A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original vol

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11.Thermodynamics

hard

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 $.....P$

A

$1$

B

$8$

C

$32$

D

$64$

(JEE MAIN-2022)

Solution

Constant entropy means process is adiabatic

$PV ^{\gamma}=$ constant

$V _{2}=\frac{ V _{1}}{8}$

$P _{1} V _{1}^{\gamma}= P _{2} V _{2}^{\gamma}$

$P _{1} V _{1}^{\gamma}= P _{2}\left(\frac{ V _{1}}{8}\right)^{5 / 3}$

$P _{1} V _{1}^{5 / 3}=\frac{ P _{2} V _{1}^{5 / 3}}{32}$

$P _{2}=32 P _{1}$

Standard 11

Physics

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