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Question

# The temperature of n moles of an ideal gas is increased from T to 4T through a process for which pressure p=aT−1 where a is a constant . Then , the work done by the gas is ( R is universal gas constant)

A
nRT
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B
4nRT
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C
2nRT
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D
6nRT
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Solution

## The correct option is D 6nRTChange in temperature=ΔT=4T−T=3TFor given process, pT=a=constantApplying ideal gas equation, p2V=constant⇒pV1/2=constantSo process is polytropic , i.e. of the form pVx=constant with x=1/2Now molar heat capacity=C=R1−x+Cv, where Cv= molar heat capacity at constant volume⇒C=2R+CvHence heat absorbed=ΔQ=nCΔT=ΔU+ΔW=nCvΔT+ΔW⇒ work done = ΔW=nCΔT−nCvΔT=2nRΔT=6nRT

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