The molar heat capacity C for an ideal gas going through a processs which is given by C=aT, where ‘a’ is a constant and T is absolute temperature. If γ=CPCV, the work done by one mole of gas during heating from temperature T0 to ηT0 through the given process will be

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1a ln η

a ln η−η−1γ−1RT0

a ln η−γ−1RT0

a ln η

answer is B.

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Detailed Solution

ΔQ=∫T0ηT0 CdT=∫T0ηT0 aTdT=a[lnηT0-lnT0] =a lnηT0T0 = alnηΔU=CvΔT=Rγ−1(η−1)T0∴ΔW=ΔQ−ΔU=aln⁡η−η−1γ−1RT0

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