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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(γ−1) B Work done by the gas is − 15V20α2P=αV PV−1=α We know for polytropic process PVx=constant ∴x=−1 We know C=Cv−Rx−1 C=Cv+R2 C=Rγ−1 +R2 C=R(γ+1)2(γ−1) dW=−PdV dW=−αVdV On integrating above equation W=−α[(4V0)22−V202] W=−α2[16V20−V20] W=−15V20α2

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