Blundell Thermal Physics · Problem 32.4

Shock waves

Physics — Statistical Mechanics · rankine-hugoniot-diatomic-strong-shock

Problem

Air is mostly nitrogen (

\mathrm{N_2}

) and oxygen (

\mathrm{O_2}

), which are both diatomic gases and for which

\gamma = 7/5

. Show that in this case, in the limit

M_1 \gg 1

we have that

\frac{\rho_2}{\rho_1} \to 6, \qquad \frac{p_2}{p_1} \to \frac{7}{6}M_1^2, \qquad \frac{T_2}{T_1} \to \frac{7}{36}M_1^2. \tag{32.32}