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(D) For a sudden compression, the process is adiabatic.For an adiabatic process, the relationship between temperature $T$ and volume $V$ is given by $

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$75$

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(D) For a sudden compression, the process is adiabatic.For an adiabatic process, the relationship between temperature $T$ and volume $V$ is given by $TV^{\gamma-1} = 	ext{constant}$.Here, $\gamma = 1.5$.Let the initial state be $(T_1, V_1)$ and the final state be $(T_2, V_2)$.Given $T_2 = 2T_1$ and $\gamma = 1.5$.Using the relation $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$, we get:$T_1 V_1^{1.5-1} = 2T_1 V_2^{1.5-1}$$V_1^{0.5} = 2 V_2^{0.5}$Squaring both sides: $V_1 = 4 V_2$, which implies $V_2 = \frac{V_1}{4} = 0.25 V_1$.The decrease in volume is $\Delta V = V_1 - V_2 = V_1 - 0.25 V_1 = 0.75 V_1$.The percentage decrease is $\frac{\Delta V}{V_1} 	imes 100 = 0.75 	imes 100 = 75\%$.

$A$ gas is suddenly compressed such that its absolute temperature is doubled. If the ratio of the specific heat capacities of the gas is $1.5$, then the percentage decrease in the volume of the gas is

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