A monoatomic gas (gamma = 5/3) is suddenly co | vedclass

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(D) For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $PV^\gamma = 	ext{constant}$.Let the initial pressure be $P

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$32$ times its initial pressure

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(D) For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $PV^\gamma = 	ext{constant}$.Let the initial pressure be $P_1$ and initial volume be $V_1$.Let the final pressure be $P_2$ and final volume be $V_2 = V_1/8$.Using the adiabatic relation: $P_1 V_1^\gamma = P_2 V_2^\gamma$.$P_2 = P_1 (V_1 / V_2)^\gamma$.Substituting the values: $P_2 = P_1 (V_1 / (V_1/8))^{5/3}$.$P_2 = P_1 (8)^{5/3}$.$P_2 = P_1 (2^3)^{5/3} = P_1 (2^5) = 32 P_1$.Therefore,the pressure becomes $32$ times its initial pressure.

$A$ monoatomic gas $(\gamma = 5/3)$ is suddenly compressed to $1/8$ of its original volume adiabatically. The pressure of the gas will change to:

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