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

Answer

B

Explanation

In the given process, `pV^(n)= constant`
`:.` Molar heat capacity,
`C=R/(gamma-1)+R/(1-n)= C_(V)+R/(1-n)`
or `C-C_(V)= R/(1-n)`
or `1-n= R/(C-C_(V))=(C_(p)-C_(V))/(C-C_(V))`
`:. N =1-(C_(p)-C_(V))/(C-C_(V))`
`n=(C-C_(V)-C_(p)+C_(V))/(C-C_(V))= (C-C_(p))/(C-C_(V))`
Chouce (b) is correct.