Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 314 / 2 / a / Solution

For one-dimensional compressible flow, define the total energy densityThe conservative mass, momentum, and energy equations areA monatomic nonrelativistic perfect gas has $\gamma =5/3$, an ultrarelativistic gas or radiation-dominated fluid has $\gamma =4/3$, and a rotationally active diatomic gas has $\gamma =7/5$.