MHTCET 11 Apr 2026 Shift 2 Paper

Concept:For an ideal gas undergoing an adiabatic change, the pressure and temperature are related as $P \propto T^{\frac{\gamma}{\gamma - 1}}$Here, $\gamma$ is the ratio of heat capacities of the gas.Explanation:Start with the adiabatic relation: $P V^{\gamma} = \text{constant}$From the ideal gas equation, $V = \frac{nRT}{P}$Substitute this value of $V$ into the adiabatic relation.$P \left(\frac{nRT}{P}\right)^{\gamma} = \text{constant}$Since $nR$ is constant, rearrange to get $T^{\gamma} P^{1-\gamma} = \text{constant}$This implies $P \propto T^{\frac{\gamma}{\gamma - 1}}$A rigid diatomic gas has 5 degrees of freedom.So $C_V = \frac{5}{2}R$ and $C_P = \frac{7}{2}R$Thus $\gamma = \frac{C_P}{C_V} = \frac{7}{5}$Then $x = \frac{\gamma}{\gamma - 1} = \frac{7/5}{7/5 - 1} = \frac{7/5}{2/5} = 3.5$Answer:The value of $x$ is $3.5$Therefore, the correct option is Option C: 3.5