=aFNvauKaF4o&amp;t=280s\" rel=\"noopener\" target=\"_blank\"><strong>Comme la force totale exerc\u00e9e est proportionnelle \u00e0 la surface, il est logique d&#8217;\u00e9tablir la d\u00e9finition suivante :<\/strong><\/a><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>D\u00e9finition<\/strong><\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"text-align:justify;\">La <strong><a href=\"https:\/\/toposuranos.com\/tag\/presion\/\" rel=\"noopener\" target=\"_blank\">Pression<\/a><\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> g\u00e9n\u00e9r\u00e9e par une force totale <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}<\/span> appliqu\u00e9e sur une surface <span class=\"katex-eq\" data-katex-display=\"false\">{A}<\/span> est d\u00e9finie comme la limite<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{\\displaystyle P = \\lim_{A\\to\\infty} \\frac{\\vec{F}\\cdot \\hat{n}}{A}}<\/span>\n<p style=\"text-align:justify;\">O\u00f9 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{n}<\/span> est le vecteur normal \u00e0 la surface.<\/p>\n<p><center><img decoding=\"async\" class=\"lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-8uSlbm03nEI\/YEfJFN4Gs-I\/AAAAAAAAEsY\/8szyQpVpGF0fy7u-7AU1BesRgwdvlRhMwCLcBGAsYHQ\/s438\/presion.PNG\" alt=\"pression et la limite thermodynamique\" width=\"300\" height=\"300\" \/><noscript><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/1.bp.blogspot.com\/-8uSlbm03nEI\/YEfJFN4Gs-I\/AAAAAAAAEsY\/8szyQpVpGF0fy7u-7AU1BesRgwdvlRhMwCLcBGAsYHQ\/s438\/presion.PNG\" alt=\"pression et la limite thermodynamique\" width=\"300\" height=\"300\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align:justify;\">Ceci est souvent \u00e9crit de mani\u00e8re r\u00e9sum\u00e9e comme<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P = \\frac{F}{A}<\/span>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">La pression introduite dans notre analogie ne change pas \u00e0 mesure que la surface augmente ; au contraire, les fluctuations de pression tendent \u00e0 dispara\u00eetre. En effet, les fluctuations peuvent \u00eatre ignor\u00e9es si nous prenons la limite o\u00f9 la surface tend vers l&#8217;infini.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>La Limite Thermodynamique<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=aFNvauKaF4o&amp;t=532s\" rel=\"noopener\" target=\"_blank\"><strong>Si l&#8217;on consid\u00e8re les mol\u00e9cules en mouvement \u00e0 l&#8217;int\u00e9rieur d&#8217;un conteneur,<\/strong><\/a> chaque fois qu&#8217;elles frappent la fronti\u00e8re, elles exercent une certaine impulsion. L&#8217;effet collectif de toutes ces impulsions est ce que nous interpr\u00e9tons comme la pression\u00a0: une force par unit\u00e9 de surface \u00e9tendue sur toute la surface. Si le conteneur \u00e9tait tr\u00e8s petit, nous devrions peut-\u00eatre nous pr\u00e9occuper des fluctuations de la force\u00a0; cependant, dans la plupart des cas, le nombre de particules est si grand que les fluctuations peuvent \u00eatre ignor\u00e9es. La pression d&#8217;un gaz dans ces conditions est consid\u00e9r\u00e9e comme totalement uniforme. Cette description que nous venons de faire est ce que l&#8217;on entend par \u00ab\u00eatre dans la <strong>limite thermodynamique<\/strong>.\u00bb<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Variables Extensives et Intensives<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=aFNvauKaF4o&amp;t=619s\" rel=\"noopener\" target=\"_blank\"><strong>Supposons qu&#8217;un conteneur de volume<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> contient un gaz \u00e0 une temp\u00e9rature <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span>, une pression <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> et que son \u00e9nergie cin\u00e9tique totale soit <span class=\"katex-eq\" data-katex-display=\"false\">U<\/span>. Imaginons maintenant que nous placions une barri\u00e8re \u00e0 l&#8217;int\u00e9rieur du conteneur qui divise le gaz en deux moiti\u00e9s \u00e9gales. Le volume de chaque moiti\u00e9 <span class=\"katex-eq\" data-katex-display=\"false\">V^*<\/span> sera donc<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle V^* = \\frac{V}{2}<\/span>\n<p style=\"text-align: justify;\">L&#8217;\u00e9nergie cin\u00e9tique totale de chaque moiti\u00e9 <span class=\"katex-eq\" data-katex-display=\"false\">U^*<\/span> sera \u00e9galement r\u00e9duite de moiti\u00e9<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle U^* = \\frac{U}{2}<\/span>\n<p style=\"text-align: justify;\">Cependant, des grandeurs telles que la temp\u00e9rature et la pression resteront les m\u00eames dans les deux moiti\u00e9s<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P^* = P<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">T^* = T<\/span>\n<p style=\"text-align: justify;\">De l\u00e0 d\u00e9coule une distinction entre les grandeurs impliqu\u00e9es dans la thermodynamique. Nous parlons de <strong>variables extensives<\/strong> lorsque les grandeurs qu&#8217;elles repr\u00e9sentent augmentent en fonction de la taille du syst\u00e8me, comme le volume ou l&#8217;\u00e9nergie, et nous parlons de <strong>variables intensives<\/strong> pour les grandeurs qui ne varient pas en fonction de la taille du syst\u00e8me, comme la pression et la temp\u00e9rature.<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>Approches de la Thermodynamique<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=aFNvauKaF4o&amp;t=786s\" rel=\"noopener\" target=\"_blank\"><strong>Historiquement, la thermodynamique s&#8217;est d\u00e9velopp\u00e9e en diff\u00e9rentes \u00e9tapes, nous l\u00e9guant plusieurs approches.<\/strong><\/a><\/p>\n<ul style=\"text-align: justify;\">\n<li><strong>La Thermodynamique Classique<\/strong> traite des propri\u00e9t\u00e9s macroscopiques telles que la pression, la temp\u00e9rature et le volume, sans se pr\u00e9occuper des aspects microscopiques de la mati\u00e8re. Elle traite des syst\u00e8mes suffisamment grands pour ignorer les fluctuations avant la limite thermodynamique et ignore la structure atomique de la mati\u00e8re.<\/li>\n<li><strong>La Th\u00e9orie Cin\u00e9tique des Gaz<\/strong> tente de d\u00e9terminer les <strong>propri\u00e9t\u00e9s des gaz<\/strong> en prenant en compte les distributions de probabilit\u00e9 associ\u00e9es au mouvement de leurs mol\u00e9cules. Ses d\u00e9buts \u00e9taient controvers\u00e9s, car \u00e0 l&#8217;\u00e9poque de sa cr\u00e9ation, il y avait encore des doutes quant \u00e0 l&#8217;existence des atomes et des mol\u00e9cules, prouv\u00e9e \u00e0 la fin du XIXe si\u00e8cle.<\/li>\n<li>La d\u00e9couverte des atomes a conduit au d\u00e9veloppement de la <strong>M\u00e9canique Statistique.<\/strong> Au lieu de commencer par la description des propri\u00e9t\u00e9s macroscopiques, comme c&#8217;est le cas en thermodynamique, son approche consiste \u00e0 tenter de d\u00e9crire les \u00e9tats des syst\u00e8mes microscopiques individuels et, ensuite, \u00e0 utiliser des m\u00e9thodes statistiques pour en d\u00e9duire les propri\u00e9t\u00e9s macroscopiques du syst\u00e8me. Cette approche b\u00e9n\u00e9ficie du d\u00e9veloppement de la <strong>m\u00e9canique quantique,<\/strong> car elle permet la description des microsyst\u00e8mes quantiques. Ainsi, ce qui est d\u00e9crit en thermodynamique est obtenu comme un processus limite de la m\u00e9canique statistique dans la limite thermodynamique.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Limite Thermodynamique, Pression et Variables Extensives et Intensives R\u00e9sum\u00e9 : Ce cours introduit le concept de Limite Thermodynamique pour expliquer comment certains syst\u00e8mes physiques sont trait\u00e9s statistiquement. Une analogie avec des particules heurtant un mur est utilis\u00e9e, o\u00f9 la pression est d\u00e9finie comme la force totale par unit\u00e9 de surface. En consid\u00e9rant une surface infinie, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29123,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":6,"footnotes":""},"categories":[901,647,931],"tags":[],"class_list":["post-29134","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mecanique-des-fluides","category-physique","category-thermodynamique"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Limite Thermodynamique, Pression et Variables - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"La limite thermodynamique explique comment, \u00e0 mesure que la taille d&#039;un syst\u00e8me augmente, les fluctuations deviennent insignifiantes, permettant de d\u00e9crire son comportement par des moyennes statistiques. 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