From 93fffba3d005a75702e0930c10f38e0bb6ce1b37 Mon Sep 17 00:00:00 2001
From: guyotv <linux@cvgg.org>
Date: Wed, 2 Nov 2022 12:20:50 +0100
Subject: [PATCH] Corrections mineurs de trois exos OS 31, 33 et 34

---
 Annexe-Exercices/Annexe-Exercices.tex     |   8 ++++----
 Annexe-Exercices/Annexe-Exercices.tex.bak |  21 ++++++++++-----------
 CoursMecaniqueOS.pdf                      | Bin 12861888 -> 12861893 bytes
 CoursMecaniqueOSDF.pdf                    | Bin 12861888 -> 12861893 bytes
 SolutionsOS.tex                           |   2 +-
 5 files changed, 15 insertions(+), 16 deletions(-)

diff --git a/Annexe-Exercices/Annexe-Exercices.tex b/Annexe-Exercices/Annexe-Exercices.tex
index 60c2462..b2c986b 100644
--- a/Annexe-Exercices/Annexe-Exercices.tex
+++ b/Annexe-Exercices/Annexe-Exercices.tex
@@ -2672,7 +2672,7 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 \begin{exos}
 	On gonfle, à une température de \SI{20}{\celsius}, un pneu de vingt pouces de rayon dont le rayon de la chambre à air vaut \SI{5}{\centi\metre} à une pression manomètrique de \SI{4}{\bar}. Après un long voyage, la température de l'air qu'il contient vaut \SI{25}{\celsius}. Quelle masse d'air doit-on retirer pour rétablir la pression à sa valeur d'origine ?
 	
-	La pression manométrique est la pression absolue à laquelle on a retiré une atmosphère. On peut considérer que la masse molaire de l'air est de \SI{29}{\gram\per\mol}. Réponses~: \SI{5}{\gram}.
+	La pression manométrique est la pression absolue à laquelle on a retiré une atmosphère. On peut considérer que la masse molaire de l'air est de \SI{29}{\gram\per\mol}. Réponses~: \SI{3}{\gram}.
 	\begin{solos}
 	La première chose à calculer est le volume de la chambre à air. Elle peut être assimilée à un cylindre de longueur L donnée par~:
 	\[L=2\cdot\pi\cdot R=2\cdot\pi\cdot 20\cdot 2,54\cdot 10^{-2}=\SI{3,192}{\metre}\]
@@ -2696,7 +2696,7 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 	Il faut donc retirer la différence~:
 	\[\Delta n=5,176-5,072=\SI{0,104}{\mol}\]
 	Soit en terme de masse~:
-	\[m=\Delta n\cdot M=0,104\cdot 29=\SI{5}{\gram}\]
+	\[m=\Delta n\cdot M=0,104\cdot 29=\SI{3}{\gram}\]
 	\end{solos}
 \end{exos}
 
@@ -2712,7 +2712,7 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 \end{exos}
 
 \begin{exos}
-	Deux moles d'un gaz parfait dans un volume de \SI{16}{\litre} passent d'une température initiale \(T_0\) à une température finale de \SI{450}{\kelvin}. Cela se fait en deux étapes~:
+	Deux moles d'un gaz parfait dans un volume de 16 litres passent d'une température initiale \(T_0\) à une température finale de \SI{450}{\kelvin}. Cela se fait en deux étapes~:
 	\begin{enumerate}
 	\item on chauffe le gaz à une pression constante de \SI{100}{\kilo\pascal} jusqu'à un volume double du premier et
 	\item on le chauffe encore à volume constant jusqu'à la température finale.
@@ -2745,7 +2745,7 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 \end{exos}
 
 \begin{exos}
-	On chauffe un gaz à volume constant, sous une pression de \SI{100}{\kilo\pascal} et une température de \SI{20}{\celsius} initiales. On le dilate ensuite à température constante lui permettant de revenir à l'état initial à pression constante. Son volume a alors doublé. Quelle température a-t-il alors ? Peut-on déterminer les volumes initiaux et finaux ? Réponse~: \SI{586,3}{\kelvin} et non.
+	On chauffe un gaz à volume constant, sous une pression de \SI{100}{\kilo\pascal} et une température de \SI{20}{\celsius} initiales. On le dilate ensuite à température constante lui permettant de revenir à sa pression initiale. Son volume a alors doublé. Quelle température a-t-il alors ? Peut-on déterminer les volumes initiaux et finaux ? Réponse~: \SI{586,3}{\kelvin} et non.
 	\begin{solos}
 	Pour chacune des transformations, on peut écrire~:
 	\begin{description}
diff --git a/Annexe-Exercices/Annexe-Exercices.tex.bak b/Annexe-Exercices/Annexe-Exercices.tex.bak
index f55d536..b2c986b 100644
--- a/Annexe-Exercices/Annexe-Exercices.tex.bak
+++ b/Annexe-Exercices/Annexe-Exercices.tex.bak
@@ -2590,7 +2590,7 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 \end{exos}
 
 \begin{exos}
-	Un gaz parfait comprenant trois moles de particules est à la pression de \SI{4}{\kilo\pascal} et à la température de \SI{20}{\celsius}. Calculez son volume. Puis recalculez-le si on augmente sa température à \SI{30}{\celsius} et diminue sa pression de 15\%. Réponses~: \SI{2,45}{\metre\cubed} et \SI{2,22}{\metre\cubed}.
+	Un gaz parfait comprenant trois moles de particules est à la pression de \SI{4}{\kilo\pascal} et à la température de \SI{20}{\celsius}. Calculez son volume. Puis recalculez-le si on augmente sa température à \SI{30}{\celsius} et diminue sa pression de 15\%. Réponses~: \SI{1,83}{\metre\cubed} et \SI{2,22}{\metre\cubed}.
 	\begin{solos}
 	De la loi des gaz parfaits, on tire~:
 	\[V=n\cdot R\cdot \frac{T}{p}=3\cdot 8,31\cdot \frac{293,15}{4\cdot 10^3}=\SI{1,83}{\metre\cubed}\]
@@ -2635,7 +2635,7 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 	\item En supposant le mobil-home étanche, calculez la pression intérieure si la température passe à \SI{25}{\celsius}.
 	\item Si il n'est pas étanche, calculez la masse d'air qui s'en échappe.
 	\end{enumerate}
-	On peut considérer que la masse molaire de l'air est de \SI{29}{\gram\per\mol}. Réponses~: \SI{238}{\kilo\gram}, \SI{1,02e5}{\pascal} et \SI{4}{\kilo\gram}.
+	On peut considérer que la masse molaire de l'air est de \SI{29}{\gram\per\mol}. Réponses~: \SI{241,183}{\kilo\gram}, \SI{1,02e5}{\pascal} et \SI{4}{\kilo\gram}.
 	\begin{solos}
 	On tire de la définition de la masse molaire~:
 	\[M=\frac{m}{n}\;\Rightarrow\;n=\frac{m}{M}\]
@@ -2670,9 +2670,9 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 \end{exos}
 
 \begin{exos}
-	On gonfle, à une température de \SI{20}{\celsius}, un pneu de vingt pouces de rayon dont le diamètre de la chambre à air vaut \SI{5}{\centi\metre} à une pression manomètrique de \SI{4}{\bar}. Après un long voyage, la température de l'air qu'il contient vaut \SI{25}{\celsius}. Quelle masse d'air doit-on retirer pour rétablir la pression à sa valeur d'origine ?
+	On gonfle, à une température de \SI{20}{\celsius}, un pneu de vingt pouces de rayon dont le rayon de la chambre à air vaut \SI{5}{\centi\metre} à une pression manomètrique de \SI{4}{\bar}. Après un long voyage, la température de l'air qu'il contient vaut \SI{25}{\celsius}. Quelle masse d'air doit-on retirer pour rétablir la pression à sa valeur d'origine ?
 	
-	La pression manométrique est la pression absolue à laquelle on a retiré une atmosphère. On peut considérer que la masse molaire de l'air est de \SI{29}{\gram\per\mol}. Réponses~: \SI{5}{\gram}.
+	La pression manométrique est la pression absolue à laquelle on a retiré une atmosphère. On peut considérer que la masse molaire de l'air est de \SI{29}{\gram\per\mol}. Réponses~: \SI{3}{\gram}.
 	\begin{solos}
 	La première chose à calculer est le volume de la chambre à air. Elle peut être assimilée à un cylindre de longueur L donnée par~:
 	\[L=2\cdot\pi\cdot R=2\cdot\pi\cdot 20\cdot 2,54\cdot 10^{-2}=\SI{3,192}{\metre}\]
@@ -2696,7 +2696,7 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 	Il faut donc retirer la différence~:
 	\[\Delta n=5,176-5,072=\SI{0,104}{\mol}\]
 	Soit en terme de masse~:
-	\[m=\Delta n\cdot M=0,104\cdot 29=\SI{5}{\gram}\]
+	\[m=\Delta n\cdot M=0,104\cdot 29=\SI{3}{\gram}\]
 	\end{solos}
 \end{exos}
 
@@ -2712,7 +2712,7 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 \end{exos}
 
 \begin{exos}
-	Deux moles d'un gaz parfait dans un volume de \SI{16}{\litre} passent d'une température initiale \(T_0\) à une température finale de \SI{450}{\kelvin}. Cela se fait en deux étapes~:
+	Deux moles d'un gaz parfait dans un volume de 16 litres passent d'une température initiale \(T_0\) à une température finale de \SI{450}{\kelvin}. Cela se fait en deux étapes~:
 	\begin{enumerate}
 	\item on chauffe le gaz à une pression constante de \SI{100}{\kilo\pascal} jusqu'à un volume double du premier et
 	\item on le chauffe encore à volume constant jusqu'à la température finale.
@@ -2745,7 +2745,7 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 \end{exos}
 
 \begin{exos}
-	On chauffe un gaz à volume constant, sous une pression de \SI{100}{\kilo\pascal} et une température de \SI{20}{\celsius} initiales. On le dilate ensuite à température constante lui permettant de revenir à l'état initial à pression constante. Son volume a alors doublé. Quelle température a-t-il alors ? Peut-on déterminer les volumes initiaux et finaux ? Réponse~: \SI{586,3}{\kelvin} et non.
+	On chauffe un gaz à volume constant, sous une pression de \SI{100}{\kilo\pascal} et une température de \SI{20}{\celsius} initiales. On le dilate ensuite à température constante lui permettant de revenir à sa pression initiale. Son volume a alors doublé. Quelle température a-t-il alors ? Peut-on déterminer les volumes initiaux et finaux ? Réponse~: \SI{586,3}{\kelvin} et non.
 	\begin{solos}
 	Pour chacune des transformations, on peut écrire~:
 	\begin{description}
@@ -2824,15 +2824,14 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r
 	&=\frac{x-x_0}{t}\cdot (\frac{I(x)+I(x_0)}{x-x_0}+\frac{I(t)}{t})\\
 	&=\frac{I(x)+I(x_0)}{t}+(x-x_0)\cdot \frac{I(t)}{t^2}
 	\end{align*}
-	On aurait pu s'arrêter à l'avant dernière égalité, mais on est allé plus loin, car
-	Dans le dernier cas, on peut aussi procéder différemment~:
+	On aurait pu s'arrêter à l'avant dernière égalité, mais on est allé plus loin, car dans le dernier cas, on peut aussi procéder différemment~:
 	\begin{align*}
 	I(v)&=I((x-x_0)/t)=I(x/t-x_0/t)\\
 	&=I(x/t)+I(x_0/t)\\
 	&=\frac{x}{t}\cdot i(x/t)+\frac{x_0}{t}\cdot i(x_0/t)\\
 	&=\frac{x}{t}\cdot (i(x)+i(t))+\frac{x_0}{t}\cdot (i(x_0)+i(t))\\
-	&=\frac{x}{t}\cdot (\frac{I(x)}{x}+\frac{I(t)}{t})\\
-	&+\frac{x_0}{t}\cdot (\frac{I(x_0)}{x_0}+\frac{I(t)}{t})\\
+	&=\frac{x}{t}\cdot (\frac{I(x)}{x}+\frac{I(t)}{t})\,+\\
+	&\;\;\;\;\frac{x_0}{t}\cdot (\frac{I(x_0)}{x_0}+\frac{I(t)}{t})\\
 	&=\frac{I(x)}{t}+\frac{x\cdot I(t)}{t^2}+\frac{I(x_0)}{t}+\frac{x_0\cdot I(t)}{t^2}\\
 	&=\frac{I(x)+I(x_0)}{t}+(x+x_0)\cdot \frac{I(t)}{t^2}
 	\end{align*}
diff --git a/CoursMecaniqueOS.pdf b/CoursMecaniqueOS.pdf
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diff --git a/SolutionsOS.tex b/SolutionsOS.tex
index 48f6bfb..df9a55a 100644
--- a/SolutionsOS.tex
+++ b/SolutionsOS.tex
@@ -996,7 +996,7 @@
 	Il faut donc retirer la différence~:
 	\[\Delta n=5,176-5,072=\SI{0,104}{\mol}\]
 	Soit en terme de masse~:
-	\[m=\Delta n\cdot M=0,104\cdot 29=\SI{5}{\gram}\]
+	\[m=\Delta n\cdot M=0,104\cdot 29=\SI{3}{\gram}\]
 	
 \end{Solution OS}
 \begin{Solution OS}{32}