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Question

A diatomic ideal gas is heated at constant volume until its pressure becomes three times. It is again heated at constant pressure until its volume is doubled. Find the molar heat capacity for the whole process.

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Solution

Let the pressure, temperature and volume of the gas at A be P,T and V respectively.
For diatomic gas, CV=52R and CP=72R
Process AB : Isochoric Process PATA=PBTB
PT=3PTB TB=3T
Heat supplied at constant volume QV=ΔU=nCV(TBTA)
QV=52nR(2T) ...............(1)

Process BC : Isobaric Process VBTB=VCTC
V3T=2VTC TC=6T
Heat supplied at constant pressure QP=nCP(TCTB)
QP=72nR(3T) ...............(2)
Let the molar heat capacity for the whole process be C
QTotal=QV+QP
OR nC(TCTA)=QV+QP

OR nC(5T)= 312nRT C=3.1R

515393_214524_ans.png

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