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=CV (4.23)
(
∂H
∂S
)
P=T (4.24)
(
∂H
∂P
)
S=V (4.25)
(
∂H
∂T
)
P=CP (4.26)
The Joule-Kelvin effect
ΔT=[
T
(∂V
∂T)
P−V
]
ΔP
CP
(4.27)
Black body radiation
Pradiatio=u
3(4.28)
whereuis the radiation density
Wein’s displacement law
λmT= 0 .29 cm - K (4.29)Planck’s radiation law
uνdν=8 πhν^3 dν
c^3 (ehν/kT−1)(4.30)
uλdλ=8 πhc
λ^5.
1
(ehc/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)