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(C) For a sudden compression,the process is adiabatic.For an adiabatic process,the relation between pressure and volume is given by $P V^{\gamma} =

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$8$

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(C) For a sudden compression,the process is adiabatic.For an adiabatic process,the relation between pressure and volume is given by $P V^{\gamma} = 	ext{constant}$.Thus,$P_1 V_1^{\gamma} = P_2 V_2^{\gamma}$,which implies $\frac{P_2}{P_1} = \left( \frac{V_1}{V_2} ight)^{\gamma}$.Given: Initial pressure $P_1 = 1 	ext{ atm}$ (at $NTP$),final volume $V_2 = \frac{V_1}{4}$,and $\gamma = \frac{3}{2}$.Substituting these values: $\frac{P_2}{1} = \left( \frac{V_1}{V_1/4} ight)^{3/2} = (4)^{3/2}$.Calculating the value: $(4)^{3/2} = (2^2)^{3/2} = 2^3 = 8$.Therefore,the final pressure $P_2 = 8 	ext{ atm}$.

$A$ gas at $NTP$ is suddenly compressed to one-fourth of its original volume. If $\gamma$ is supposed to be $\frac{3}{2}$,then the final pressure is........ atmosphere.

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