{"id":30720,"date":"2021-05-06T13:00:24","date_gmt":"2021-05-06T13:00:24","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30720"},"modified":"2025-01-01T17:27:03","modified_gmt":"2025-01-01T17:27:03","slug":"etat-microscopique-et-etat-macroscopique-en-thermodynamique","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/fr\/etat-microscopique-et-etat-macroscopique-en-thermodynamique\/","title":{"rendered":"\u00c9tat microscopique et \u00e9tat macroscopique en thermodynamique"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\ttext-align:center;\n\t}\n<\/style>\n<h1>Micro\u00e9tat et macro\u00e9tat en thermodynamique<\/h1>\n<p style=\"text-align:center;\"><em>Dans ce cours, vous apprendrez \u00e0 diff\u00e9rencier les micro\u00e9tats et les macro\u00e9tats en thermodynamique, en explorant comment les configurations microscopiques d&#8217;un syst\u00e8me d\u00e9terminent ses propri\u00e9t\u00e9s macroscopiques. \u00c0 travers des exemples concrets, comme le calcul des combinaisons dans des syst\u00e8mes avec de multiples \u00e9tats possibles, vous comprendrez des concepts cl\u00e9s qui relient le microscopique \u00e0 l&#8217;observable. D\u00e9couvrez comment ces id\u00e9es sont fondamentales pour interpr\u00e9ter le comportement de syst\u00e8mes thermiques complexes et d\u00e9veloppez une nouvelle perspective sur les principes qui gouvernent la mati\u00e8re.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Objectifs d&#8217;apprentissage :<\/strong><br \/>\n\u00c0 la fin de ce cours, l&#8217;\u00e9tudiant sera capable de :\n<\/p>\n<ol>\n<li><strong>Distinguer<\/strong> entre micro\u00e9tat et macro\u00e9tat, en comprenant leurs d\u00e9finitions et leurs applications en thermodynamique.<\/li>\n<li><strong>Classer<\/strong> les micro\u00e9tats dans des macro\u00e9tats selon des qualit\u00e9s communes et calculer leur nombre gr\u00e2ce \u00e0 des combinaisons.<\/li>\n<li><strong>Expliquer<\/strong> comment l&#8217;\u00e9quiprobabilit\u00e9 des micro\u00e9tats d\u00e9termine la probabilit\u00e9 des macro\u00e9tats dans les syst\u00e8mes thermodynamiques.<\/li>\n<li><strong>Relier<\/strong> les propri\u00e9t\u00e9s microscopiques d&#8217;un syst\u00e8me \u00e0 ses propri\u00e9t\u00e9s macroscopiques telles que la pression, le volume et l&#8217;\u00e9nergie.<\/li>\n<li><strong>Analyser<\/strong> les syst\u00e8mes thermiques \u00e0 travers des exemples pratiques, en mettant en avant la pertinence des micro\u00e9tats et des macro\u00e9tats.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>TABLE DES MATI\u00c8RES<\/u> :<\/strong><br \/>\n<a href=\"#1\">La distinction entre micro\u00e9tat et macro\u00e9tat en thermodynamique<\/a><br \/>\n<a href=\"#2\">Caract\u00e9ristiques des macro\u00e9tats en thermodynamique<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/O5RKp4Dt8Z0\" title=\"Lecteur vid\u00e9o YouTube\" 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>La distinction entre micro\u00e9tat et macro\u00e9tat en thermodynamique<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=O5RKp4Dt8Z0&amp;t=7s\" target=\"_blank\" rel=\"noopener\"><strong>Une distinction d&#8217;une importance capitale en thermodynamique <\/strong><\/a>r\u00e9side dans la diff\u00e9rence entre micro\u00e9tat et macro\u00e9tat. On dit g\u00e9n\u00e9ralement que le micro\u00e9tat est li\u00e9 aux aspects microscopiques de la mati\u00e8re, tandis que le macro\u00e9tat concerne la totalit\u00e9 d&#8217;un syst\u00e8me compos\u00e9 de nombreux microsyst\u00e8mes. Bien que cette distinction aide \u00e0 une premi\u00e8re approche de ces id\u00e9es, elle ne couvre pas, \u00e0 elle seule, l&#8217;essence des notions de micro\u00e9tat et de macro\u00e9tat.<\/p>\n<p>Pour avoir une id\u00e9e plus pr\u00e9cise de ces concepts, examinons l&#8217;exemple suivant :<\/p>\n<h3>Micro\u00e9tats et macro\u00e9tats avec des pi\u00e8ces<\/h3>\n<p><strong><a href=\"https:\/\/www.youtube.com\/watch?v=O5RKp4Dt8Z0&amp;t=218s\" target=\"_blank\" rel=\"noopener\">Imaginez que vous avez une bo\u00eete avec 100 pi\u00e8ces,<\/a><\/strong> qui reste ferm\u00e9e en permanence. Si vous secouez cette bo\u00eete avec force, les pi\u00e8ces sautent \u00e0 l&#8217;int\u00e9rieur et tombent dans une position quelconque : face ou pile. Le syst\u00e8me complet dispose donc de nombreuses configurations possibles : <span class=\"katex-eq\" data-katex-display=\"false\">2^{100}<\/span> au total (essayez d&#8217;estimer l&#8217;ordre de grandeur de ce nombre !). Par \u00ab\u00e9tat\u00bb, nous faisons r\u00e9f\u00e9rence aux diff\u00e9rentes configurations de faces et de piles qui pourraient se produire. On suppose que chacune de ces configurations est \u00e9galement probable, de sorte que chacune a une probabilit\u00e9 de <span class=\"katex-eq\" data-katex-display=\"false\">1\/2^{100}<\/span> de se produire.<\/p>\n<h4>Chaque configuration particuli\u00e8re est un micro\u00e9tat<\/h4>\n<p>Nous dirons que chaque configuration particuli\u00e8re est un micro\u00e9tat de ce syst\u00e8me. Par exemple, la premi\u00e8re pi\u00e8ce est face, la deuxi\u00e8me pile, la troisi\u00e8me face, et ainsi de suite. Pour identifier un micro\u00e9tat, il est n\u00e9cessaire d&#8217;identifier chaque pi\u00e8ce individuellement, ce qui, en pratique, peut \u00eatre fastidieux.<\/p>\n<h4>Un macro\u00e9tat est la famille de tous les micro\u00e9tats ayant une qualit\u00e9 commune<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=O5RKp4Dt8Z0&amp;t=372s\" target=\"_blank\" rel=\"noopener\"><strong>\u00c0 ce stade, au lieu d&#8217;\u00e9tudier<\/strong><\/a> chaque micro\u00e9tat en particulier, nous pouvons choisir de classer les micro\u00e9tats possibles en familles ayant une qualit\u00e9 commune : ceux qui ont une seule face, ceux qui ont 2 faces, ceux qui ont 3 faces, etc. En \u00e9tudiant les nombres de combinaisons, nous arriverions \u00e0 ce que les micro\u00e9tats ayant :<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>0 faces et 100 piles sont : <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{0}} = \\frac{100!}{(100 - 0)! 0!} = 1 <\/span> \u00e9tat au total<\/li>\n<li>1 face et 99 piles sont : <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{100}\\choose{1}} = \\frac{100!}{(100 - 1)! 1!}= \\frac{100!}{99!} = 100 <\/span> \u00e9tats au total<\/li>\n<li>2 faces et 98 piles sont : <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{100}\\choose{2}} = \\frac{100!}{(100 - 2)! 2!}= \\frac{100!}{98!2!} = \\frac{99\\cdot 100}{2} = 99 \\cdot 50 = 4950 <\/span> \u00e9tats au total<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>49 faces et 51 piles sont : <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{49}} = \\frac{100!}{(100 - 49)! 49!}= \\frac{100!}{51!49!}\\approx 9.89\\cdot 10^{28}<\/span> \u00e9tats au total<\/li>\n<li>50 faces et 50 piles sont : <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{50}} = \\frac{100!}{(100 - 50)! 50!}= \\frac{100!}{50!50!}\\approx 10^{29}<\/span> \u00e9tats au total<\/li>\n<li>51 faces et 49 piles sont : <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{51}} = \\frac{100!}{(100 - 51)! 51!}= \\frac{100!}{49!51!}\\approx 9.89\\cdot 10^{28}<\/span> \u00e9tats au total<\/li>\n<li>52 faces et 48 piles sont : <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{52}} = \\frac{100!}{(100 - 52)! 52!}= \\frac{100!}{48!52!}\\approx 9.32\\cdot 10^{28}<\/span> \u00e9tats au total<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>70 faces et 30 piles sont : <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{70}} = \\frac{100!}{(100 - 70)! 70!}= \\frac{100!}{30!70!}\\approx 2.93\\cdot 10^{25}<\/span> \u00e9tats au total<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span>\n<ul>\n<li>100 faces et 0 piles sont : <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{100}} = \\frac{100!}{(100 - 100)! 100!}= \\frac{100!}{0!100!} = 1<\/span> \u00e9tat au total<\/li>\n<\/ul>\n<p>Ainsi, le macro\u00e9tat \u00ab0 face\u00bb contient un seul micro\u00e9tat, le macro\u00e9tat \u00ab1 face\u00bb contient 100 micro\u00e9tats, le macro\u00e9tat \u00ab2 faces\u00bb contient 4950 micro\u00e9tats, et ainsi de suite.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Caract\u00e9ristiques des macro\u00e9tats en thermodynamique<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=O5RKp4Dt8Z0&amp;t=607s\" target=\"_blank\" rel=\"noopener\"><strong>En g\u00e9n\u00e9ral, un macro\u00e9tat est compos\u00e9<\/strong><\/a> d&#8217;un grand nombre de micro\u00e9tats \u00e9galement probables.<\/p>\n<p>Bien que les micro\u00e9tats soient tous \u00e9quiprobables, les macro\u00e9tats, en g\u00e9n\u00e9ral, ne le sont pas. La probabilit\u00e9 d&#8217;un macro\u00e9tat est proportionnelle au nombre de micro\u00e9tats qu&#8217;il contient. Le macro\u00e9tat le plus probable est celui qui contient le plus grand nombre de micro\u00e9tats.<\/p>\n<p>Les syst\u00e8mes thermiques se comportent de mani\u00e8re tr\u00e8s similaire \u00e0 l&#8217;exemple que nous venons de voir. Pour sp\u00e9cifier un micro\u00e9tat dans un syst\u00e8me thermodynamique, il est n\u00e9cessaire d&#8217;indiquer les grandeurs qui d\u00e9finissent une certaine configuration du syst\u00e8me au niveau microscopique : cela peut \u00eatre la position, la vitesse ou l&#8217;\u00e9nergie des atomes qui composent le syst\u00e8me.<\/p>\n<p>En pratique, il est impossible de mesurer chacun des micro\u00e9tats du syst\u00e8me. En revanche, les macro\u00e9tats peuvent \u00eatre d\u00e9crits uniquement en termes des propri\u00e9t\u00e9s macroscopiques du syst\u00e8me, telles que la pression, l&#8217;\u00e9nergie totale ou le volume. Une configuration macroscopique d&#8217;un syst\u00e8me de <span class=\"katex-eq\" data-katex-display=\"false\">2[m^3]<\/span> de volume soumis \u00e0 une pression de <span class=\"katex-eq\" data-katex-display=\"false\">35[kPa]<\/span> peut \u00eatre associ\u00e9e \u00e0 un grand nombre de configurations microscopiques.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Micro\u00e9tat et macro\u00e9tat en thermodynamique Dans ce cours, vous apprendrez \u00e0 diff\u00e9rencier les micro\u00e9tats et les macro\u00e9tats en thermodynamique, en explorant comment les configurations microscopiques d&#8217;un syst\u00e8me d\u00e9terminent ses propri\u00e9t\u00e9s macroscopiques. \u00c0 travers des exemples concrets, comme le calcul des combinaisons dans des syst\u00e8mes avec de multiples \u00e9tats possibles, vous comprendrez des concepts cl\u00e9s qui 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