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m_>J%Uy6<`X-QV-;zx#8)@*NZh=Z5X|JD>X0r$6&;@BDup@FFJw diff --git a/Dessins/Moteur1_backup.svg b/Dessins/Moteur1_backup.svg new file mode 100644 index 0000000..2baa9fc --- /dev/null +++ b/Dessins/Moteur1_backup.svg @@ -0,0 +1,366 @@ + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Etape1 : isochore + + + diff --git a/Dessins/Moteur3_backup.svg b/Dessins/Moteur3_backup.svg new file mode 100644 index 0000000..41b1272 --- /dev/null +++ b/Dessins/Moteur3_backup.svg @@ -0,0 +1,362 @@ + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Etape3 : isochore + + diff --git a/ThermodynamiqueOS/ThermodynamiqueOS.tex b/ThermodynamiqueOS/ThermodynamiqueOS.tex index 88c9dd1..823f922 100644 --- a/ThermodynamiqueOS/ThermodynamiqueOS.tex +++ b/ThermodynamiqueOS/ThermodynamiqueOS.tex @@ -957,14 +957,14 @@ Par contre, on peut relever que le c\oe fficient \(\gamma\) de l'équation \ref{ \begin{figure*}[th!] \centering -\psfrag{Etape1~: isochore}{Étape A~: isochore} -\psfrag{Etape2~: isobare}{Étape B~: isobare} -\psfrag{Etape3~: isochore}{Étape C~: isochore} -\psfrag{Etape4~: isobare}{Étape D~: isobare} -\psfrag{Chauffage}{Chauffage} -\psfrag{Chargement}{Chargement} -\psfrag{Déchargement}{Déchargement} -\psfrag{Refroidissement}{Refroidissement} +%\psfrag{Etape1~: isochore}{Étape A~: isochore} +%\psfrag{Etape2~: isobare}{Étape B~: isobare} +%\psfrag{Etape3~: isochore}{Étape C~: isochore} +%\psfrag{Etape4~: isobare}{Étape D~: isobare} +%\psfrag{Chauffage}{Chauffage} +%\psfrag{Chargement}{Chargement} +%\psfrag{Déchargement}{Déchargement} +%\psfrag{Refroidissement}{Refroidissement} \subfigure[Chargement\label{moteur1}]{\includegraphics[width=6cm]{Moteur1.eps}}\qquad \subfigure[Chauffage\label{moteur2}]{\includegraphics[width=6cm]{Moteur2.eps}}\\ \subfigure[Déchargement\label{moteur3}]{\includegraphics[width=6cm]{Moteur3.eps}}\qquad diff --git a/ThermodynamiqueOS/ThermodynamiqueOS.tex.bak b/ThermodynamiqueOS/ThermodynamiqueOS.tex.bak index b459dcd..823f922 100644 --- a/ThermodynamiqueOS/ThermodynamiqueOS.tex.bak +++ b/ThermodynamiqueOS/ThermodynamiqueOS.tex.bak @@ -153,7 +153,7 @@ Mercure & \num{7e-4}\\ Considérons l'exemple suivant~: \smallskip -Une piscine de \SI{10 x 5 x 2}{\metre} est remplie d'eau. Si on suppose que la matière du récipient qui la constitue ne se dilate pas, calculez le volume d'eau qui déborde de celle-ci quand elle est entièrement remplie à \SI{17}{\celsius} et que sa température s'élève à \SI{25}{\celsius}. +Une piscine de 10 x 5 x 2 \si{\metre} est remplie d'eau. Si on suppose que la matière du récipient qui la constitue ne se dilate pas, calculez le volume d'eau qui déborde de celle-ci quand elle est entièrement remplie à \SI{17}{\celsius} et que sa température s'élève à \SI{25}{\celsius}. \smallskip Réponse~: @@ -164,8 +164,8 @@ On commence par calculer le volume initial~: Puis, on détermine la variation de volume~: \begin{align*} -\Delta V&=100\cdot 2\cdot 10^{-4}\cdot (25-17)\\ -&=\SI{0,16}{\metre\cubed}=\SI{160}{\deci\metre\cubed}=\SI{160}{\liter} +\Delta V&=100\cdot 3\cdot 2\cdot 10^{-4}\cdot (25-17)\\ +&=\SI{0,48}{\metre\cubed}=\SI{480}{\deci\metre\cubed}=\SI{480}{\liter} \end{align*} \section{Chaleurs spécifique et latente} @@ -282,7 +282,8 @@ Lorsque plusieurs matières, ou états de la matière, à températures différe Considérons maintenant les deux exemples suivants~: \medskip -Un thermos d'un litre est remplis au deux tiers d'eau chaude à \SI{80}{\celsius}. La température moyenne du thermos est alors de \SI{60}{\celsius}. Si la capacité thermique du thermos vaut \SI{0,4}{\celsius}, quelle doit être en grammes la masse d'eau froide à \SI{0}{\celsius} qu'il faut mettre dans le thermos pour que la température d'équilibre s'établisse à \SI{40}{\celsius} ? Est-ce possible ? +Un thermos d'un litre est remplis au deux tiers d'eau chaude à \SI{80}{\celsius}. Quelle doit être en gramme la masse d'eau froide à \SI{0}{\celsius} qu'il faut mettre dans le thermos pour que la température d'équilibre soit de \SI{40}{\celsius} ? Initialement la température du thermos est de \SI{60}{\celsius} et sa capacité thermique \SI{0,4}{\joule\per\celsius}. Est-ce possible ? + \smallskip Réponse~: @@ -294,7 +295,7 @@ Q_m&=m\cdot c_{eau}\cdot (\theta_{\acute{e}q}-\theta_{froide})\\ &=m\cdot 4,18\cdot 10^3\cdot (40-0)\\ &=167'200\cdot m \end{align*} -La chaleur cédée par l'eau chaude à \SI{90}{\celsius} vaut~: +La chaleur cédée par l'eau chaude à \SI{80}{\celsius} vaut~: \begin{align*} Q_{chaude}&=V_{chaude}\cdot \rho_{eau}\cdot c_{eau}\cdot (\theta_{\acute{e}q}-\theta_{chaude})\\ &=\frac{2}{3}\cdot 10^{-3}\cdot 10^3\cdot 4,18\cdot 10^3\cdot (40-80)\\ @@ -316,7 +317,8 @@ Q_m+Q_{chaude}+Q_{thermos}&=0\\ m&=\SI{0,666}{\kilo\gram} \end{align*} Soit en terme de volume~: \SI{0,666}{\liter}. Il n'est donc pas possible de mettre cette quantité d'eau dans le thermos puisqu'il ne reste qu'un tiers de litre. -\medskip + +\bigskip L'exemple suivant est plus complexe, car il fait intervenir un changement d'état. Un récipient de capacité thermique négligeable contient un demi-litre d'eau à \SI{10}{\celsius}. On y verse \SI{200}{\gram} de glace à \SI{-20}{\celsius}. Quel est l'état d'équilibre final et quelle est sa température ? \medskip @@ -563,7 +565,7 @@ Alors que pour une molécule triatomique rigide, on a trois degrés de liberté E=\frac{6}{2}\cdot n\cdot R\cdot T \end{equation} -L'épreuve du théorème de l'équipartition de l'énergie va venir de sa confrontation avec les chaleurs spécifiques. En effet, comme on le verra par la suite au paragraphe \ref{par:chalspe, on peut montrer que : +L'épreuve du théorème de l'équipartition de l'énergie va venir de sa confrontation avec les chaleurs spécifiques. En effet, comme on le verra par la suite au paragraphe \ref{par:chalspec}, page \pageref{par:chalspec}, on peut montrer que : \begin{align} C_V&=\frac{i}{2}\cdot R\\ C_p&=(\frac{i}{2}+1)\cdot R=\frac{i+2}{2}\cdot R @@ -594,7 +596,7 @@ Polyatomique & \color{violet}{i=7} & & & & & & & & \\ \end{center} \end{shaded} %\end{figure*} -\caption{Modèle de l'équipartition de l'énergie\\\color{red}{\(C_V=3R/2\)}, \color{blue}{\(C_V=5R/2\)}, \color{green}{\(C_V=6R/2\)}, \color{violet}{\(C_V=7R/2\)}\\\color{red}{\(C_p=5R/2\)}, \color{blue}{\(C_p=7R/2\)}, \color{green}{\(C_p=8R/2\)}, \color{violet}{\(C_p=9R/2\)}\label{tab:equipartition}} +\caption[Modèle de l'équipartition de l'énergie]{Modèle de l'équipartition de l'énergie\\\color{red}{\(C_V=3R/2\)}, \color{blue}{\(C_V=5R/2\)}, \color{green}{\(C_V=6R/2\)}, \color{violet}{\(C_V=7R/2\)}\\\color{red}{\(C_p=5R/2\)}, \color{blue}{\(C_p=7R/2\)}, \color{green}{\(C_p=8R/2\)}, \color{violet}{\(C_p=9R/2\)}\label{tab:equipartition}} \end{sidewaysfigure*} \subsection{Premier principe} @@ -916,7 +918,7 @@ Q&=0\\ }} \end{center} -\subsection{Chaleurs spécifiques} +\subsection{Chaleurs spécifiques}\label{par:chalspec} Rappelons que la chaleur spécifique molaire est définie comme la quantité de chaleur nécessaire pour élever la température d'une mole d'un gaz de un degré. Soit~: \begin{equation} C=\frac{Q}{n\cdot \Delta \theta}\;\Rightarrow\;Q=n\cdot C\cdot \Delta \theta @@ -955,14 +957,14 @@ Par contre, on peut relever que le c\oe fficient \(\gamma\) de l'équation \ref{ \begin{figure*}[th!] \centering -\psfrag{Etape1~: isochore}{Étape A~: isochore} -\psfrag{Etape2~: isobare}{Étape B~: isobare} -\psfrag{Etape3~: isochore}{Étape C~: isochore} -\psfrag{Etape4~: isobare}{Étape D~: isobare} -\psfrag{Chauffage}{Chauffage} -\psfrag{Chargement}{Chargement} -\psfrag{Déchargement}{Déchargement} -\psfrag{Refroidissement}{Refroidissement} +%\psfrag{Etape1~: isochore}{Étape A~: isochore} +%\psfrag{Etape2~: isobare}{Étape B~: isobare} +%\psfrag{Etape3~: isochore}{Étape C~: isochore} +%\psfrag{Etape4~: isobare}{Étape D~: isobare} +%\psfrag{Chauffage}{Chauffage} +%\psfrag{Chargement}{Chargement} +%\psfrag{Déchargement}{Déchargement} +%\psfrag{Refroidissement}{Refroidissement} \subfigure[Chargement\label{moteur1}]{\includegraphics[width=6cm]{Moteur1.eps}}\qquad \subfigure[Chauffage\label{moteur2}]{\includegraphics[width=6cm]{Moteur2.eps}}\\ \subfigure[Déchargement\label{moteur3}]{\includegraphics[width=6cm]{Moteur3.eps}}\qquad