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On a donc~: +La différence constitue le travail fourni par le système pendant le cycle, une partie étant produite par le gaz pendant le temps moteur et une autre absorbée par celui-ci pendant la compression. Attention, \(Q_{rej}<0\) et il faut donc soit additionner les deux chaleur pour avoir le travail qui constitue leur différence ou soustraire l'opposé de la chaleur rejetée, soit \(|Q_{rej}|=n\cdot C_V\cdot (T_4-T_1)\). On a donc~: \[A=Q_{abs}-Q_{rej}=n\cdot C_V\cdot (T_3-T_2-T_4+T_1)\] Le rendement est alors~: \begin{align*} @@ -1224,6 +1264,9 @@ Le fonctionnement d'un moteur diésel n'est pas très différent de celui d'un m \psfrag{A}{\(A\)} \psfrag{V1}{\(V_1\)} \psfrag{V2}{\(V_2\)} +\psfrag{V3}{\(V_3\)} +\psfrag{p1}{\(p_1\)} +\psfrag{p2}{\(p_2\)} \psfrag{a ; f}{(a) ; (f)} \psfrag{b}{(b)} \psfrag{c}{(c)} @@ -1237,7 +1280,7 @@ Comme le cycle d'Otto, le cycle Diesel est donc aussi constitué de deux adiabat \[Q_{abs}=n\cdot C_P\cdot (T_3-T_2)\] et, comme chaleur rejetée~: \[Q_{rej}=n\cdot C_V\cdot (T_1-T_4)\] -La différence constitue le travail fourni par le système pendant le cycle, une partie étant produite par le gaz pendant le temps moteur et une autre absorbée par celui-ci pendant la compression. Attention, \(Q_{rej}>0\) et il faut donc soit additionner les deux chaleur pour avoir le travail qui constitue leur différence ou soustraire l'opposé de la chaleur rejetée, soit \(|Q_{rej}|=n\cdot C_V\cdot (T_4-T_1)\). On a donc~: +La différence constitue le travail fourni par le système pendant le cycle, une partie étant produite par le gaz pendant le temps moteur et une autre absorbée par celui-ci pendant la compression. Attention, \(Q_{rej}<0\) et il faut donc soit additionner les deux chaleur pour avoir le travail qui constitue leur différence ou soustraire l'opposé de la chaleur rejetée, soit \(|Q_{rej}|=n\cdot C_V\cdot (T_4-T_1)\). On a donc~: \begin{align*} A&=Q_{abs}-Q_{rej}\\ &=n\cdot C_P\cdot (T_3-T_2)-n\cdot C_V\cdot (T_4-T_1) @@ -1245,7 +1288,7 @@ A&=Q_{abs}-Q_{rej}\\ Le rendement est alors~: \begin{align*} \eta&=\frac{n\cdot C_P\cdot (T_3-T_2)-n\cdot C_V\cdot (T_4+T_1)}{n\cdot C_V\cdot (T_3-T_2)}\\ -&=1-\frac{C_V\cdot (T_4-T_1)}{n\cdot C_P\cdot (T_3-T_2)}\\ +&=1-\frac{C_V\cdot (T_4-T_1)}{C_P\cdot (T_3-T_2)}\\ &=1-\frac{T_1\cdot C_V\cdot (T_4/T_1-1)}{T_2\cdot C_P\cdot (T_3/T_2-1)} \end{align*} Or, l'équation \ref{adiavariation1}, valable pour une transformation adiabatique, peut s'écrire~: @@ -1359,7 +1402,7 @@ En résumé, pour un cycle de Carnot, le rendement ne dépend que des températu Le rendement d'une machine thermique réelle ne pouvant dépasser celle de Carnot, comme on le montrera au paragraphe \ref{secondprincipe}, elle ne peut jamais être de 100\%. \section{Thermodynamique statistique}\label{thermostat} -Au paragraphe \ref{apprmolecul}, nous avons considéré un gaz parfait du point de vue de ses éléments constitutifs. Reprenons cette approche pour déterminer comment un état donné est réalisé microscopiquement par un gaz. Pour cela, partons d'un volume divisé en trois parties et qui contient trois molécules sans interactions mutuelles. Nous ne prendrons pas en compte les différentes manières de répartir l'énergie interne entre les quatre molécules. Dénombrons le nombre d'états possibles, c'est-à-dire le nombre de manières différentes de placer les trois molécules dans les trois parties. On suppose que les molécules sont identiques. La figure \ref{} ... montre qu'il existe dix états microscopique différent, dont un comporte une seule molécule dans chaque partie, six comportent deux molécules dans l'une et/ou l'autre des parties et trois comportent trois molécules dans l'une des parties. Visiblement, sur la base du seul critère de la position des molécules, la probabilité de réalisation d'un état avec une, deux ou trois molécules dans une partie est très différente. Certains états sont réalisés plus souvent que d'autres, comme ici celui avec deux molécules dans l'une des parties. Visuellement cet état est aussi le plus désordonné. +Au paragraphe \ref{apprmolecul}, nous avons considéré un gaz parfait du point de vue de ses éléments constitutifs. Reprenons cette approche pour déterminer comment un état donné est réalisé microscopiquement par un gaz. Pour cela, partons d'un volume divisé en trois parties et qui contient trois molécules sans interactions mutuelles. Nous ne prendrons pas en compte les différentes manières de répartir l'énergie interne entre les quatre molécules. Dénombrons le nombre d'états possibles, c'est-à-dire le nombre de manières différentes de placer les trois molécules dans les trois parties. On suppose que les molécules sont identiques. La figure ... montre qu'il existe dix états microscopique différent, dont un comporte une seule molécule dans chaque partie, six comportent deux molécules dans l'une et/ou l'autre des parties et trois comportent trois molécules dans l'une des parties. Visiblement, sur la base du seul critère de la position des molécules, la probabilité de réalisation d'un état avec une, deux ou trois molécules dans une partie est très différente. Certains états sont réalisés plus souvent que d'autres, comme ici celui avec deux molécules dans l'une des parties. Visuellement cet état est aussi le plus désordonné. De manière plus générale, considérons un volume \(V\) décomposé en \(n\) parties de volume \(v=V/n\) contenant \(N\) particules différentes. On peut mettre la première particule dans l'une ou l'autre des \(n\) parties. De la même manière, on peut placer les \(N\) particules suivantes de \(n\) manières différentes. Au total, on a donc \(n^N\) manières de peupler notre volume \(V\). Or, comme \(n=V/v\), on a~: \[n^N=(\frac{V}{v})^N\sim V^N\]

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