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(B) For a sudden compression,the process is adiabatic. The adiabatic equation is $P V^{\gamma} = 	ext{constant}$.Let the initial pressure be $P_1 = P

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More than $P$

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(B) For a sudden compression,the process is adiabatic. The adiabatic equation is $P V^{\gamma} = 	ext{constant}$.Let the initial pressure be $P_1 = P$ and initial volume be $V_1 = V$.The final volume is $V_2 = V/4$.Using the relation $\frac{P_2}{P_1} = \left( \frac{V_1}{V_2} ight)^{\gamma}$,we get:$\frac{P_2}{P} = \left( \frac{V}{V/4} ight)^{\gamma} = 4^{\gamma}$.Therefore,$P_2 = 4^{\gamma} P$.Since the adiabatic index $\gamma$ for any gas is greater than $1$ (e.g.,$1.4$ for diatomic,$1.67$ for monatomic),$4^{\gamma}$ will be greater than $4$.Thus,$P_2 > 4P$,which means the final pressure is much more than $P$.

$A$ gas is suddenly compressed to one fourth of its original volume. What will be its final pressure,if its initial pressure is $P$?

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