The molar specific heat of an ideal gas at constant pressure and constant volume is `C_(p)` and `C_(v)` respectively. If R is the universal gas constant and the ratio of `C_(p)` to `C_(v)` is `gamma`, then `C_(v)`.

Options

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

Answer

D

Explanation

According to Mayer formula,
`C_(p)-C_(v)=R` . . .(i)
where, `C_(p)` = specific heat at constant pressure,
`C_(v)` = specific heat at constant volume
and R = gas constant
Now , `gamma=(C_(p))/(C_(v))`
`rArr" "C_(p)=gammaC_(v)` . . . .(ii)
From Eqs. (i) and (ii), we get
`rArr" "gammaC_(v)-C_(v)=RrArrC_(v)(gamma-1)=R`
`rArr" "C_(v)=(R)/(gamma-1)`