A monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be $.....P$
JEE MAIN 2022, Diffcult
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Constant entropy means process is adiabatic
$PV ^{\gamma}=$ constant
$V _{2}=\frac{ V _{1}}{8}$
$P _{1} V _{1}^{\gamma}= P _{2} V _{2}^{\gamma}$
$P _{1} V _{1}^{\gamma}= P _{2}\left(\frac{ V _{1}}{8}\right)^{5 / 3}$
$P _{1} V _{1}^{5 / 3}=\frac{ P _{2} V _{1}^{5 / 3}}{32}$
$P _{2}=32 P _{1}$
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