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