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
νrms=√
3 P/ρ (4.2)
νrms=√
3 kT/m=√
3 RT/M (4.3)
Average speed
<ν>=√
8 kT
πm=
√
8 RT
πM(4.4)
Most probable speed
νp=√
2 kT
m=
√
2 RT
M
(4.5)
wheremis the mass of the molecule,Mis the molar weight,ρthe 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.
νp:<ν>:νrms::√
2:
√
8 /π:√
3 (4.6)
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