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Question

An ideal monoatomic gas is enclosed in a non-conducting cylinder having a piston which can move freely. Suddenly the gas is compressed to 1/8 of its initial volume. Find the final pressure and temperature if initial pressure and temperature are P0 and T0 respectively.
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Solution

Since process is adiabatic therefore
P0V53=Pfinal(V8)53[γ=CPCV=5R2/3R2=53]
Pfinal=32P0
Since process is adiabatic therefore
T1Vγ11=T2Vγ12T0V2/30=Tfinal(V08)2/3T=4T0

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