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(γ−1)
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B
pV
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C
pVγ−1
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D
γpVγ−1
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Solution
The correct option is CpVγ−1 we know, at constant pressure change in internal energy is given as: △U=nCv△T
Now CpCv=γ and Cp−Cv=R
so, 1+RCv=γ Cv=(Rγ−1)
putting value of Cv : △U=nCv△T=n(Rγ−1)△TusingP△V=nR△Tunder constant P,⇒△U=P△V(γ−1)=P(2V−V)γ−1=PV(γ−1)