Q 11-11-176JEE MainJEE Main 2025 (8 Apr, Shift 2)Easy
A monoatomic gas having $\gamma = \dfrac53$ is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\dfrac18\right)^{\text{th}}$ of its initial volume. The ratio of final pressure to initial pressure is: ($\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume)
Answer: (C) $32$
Sudden compression in an insulated container is adiabatic: $PV^\gamma = \text{constant}$.
$$\frac{P_f}{P_i} = \left(\frac{V_i}{V_f}\right)^\gamma = 8^{5/3} = 2^5 = 32$$
Solution by Sreeraj P, M.Sc Physics