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Question

The molar heat capacity C for an ideal gas going through a process is given by C=aT, where 'a' is a constant. If γ=CPCV, the work done by one mole of gas during heating from T0 and ηT0 will be:

A
a ln(η)
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B
1a ln(η)
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C
a ln(η)(η1γ1)RT0
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D
a ln(η)(γ1)RT0
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Solution

The correct option is C a ln(η)(η1γ1)RT0
Q=w+Au
w=Q-Au Q=cdt (for 1 mole)
Q=T1T0[atdT]=alnn
Au=ηRγ1At (here n=1mole)
Au=Rγ1T0(γ1)
w=aln(γ)(η1γ1)RT0

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