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Question

# One mole of an ideal gas with heat capacity at constant pressure Cp undergoes the process T=T0+αV where T0 and α are constants. If its volume increases from V1 to V2, the amount of heat transfered to the gas is

A
CpRT0lnV2V1
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B
αCp(V2V1)RT0lnV2V1
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C
αCp(V2V1)+RT0lnV2V1
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D
RT0V2V1αCp(V2V1)
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Solution

## The correct option is C αCp(V2−V1)+RT0lnV2V1From ideal gas equation, p=RTV=R(T0+αV)V Work done by the gas W=∫V2V1p×dV=∫V2V1R(T0+αV)V×dV =RT0lnV2V1+Rα(V2−V1) Change in internal energy ΔU=nCVΔT =(Cp−R)[(T0+αV2)−(T0+αV1)] =α(Cp−R)(V2−V1) Hence, amount of heat transferred Q=W+ΔU =RT0lnV2V1+αCp(V2−V1)

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