MHTCET 11 May 2024 Shift 2 Paper

Concept:For an ideal gas, the same heat produces different temperature rises depending on whether the process occurs at constant pressure or constant volume.Explanation:In cylinder A, the piston is free to move, so the gas is heated at constant pressure.In cylinder B, the piston is held fixed, so the gas is heated at constant volume.The same amount of heat is supplied to both cylinders, hence $Q_A = Q_B$.For constant pressure heating, $Q_A = n C_p \, dT_A$.For constant volume heating, $Q_B = n C_v \, dT_B$.Equating the two expressions gives $n C_p \, dT_A = n C_v \, dT_B$.Cancelling $n$ from both sides, $C_p \, dT_A = C_v \, dT_B$.Rearranging, $dT_B = \frac{C_p}{C_v} dT_A = \gamma \, dT_A$.Answer:The rise in temperature of the gas in cylinder B is $\gamma \, dT_A$.Therefore, the correct option is C.