250
4 Thermodynamics and Statistical Physics
Thermodynamical potentials
(i) Internal energy (U )
(ii) Free energy (F)
(iii) Gibb’s function (G)
(iv) Enthalpy (H )
H = U + PV
(4.22)
∂U
∂ T
V
= C V
(4.23)
∂ H
∂ S
P
= T
(4.24)
∂ H
∂ P
S
= V
(4.25)
∂ H
∂ T
P
= C P
(4.26)
The Joule-Kelvin effect
ΔT =
T
∂ V
∂ T
P
− V
ΔP
C P
(4.27)
Black body radiation
P radiatio =
u
3
(4.28)
where u is the radiation density
Wein’s displacement law
λ m T = 0.29 cm - K
(4.29)
Planck’s radiation law
u ν dν =
8π hν
3 dν
c 3 (e hν/kT − 1)
(4.30)
u λ dλ =
8π hc
λ 5 .
1
(e hc/λkT − 1)
(4.31)
σ =
2
15
.
π
5 k
4
h 3 c 2
(4.32)
ΔS =
ΔQ
T
(4.33)
ΔS = kln(ΔW )
(4.34)