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Question:

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PVn=constant, then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively).

n=CP/CV

n=(C-CP)/(C-CV)

n=(CP-C)/(CP-CV)

n=(C-CV)/(C-CP)

Solution:

For a polytropic process given as PVn=constant
The specific heat is given as, C=Rγ-n+R1-n
C=Cvγ-n1-n
C=Cp-Cvn1-n
∴n=C-CpC-Cv