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 [6]
The mean thermal velocity is
\[\overline c=\sqrt{\frac{8\cdot R\cdot T}{\pi\cdot M}}\quad\mbox{oder}\quad \overline c=\sqrt{\frac{8\cdot k\cdot T}{\pi\cdot m}}\]
Formula 1-10: Mean speed [7]
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 [8]
