Figure 1.

Dependence of $\overline{\chi }$ (left) and $\overline{\mu }$ (right) for diatomic (red solid line) and monatomic (black dashed line) gases on $\gamma$. The dotted line indicates the corresponding value in the classical limit. In the ultra-relativistic limit ($\gamma \to 0$), ${\overline{\chi }}_{\mathrm{ultra}}=0,{\overline{\mu }}_{\mathrm{ultra}}=2/3$ both for monatomic and diatomic gases. In the classical limit ($\gamma \to \infty$), ${\overline{\chi }}_{\mathrm{class}}=2.5,{\overline{\mu }}_{\mathrm{class}}=1$ for monatomic gas, and ${\overline{\chi }}_{\mathrm{class}}=3.5,{\overline{\mu }}_{\mathrm{class}}=1$ for diatomic gas.