In an adiabatic change, the pressure and temperature of a rigid diatomic ideal gas are related as $P

Question

In an adiabatic change, the pressure and temperature of a rigid diatomic ideal gas are related as $P \propto T^C$. The value of $C$ equals

Professor PC Thomas Classes · Answer

(c) : For an adiabatic process, $P^{1-\gamma} T^\gamma = 	ext{constant}$. This can be rewritten as $P \propto T^{\frac{\gamma}{\gamma-1}}$. For a rigid diatomic gas, the specific heat ratio is $\gamma = 7/5$. Thus, the exponent $C = \frac{7/5}{(7/5) - 1} = \frac{7/5}{2/5} = \frac{7}{2}$.