Blundell Thermal Physics · Problem 32.2

Shock waves

Physics — Statistical Mechanics · rankine-hugoniot-temperature-ratio

Problem

Use eqn 32.24 to show that

\frac{T_2}{T_1} = \frac{[2\gamma M_1^2 - (\gamma - 1)][2 + (\gamma - 1)M_1^2]}{(\gamma + 1)^2 M_1^2}, \tag{32.29}

and hence for

M_1 \gg 1

we have that

\frac{T_2}{T_1} \to \frac{2\gamma(\gamma - 1)M_1^2}{(\gamma + 1)^2}. \tag{32.30}