An ideal gas under goes 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 `PV^n=constant`, then n is given by (Here `C_P and C_V` are molar specific heat at constant pressure and constant volume, respectively):

Options

A. `n = (C- C_(V))/(C - C_(P))`
B. `n= (C_(P))/(C_(V))`
C. `n = (C- C_(P))/(C - C_(V))`
D. `n = (C_(P)- C)/(C - C_(V))`

Answer

C

Explanation

Specific heat `C = (R)/(1-n) + C_(V)` for polytropic process `therefore (R)/(1-n) + C_(V) = C`
`(R)/(1-n) = C -C_(V) implies (R)/(C - C_(V)) = 1-n` (Where `R = C_(P) -C_(V)`)
`implies n = (C- C_(P))/(C- C_(V))`