The molar specific heats of an ideal gas at constant pressure and volume are denotes by `C_(P)` and `C_(upsilon)` respectively. If `gamma = (C_(P))/(C_(upsilon))` and `R` is the universal gas constant, then `C_(upsilon)` is equal to

Options

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

Answer

B

Explanation

`C_(p)-C_(v)=R`
`rArr(C_(p))/(C_(v))-(C_(v))/(C_(v))=(R)/(C_(v))`
`gamma-1=(R)/(C_(v))`
`therefore C_(v)=(R)/(gamma-1)`