Chapter 4
Thermodynamics and Statistical Physics
4.1 Basic Concepts and Formulae
Kinetic theory of gases
Pressure
p =
1
3
ρ < ν
2
>
(4.1)
Root-mean-square velocity
ν rms =
3P/ρ
(4.2)
ν rms =
3kT /m =
3RT /M
(4.3)
Average speed
< ν >=
8kT
πm
=
8RT
π M
(4.4)
Most probable speed
ν p =
2kT
m
=
2RT
M
(4.5)
where m is the mass of the molecule, M is the molar weight, ρ the gas density,
k = 1.38 × 10
−23
/K, the Boltzmann constant, R = 8.31 J/mol-K, is the universal
gas constant, and K is the Kelvin (absolute) temperature.
ν p :< ν >: ν rms ::
√
2 :
8/π :
√
3
(4.6)
247
Thermodynamics and Statistical Physics
4.1 Basic Concepts and Formulae
Kinetic theory of gases
Pressure
p =
1
3
ρ < ν
2
>
(4.1)
Root-mean-square velocity
ν rms =
3P/ρ
(4.2)
ν rms =
3kT /m =
3RT /M
(4.3)
Average speed
< ν >=
8kT
πm
=
8RT
π M
(4.4)
Most probable speed
ν p =
2kT
m
=
2RT
M
(4.5)
where m is the mass of the molecule, M is the molar weight, ρ the gas density,
k = 1.38 × 10
−23
/K, the Boltzmann constant, R = 8.31 J/mol-K, is the universal
gas constant, and K is the Kelvin (absolute) temperature.
ν p :< ν >: ν rms ::
√
2 :
8/π :
√
3
(4.6)
247