For an ideal gas `(C_(p,m))/(C_(v,m))=gamma`. The molecular mass of the gas is M, its specific heat capacity at constant volume is :

Options

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

Answer

A

Explanation

`because(C_(p,m))/(C_(V,m))=gamma andC_(P,m)-C_(V,m)=R`
`thereforeC_(V,m)=(R)/(gamma-1)`
`C_(V,m)=(C_(V))/(n)and C_(V)=m.c_(V)`
`therefore(R)/(gamma-1)=(m.c_(V))/(m)xxM`
`therefore" "C_(V)=(R)/((gamma-1)M)`