Cours de thermodynamique de L2

ELEMENTS DE THERMODYNAMIQUE ET THERMIQUE
!"
#$%
Université Paris VI – Licence de mécanique – Module LA200 - Frédéric Doumenc – 2008/2009&

Table des matières
Bibliographie.................................................................................4
A – Systèmes thermodynamiques................................................5
'()*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+
&"), - $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+
. -)/ -$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$0
123,3 - $$$$$$$$$$$$$$$$$$$$0
a) Distinction entre travail et chaleur...............................................................................................7
b) Quelques définitions supplémentaires...........................................................................................8
%2*4 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
a) État stationnaire...........................................................................................................................9
b) État d'équilibre thermodynamique..............................................................................................10
c) Transformation réversible...........................................................................................................12
d) Différents types de transformations............................................................................................12
+#4*,$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&1
a) Définition et classification..........................................................................................................13
b) La pression d'un fluide................................................................................................................13
c) La température............................................................................................................................14
'2,$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&0
&")$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&0
))*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&0
12,,356)$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&0
a) Définition d'un gaz parfait..........................................................................................................17
b) Loi des gaz parfaits.....................................................................................................................18
%75*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&
a) Développements du viriel............................................................................................................21
b) Équation de van der Waals.........................................................................................................21
+2,,*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&
82,,**$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
02,,*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%
'*3 -$$$$$$$$$$$$$$$$$$$$$$$$$$$$+
&*966$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+
*96)*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$8
1**966:**6)$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1
%*,*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1
+;3**,<6*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1&
B – Premier et deuxième principes appliqués à un système
fermé. ...........................................................................................32
=66* $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1
&;66**,3$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1
2666* $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$11
1*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1%
a) Définition des coefficients calorimétriques.................................................................................34
b) Relations entre les coefficients calorimétriques et les coefficients thermoélastiques..................35
c) Variation d'énergie interne d'un système simple.........................................................................36
%66*>)*64*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$10
+66*<356)$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$10
a) Détente de Joule et Gay-Lussac..................................................................................................37
b) Coefficients calorimétriques d'un gaz parfait.............................................................................38
Université Paris VI – Licence de mécanique – Module LA200 - Frédéric Doumenc – 2008/2009

c) Transformation adiabatique réversible d'un gaz parfait.............................................................39
d) Transformation polytropique réversible d'un gaz parfait............................................................39
="<-66* $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%
&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%
2-66* $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%
1*,6$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%&
%66*-66> * $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%1
+#,6, -6*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%+
a) Cas général (fluide quelconque). ...............................................................................................45
b) Cas d'un fluide incompressible. .................................................................................................46
c) Cas d'un gaz parfait....................................................................................................................46
8)44*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%0
=! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%
&2)*744$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%
)3$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%
166*<))*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%
a) Fluide quelconque.......................................................................................................................49
b) Retour sur les gaz parfaits..........................................................................................................50
c) Liquide réel.................................................................................................................................50
%;*) $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+&
C – Changement de phase d'un corps pur................................53
2<6*36$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+1
&36$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+1
a) Définition....................................................................................................................................53
b) Exemples.....................................................................................................................................53
c) Interprétation qualitative du changement de phase.....................................................................54
2*4*6$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$++
a) Isothermes d'Andrews.................................................................................................................55
b) Règle des moments......................................................................................................................57
c) Pression de vapeur saturante......................................................................................................58
1*4$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+
%;-3**$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+
2*6 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$8&
&**36$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$8&
2*46$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$8
124**,*6 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$81
%66**,*6 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$8%
a) Équilibre solide-vapeur..............................................................................................................64
b) Équilibre solide-liquide..............................................................................................................65
c) Équilibre liquide-vapeur.............................................................................................................66
+&--6-$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$80
D – Machines thermiques...........................................................69
"$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$8
"$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$8
&63*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$8
 *$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$0
1) *? *;@A$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$01
%;6$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$08
"6$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$08
&))6)$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$08
>? *B*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$00
1>)*4*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$00
Université Paris VI – Licence de mécanique – Module LA200 - Frédéric Doumenc – 2008/20091

=4*36
Thermodynamique, fondements et applications -José-Philippe Pérez/$"/
&/+%63$
Thermodynamique, bases et applications -Jean-Noël FoussardEdmond Julien/
$"/+/163$
Thermodynamique -Michel Hulin/Nicole Hulin adeleine Veyssié/$"/
&%/1063$
Advanced engineering thermodynamics  Adrian Bejan, $B$C* /(DE@
&0/+63$
Thermodynamique et énergétique'Lucien Borel/$6*  
/&&/863$
Université Paris VI – Licence de mécanique – Module LA200 - Frédéric Doumenc – 2008/2009%

'. - $
'()*$
I-1 Définition d'un système thermodynamique.
 64F66* *,6-G*/
6/$$$H6*<6-G*/6/$$$H/<
6    6$  I**      JJ- -*    *    6  *
)64*,-**$I
-*6666* /**6*6*
*,/6**6 ***
*F:*G*3/6/$$H/,6*)
G/4*3/$$$H$
Remarque : le mot « thermodynamique » est écrit en chinois sur la première page de ce document,avec deux jeux de
pictogrammes différents. Les pictogrammes traditionnels :
et les pictogrammes anciens :
Ces derniers, moins stylisés, sont plus faciles à interpréter. Celui de gauche, sur lequel on reconnait une coupe pleine
d'eau au-dessus d'une flamme, signifie « chaleur ». Celui de droite, représentant un lapin, signifie « mouvement ». La
réunion des deux signifie « thermodynamique », ce qui est, on le voit, une application directe de la définition donnée ci-
dessus.
 ,>*6 systèmes thermodynamiques$
   -         ,  -  3  4    6*  G/
**//$$$H/3**,4,3GNa=6,02.1023H$* -
6*K>*,**663G*/6/
6//$$$H/* 66
6** -$366* variables
d'état$
Remarque 1 : 4&*,>*6>*64/
&&8**/F)6**,666G,>H$
Remarque 2 : **6**4*,$6
) *   )9 6$  I /   *,* 6 > *   
LM     L)M 6 6  *  /          *,))   
)$
Université Paris VI – Licence de mécanique – Module LA200 - Frédéric Doumenc – 2008/2009+