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Question

An ideal gas whose adiabatic exponent γ is expanded according to the law P=αV, where α is a constant. The initial volume of the gas is equal to V0. As a result of expansion, the volume increases 4 times. Select the correct option for above information.

A
Molar heat capacity of gas in the process is R(γ+1)2(γ1)
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B
Work done by the gas is 15V20α2
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C
Molar heat capacity of gas in the process is R(γ1)2(γ+1)
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D
Work done by the gas is + 15V20α2
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Solution

The correct options are
A Molar heat capacity of gas in the process is R(γ+1)2(γ1)
B Work done by the gas is 15V20α2
P=αV
PV1=α
We know for polytropic process
PVx=constant
x=1
We know C=CvRx1
C=Cv+R2
C=Rγ1 +R2
C=R(γ+1)2(γ1)

dW=PdV
dW=αVdV
On integrating above equation
W=α[(4V0)22V202]
W=α2[16V20V20]
W=15V20α2

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