From 4203a10bc232c3523385ed9dc96c8f0e3888e42a Mon Sep 17 00:00:00 2001 From: guyotv Date: Sun, 11 Sep 2022 20:00:45 +0200 Subject: [PATCH] Correction d'exos de thermo. --- Annexe-Exercices/Annexe-Exercices.tex | 39 ++++++++++++------- Annexe-Exercices/Annexe-Exercices.tex.bak | 44 ++++++++++++++-------- CoursMecaniqueOS.pdf | Bin 12826076 -> 12827241 bytes CoursMecaniqueOSDF.pdf | Bin 12826076 -> 12827241 bytes Solutions.tex | 18 +++++++-- SolutionsOS.tex | 15 ++++---- 6 files changed, 76 insertions(+), 40 deletions(-) diff --git a/Annexe-Exercices/Annexe-Exercices.tex b/Annexe-Exercices/Annexe-Exercices.tex index 22bb77b..5a93024 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex +++ b/Annexe-Exercices/Annexe-Exercices.tex @@ -1889,12 +1889,12 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \end{solos} \end{exos} -\begin{exos} - Une étoile se déplace ... autour du centre de la Galaxie. Calculez la masse de La Galaxie. - \begin{solos} - Un autre corrigé de test. - \end{solos} -\end{exos} +%\begin{exos} +% Une étoile se déplace ... autour du centre de la Galaxie. Calculez la masse de La Galaxie. +% \begin{solos} +% Un autre corrigé de test. +% \end{solos} +%\end{exos} %\begin{exos} % Un énoncé de test. @@ -2411,28 +2411,39 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r \begin{sol} Pour augmenter la température du lait, il faut la chaleur suivante~: \begin{align*} - Q&=m\cdot c_{eau}\cdot\Delta\theta\\ + Q_{lait} &=m\cdot c_{eau}\cdot\Delta\theta\\ &=0,2\cdot 4,18\cdot 10^3\cdot (50-20)=\SI{25080}{\joule} \end{align*} - Cette chaleur va lui être fournie par la vapeur devenant de l'eau liquide à \SI{100}{\celsius}. La chaleur latente de vaporisation de l'eau étant donnée dans la table \ref{tabchaleurlat}, page \pageref{tabchaleurlat}, on trouve la masse nécessaire par~: - \[m=\frac{Q}{L_v}=\frac{25'080}{23\cdot 10^5}=\SI{0,011}{\kilo\gram}\] - Il faudra donc mettre \SI{11}{\gram} de vapeur d'eau. + Cette chaleur va lui être fournie par la vapeur devenant de l'eau liquide à \SI{100}{\celsius} et l'eau provenant de cette vapeur passant de \SI{100}{\celsius} à \SI{50}{\celsius}. La chaleur latente de vaporisation de l'eau étant donnée dans la table \ref{tabchaleurlat}, page \pageref{tabchaleurlat}, on trouve la masse m de vapeur nécessaire, en tenant compte du fait que la chaleur latente fournie au lait doit être négative, par~: + \begin{align*} + -m\cdot L_v+m\cdot c_{eau}\cdot\Delta\theta+Q_{lait}=0\\ + -m\cdot 23\cdot 10^5+m\cdot 4180\cdot (50-100)+ 25 080=0\\ + m=\frac{Q}{L_v}=\frac{25 080}{23\cdot 10^5+209 000}\\ + =\SI{0,0099}{\kilo\gram} + \end{align*} + Il faudra donc mettre environ \SI{10}{\gram} de vapeur d'eau. + + \smallskip + Remarquez qu'en omettant le terme de chaleur échangée entre le lait et l'eau à \SI{100}{\celsius}, la masse de vapeur passe à \SI{11}{\gram} ou que le rapport d'énergie fournie par l'eau avec celle fournie par le gaz vaut : + \[\frac{209 000}{2300 000}=0,09=9\%\] + C'est donc essentiellement la vapeur d'eau qui chauffe le lait. \end{sol} \end{ex} \optv{OS}{ \begin{exos} - On veut refroidir un verre de \SI{2}{\deci\litre} de thé froid à \SI{20}{\celsius} pour en faire du thé glacé. Pour cela, on y introduit~: + On veut refroidir un verre de \SI{2}{\deci\litre} de thé froid à \SI{20}{\celsius} pour en faire du thé glacé. Pour cela, on y introduit soit~: \begin{itemize} -\item \SI{20}{\gram} d'eau à la température de la glace fondante, -\item \SI{20}{\gram} de glaçons à \SI{0}{\celsius}, +\item \SI{20}{\gram} d'eau à la température de la glace fondante, soit +\item \SI{20}{\gram} de glaçons à \SI{0}{\celsius} soit \item \SI{20}{\gram} de glaçons à \SI{-10}{\celsius}. \end{itemize} Dans chaque cas, calculez la température d'équilibre. Réponse~: \SI{18,2}{\celsius}, \SI{11,0}{\celsius} et \SI{10,6}{\celsius} \begin{solos} Commençons par calculer toutes les grandeurs en jeu. + \smallskip À deux décilitre d'eau correspond une masse de \SI{0,2}{\kilo\gram}. Pour que l'eau du thé descende sa température à \SI{0}{\celsius}, il faut lui transmettre une énergie de~: @@ -2442,12 +2453,14 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r \end{align*} Cette énergie est négative, car on la retire à l'eau. + \smallskip Pour faire fondre \SI{20}{\gram} de glace, il faut une énergie de~: \begin{align*} Q_{glace}&=m\cdot L_f=0,02\cdot 3,3\cdot 10^5\\ &=\SI{6600}{\joule} \end{align*} + \smallskip Pour faire passer la glace de \SI{-10}{\celsius} à \SI{0}{\celsius}, il faut une énergie de~: \begin{align*} Q_{glace}&=m\cdot c_{glace}\cdot\Delta\theta=0,02\cdot 2060\cdot (0-(-10)\\ diff --git a/Annexe-Exercices/Annexe-Exercices.tex.bak b/Annexe-Exercices/Annexe-Exercices.tex.bak index ac5681e..5a93024 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex.bak +++ b/Annexe-Exercices/Annexe-Exercices.tex.bak @@ -1882,18 +1882,19 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \begin{align*} M+m&=\frac{4\cdot \pi^2\cdot a^3}{G\cdot T^2}\\ &=\frac{4\cdot \pi^2\cdot 9 723 861 595.5^3}{6,67\cdot 10^{-11}\cdot 247743.36^2}\\ - &=\SI{8,87e30}{\kilo\gram}=\frac{8,87\cdot 10^{30}}{1,9889\cdot 10^{30}}=\SI{4,46}{M_{soleil}} + &=\SI{8,87e30}{\kilo\gram}=\frac{8,87\cdot 10^{30}}{1,9889\cdot 10^{30}}\\ + &=\SI{4,46}{M_{soleil}} \end{align*} - Imaginez donc deux étoiles à une distance de 6,5\% de la distance Terre-Soleil (\SI{0,065}{\astronomicalunit}), dont la masse vaut + Imaginez donc deux étoiles à une distance de 6,5\% de la distance Terre-Soleil (\SI{0,065}{\astronomicalunit}), dont la masse totale vaut plus de quatre masses solaires et qui tournent l'une autour de l'autre en un peu moins de trois jours ! \end{solos} \end{exos} -\begin{exos} - Une étoile se déplace ... autour du centre de la Galaxie. Calculez la masse de La Galaxie. - \begin{solos} - Un autre corrigé de test. - \end{solos} -\end{exos} +%\begin{exos} +% Une étoile se déplace ... autour du centre de la Galaxie. Calculez la masse de La Galaxie. +% \begin{solos} +% Un autre corrigé de test. +% \end{solos} +%\end{exos} %\begin{exos} % Un énoncé de test. @@ -2410,28 +2411,39 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r \begin{sol} Pour augmenter la température du lait, il faut la chaleur suivante~: \begin{align*} - Q&=m\cdot c_{eau}\cdot\Delta\theta\\ + Q_{lait} &=m\cdot c_{eau}\cdot\Delta\theta\\ &=0,2\cdot 4,18\cdot 10^3\cdot (50-20)=\SI{25080}{\joule} \end{align*} - Cette chaleur va lui être fournie par la vapeur devenant de l'eau liquide à \SI{100}{\celsius}. La chaleur latente de vaporisation de l'eau étant donnée dans la table \ref{tabchaleurlat}, page \pageref{tabchaleurlat}, on trouve la masse nécessaire par~: - \[m=\frac{Q}{L_v}=\frac{25'080}{23\cdot 10^5}=\SI{0,011}{\kilo\gram}\] - Il faudra donc mettre \SI{11}{\gram} de vapeur d'eau. + Cette chaleur va lui être fournie par la vapeur devenant de l'eau liquide à \SI{100}{\celsius} et l'eau provenant de cette vapeur passant de \SI{100}{\celsius} à \SI{50}{\celsius}. La chaleur latente de vaporisation de l'eau étant donnée dans la table \ref{tabchaleurlat}, page \pageref{tabchaleurlat}, on trouve la masse m de vapeur nécessaire, en tenant compte du fait que la chaleur latente fournie au lait doit être négative, par~: + \begin{align*} + -m\cdot L_v+m\cdot c_{eau}\cdot\Delta\theta+Q_{lait}=0\\ + -m\cdot 23\cdot 10^5+m\cdot 4180\cdot (50-100)+ 25 080=0\\ + m=\frac{Q}{L_v}=\frac{25 080}{23\cdot 10^5+209 000}\\ + =\SI{0,0099}{\kilo\gram} + \end{align*} + Il faudra donc mettre environ \SI{10}{\gram} de vapeur d'eau. + + \smallskip + Remarquez qu'en omettant le terme de chaleur échangée entre le lait et l'eau à \SI{100}{\celsius}, la masse de vapeur passe à \SI{11}{\gram} ou que le rapport d'énergie fournie par l'eau avec celle fournie par le gaz vaut : + \[\frac{209 000}{2300 000}=0,09=9\%\] + C'est donc essentiellement la vapeur d'eau qui chauffe le lait. \end{sol} \end{ex} \optv{OS}{ \begin{exos} - On veut refroidir un verre de \SI{2}{\deci\litre} de thé froid à \SI{20}{\celsius} pour en faire du thé glacé. Pour cela, on y introduit~: + On veut refroidir un verre de \SI{2}{\deci\litre} de thé froid à \SI{20}{\celsius} pour en faire du thé glacé. Pour cela, on y introduit soit~: \begin{itemize} -\item \SI{20}{\gram} d'eau à la température de la glace fondante, -\item \SI{20}{\gram} de glaçons à \SI{0}{\celsius}, +\item \SI{20}{\gram} d'eau à la température de la glace fondante, soit +\item \SI{20}{\gram} de glaçons à \SI{0}{\celsius} soit \item \SI{20}{\gram} de glaçons à \SI{-10}{\celsius}. \end{itemize} Dans chaque cas, calculez la température d'équilibre. Réponse~: \SI{18,2}{\celsius}, \SI{11,0}{\celsius} et \SI{10,6}{\celsius} \begin{solos} Commençons par calculer toutes les grandeurs en jeu. + \smallskip À deux décilitre d'eau correspond une masse de \SI{0,2}{\kilo\gram}. Pour que l'eau du thé descende sa température à \SI{0}{\celsius}, il faut lui transmettre une énergie de~: @@ -2441,12 +2453,14 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r \end{align*} Cette énergie est négative, car on la retire à l'eau. + \smallskip Pour faire fondre \SI{20}{\gram} de glace, il faut une énergie de~: \begin{align*} Q_{glace}&=m\cdot L_f=0,02\cdot 3,3\cdot 10^5\\ &=\SI{6600}{\joule} \end{align*} + \smallskip Pour faire passer la glace de \SI{-10}{\celsius} à \SI{0}{\celsius}, il faut une énergie de~: \begin{align*} Q_{glace}&=m\cdot c_{glace}\cdot\Delta\theta=0,02\cdot 2060\cdot (0-(-10)\\ diff --git a/CoursMecaniqueOS.pdf b/CoursMecaniqueOS.pdf index 54aa1db730d1de45e0548d43821498ab5efe8b5b..7f6c57ac81e0626037db45e4f0cccce49f9e8577 100644 GIT binary patch delta 156893 zcmY(~Q*fY7v@YP-wr$&*U}9%t+qS-BV%zq_nb>wFwr$(V`FGXX7yII=?&_Ofm#gbt zy>T83b@~tsRfi7>2qt2%B81!vg^AXp!uM6NKoH zcuY^ZqAC%tJU&!Cub!EZ9f9+32pGZHd}c7@ngX!~z$ 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