The molar specific heat of an ideal gas at constant pressure and constant volume is `C_(p)` and `C_(v)` respectively. If R is the universal gas constant and the ratio of `C_(p)` to `C_(v)` is `gamma`, then `C_(v)`.

Options

A. `(1-gamma)/(1+gamma)`
B. `(1+gamma)/(1-gamma)`
C. `(gamma-1)/(R )`
D. `(R )/(gamma-1)`

Answer

D

Explanation

`C_(P) -C_(V) =R, (C_(P))/(C_(V))=gamma implies C_(P)=gammaC_(V)`
`gamma C_(V) -C_(V)=R`
`C_(V) =(R)/((gamma-1))`