Q 11-11-068JEE MainJEE Main 2024 (27 Jan, Shift 2)Medium
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\dfrac{C_p}{C_v}$ for the gas is:
Answer: (B) $\dfrac32$
For an adiabatic process $P^{1-\gamma}T^\gamma = \text{constant}$, so
$$P \propto T^{\frac{\gamma}{\gamma-1}}$$
Given $P \propto T^3$: $\dfrac{\gamma}{\gamma-1} = 3 \Rightarrow \gamma = \dfrac32$.
Solution by Sreeraj P, M.Sc Physics