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

Answer

A

Explanation

`(C_(p))/(C_(v))=gammarArrC_(v)=(C_(p))/(gamma)`.
But `C_(p)-C_(v)=R`
`thereforeC_(p)=R+C_(v)thereforegammaC_(v)=C_(v)+R`
`rArrC_(v)(gamma-1)=RrArrC_(v)=(R)/(gamma-1)`.