Given that `C_(p)-C_(V)=R and gamma=C_(p)//C_(V)`, where `C_p`=Molar specific heat at constant pressure, `C_(V)`=molar specific heat at constant volume. Then `C_(V)`=

Options

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

Answer

B

Explanation

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