Nathalie Van d e Wiele - Physique Sup PCSI - Lycée les Eucalyptus - Nice Série d’exercices 25
4
Réponses.
Exercice 1.
1) W = R T0 ln 2 . 2) W = - R T0 ln b V
b V
i f
−
− + a ( )
V 1 V
1
f i
− .
Exercice 2.
2.a) W = 0 . 2.b) W = α P0 V0 ( T0 – T1 ) . 2.c) W = 2
V0
χT
( P1 2 – P0
2 ) .
Exercice 3.
1) W = 2
V χT
( P2 2 – P1
2 ) = 5,13.10-1 J . 2) Wqs = P1 V ln
1 2
P
P = 4,67.102 J .
Exercice 4.
W1 = 2 R TA ln 3 = 5,48.103 J ; W2 = 3
8 R TA = 6,65.103 J ; W3 = 4 R TA = 9,98.103 J .
Exercice 5.
2.a) Wa = ( k – 1 ) P0 V0 [ ( 2
1
k+ ) χT P0 - α T0 ] . 2.b) Wb = 2
1 k2 −
P0 V0 ( χT P0 - α T0 ) .
Exercice 6.
1) Qv = ( MC + MO ) [ A0 ( Tf – Ti ) – A1 ln
i f
T T - A2 (
i
f T
1 T
1 − ) = 3,72.103 J . 2)
) T T ( ) M M ( c Q
i f O C
v
v= + − = 1,33 J.K-1.g-1 .
Exercice 7.
Lf, , t = Lf, , tn + ( cl – cs ) ( t – tn ) = 2,5 + 0,05 t pour t en °C et L en cal.g-1 . Exercice 8.
1) θ = θe + ( θ0 - θe ) exp ( - c
a t ) . 2) t2 = t1
e 1
e 0
e 2
e 0
ln ln
θ
− θ
θ
− θ
θ
− θ
θ
− θ
13,5 min .
Exercice 9.
1) θ = θ1 + ( θ0 - θ1 ) exp ( - Γ
c
k t ) . 2) θ2 =
c m
c
m 1
0
+ Γ
θ + θ
Γ = 20,9 ° . 3) c = t k
Γ
1 1
ln 0
θ
− θ
θ
−
θ = 3,37 cal.°C-1.g-1 = 1,41.104 J.K-1.kg-1 .
Exercice 10.
1) Compression isotherme à 2 T0 , pression maximale atteinte 2 P0 . 3) W1 = - P0 V0 = - 2,8.103 J ; Q1 =
1
− γ
γ P0 V0 = 9,8.103 J ; W2= 2 P0 V0 ln 2 = 3,9.103 J ; Q2 = - 2 P0 V0 ln 2 = - 3,9.103 J ;
W3 = 0 et Q3 = - 1
− γ
1 P0 V0 = - 7,0.103 J . 4) ∆Ucycle = 0 .
Exercice 11.
Q = n R ( T2 – T1 )
) 1 q q
− ( ) 1
− γ (
γ
− : 1) si q > γ ou q < 1 et 2) si 1 < q < γ .
Exercice 12.
2) W = 1
− γ
1 P1 V1 ( 2( γ - 1 ) / γ − 1 ) = 54,8 J .
Nathalie Van d e Wiele - Physique Sup PCSI - Lycée les Eucalyptus - Nice Série d’exercices 25
5
Exercice 13.
2) W = 1
− γ
R [ T3 – T2 + ( γ - 1 ) ( T3 – T1 )] . 3) r = 1 - γ
1 T T
1 T T
1 2
1 3
−
− = r = 1 - γ 1 a
1 a
−
−
γ = 0,296 ≈ 30 % .
Exercice 14.
U = U0 + P V0 . Exercice 15.
∆T = -
1 1 m ,
V RT
P C 2
a = - 0,14 K .
