From 93fffba3d005a75702e0930c10f38e0bb6ce1b37 Mon Sep 17 00:00:00 2001 From: guyotv 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 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ziwZNiVyZaidl@np!6Pdf)DTz&MmU4=02TjXGP++?CX?UuU~4o$XryuRK}rkh?N$e;#tF`Kn{Xi%j^VY z6V~cs2{h8M zEQ1iX$~b)2R4*;j-y$RWIOxhbSr~8C%)&5@5MrWPpVRhZ&}`R7;J_0*_80b*2pvWJ zdHtk3M|2%K@ExU&d^?+d|KEs_8g_OX(<1z*M$DQzK2QVZgnSt%)i5=6bnmb6e?rNB AmH+?% 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}