 # 1.2.4 Thermal velocity

Gas molecules enclosed in a vessel collide entirely randomly with each other. Energy and impulses are transmitted in the process. As a result of this transmission, a distribution of velocity and/or kinetic energy occurs. The velocity distribution corresponds to a bell curve (Maxwell-Boltzmann distribution) having its peak at the most probable velocity.

$c_w=\sqrt{\frac{2\cdot R\cdot T}M}\quad\mbox{oder}\quad c_w=\sqrt{\frac{2\cdot k\cdot T}m}$

Formula 1-9: Most probable speed 

The mean thermal velocity is

$c_w=\sqrt{\frac{2\cdot R\cdot T}M}\quad\mbox{oder}\quad \overline c=\sqrt{\frac{8\cdot k\cdot T}{\pi\cdot m}}$

Formula 1-10: Mean speed 

The following table shows the mean thermal velocity for selected gases at a temperature of 20°C.

Gas Chemical Symbol Molar Mass
[g mol-1]
Mean Velocity
[m s-1]
Mach Number
Hydrogen H2 2 1,754 5.3
Helium He 4 1,245 3.7
Water vapor H2O 18 585 1.8
Nitrogen N2 28 470 1.4
Air 29 464 1.4
Argon Ar 40 394 1.2
Carbon dioxide CO2 44 375 1.1

Table 1.4: Molar masses and mean thermal velocities of various gases