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Question

If the ratio of specific heat of a gas at constant pressure to that at constant volume is γ, the change in internal energy of a mass of gas, when the volume changes from V to 2V under constant pressure P, is

A
R(γ1)
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B
pV
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C
pVγ1
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D
γpVγ1
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Solution

The correct option is C pVγ1
we know, at constant pressure change in internal energy is given as:
U=nCvT

Now CpCv=γ and CpCv=R
so, 1+RCv=γ
Cv=(Rγ1)

putting value of Cv :
U=nCvT=n(Rγ1)Tusing PV=nRT under constant P,U=PV(γ1)=P(2VV)γ1=PV(γ1)

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