Specific heat of constatn pressure of a diatomic gas having molar mass `M` is approximately equal to

Options

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

Explanation

We know that: `C_(P) - C_(V) = R`
`C_(P) - C_(V) = (R )/(M) ..(i)`
`(C_(P))/(C_(V)) = gamma …(ii)`
Substituting equation (ii) in (i), we get
`C_(P) - (C_(P))/(gamma) = (R )/(M)`
`C_(P) ((gamma-1))/(gamma) = (R )/(M)`
`C_(P) = (R gamma)/((gamma - 1)M)`