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

We have `C_(p)-C_(v)=R`...(i)
and `(C_p)/(C_v) = gamma` ...(ii)
From (i) and (ii), we get `C_(v) = (R)/((gamma-1))`.