During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its ab

Question

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $\frac{C p}{C v}$ for the gas is

Professor PC Thomas Classes · Answer

Adiabatic relation $P \propto T^{\frac{\gamma}{\gamma-1}}$. Given $P \propto T^3$, we find $\frac{\gamma}{\gamma-1} = 3 \Rightarrow \gamma = 1.5 = \frac{3}{2}$.