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(A) For an adiabatic process,the relation between temperature and volume is given by $T V^{\gamma - 1} = 	ext{constant}$.Given: Initial volume $V_1 =

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$273$

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(A) For an adiabatic process,the relation between temperature and volume is given by $T V^{\gamma - 1} = 	ext{constant}$.Given: Initial volume $V_1 = V$,final volume $V_2 = V/4$,initial temperature $T_1 = 273 \, K$,and $\gamma = 1.5$.Using the adiabatic relation: $T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1}$.Substituting the values: $T_2 = T_1 \left( \frac{V_1}{V_2} ight)^{\gamma - 1} = T_1 \left( \frac{V}{V/4} ight)^{1.5 - 1} = T_1 (4)^{0.5} = T_1 	imes 2$.Thus,$T_2 = 2 	imes 273 = 546 \, K$.The increase in temperature is $\Delta T = T_2 - T_1 = 546 - 273 = 273 \, K$.

$A$ gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$

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