If ` gamma ` is the ratio of specific heats and R is the universal gas constant, then the molar specific heat at constant volume `C_V ` is given by

Options

A. `(R)/(y-1)`
B. `(YR)/(Y-1)`
C. `YR`
D. `((Y-1)R)/(Y)`

Answer

A

Explanation

`(C_p)/(C_v) = gamma rArr C_p = gamma C_(v)`
and `C_(p) = C_(v) = R rArr C_(v) = C_(p) - R`
`rArr C_(v) + R = C_(p) rArr C_(v) + R = gamma C_(v)`
`rArr C_v = (R)/(gamma - 1)`