PHQ812 Physique Statistique

G
G=H−T S
H=U+pV
S=−∂G
∂T p
V=∂G
∂p T
G=U−T S +pV
dG= dU−TdS−SdT+pdV+Vdp
= TdS−
HH
H
pdV+µdN− TdS−SdT+HH
H
pdV+Vdp
N= cte
=−SdT+Vdp
dG=∂G
∂T p
dT+∂G
∂p T
dp
Cp=∂H
∂T p
Cp=−T∂2G
∂T 2p
dH=TdS+Vdp+µdN
G=H−T S
G
T=H T
−S
dG
T= dH T−dS
=dH
T+Hd1 T
−dS

N= cte
= dS+V
Tdp+Hd1 T
− dS
H=dG
T
d1
T
=1
d1
TdG
T+G
d1
T
=dG
T
1
−
dT
T2
+G
=−TdG
dT+G
Cp=
∂G
∂T
−
∂G
∂T
−T∂2G
∂T 2
=−T∂2G
∂T 2p
(a)
(b)
M
N
T
p
dp
dT
tangente
(p, T )
GA(p, T ) = GB(p, T )
G(a) (b)
dGA(p, T )− dGB(p, T ) = −(SA−SB) dT+ (VA−VB) dp
(SA−SB) dT= (VA−VB) dp
dp
dT=SA−SB VA−VB
dp
dT=∆S ∆V

∆S=Q/
T
L=Q
dp
dT=L T∆V
L=T∆Vdp
dT
η
ΓaaΓbb
ΓaΓb
ΓaΓb
η
T
η
T
c
T
η
T
c
η(T)
Tc
T Tc