For polytropic process `PV^(n)` = constant, molar heat capacity `(C_(m))` of an ideal gas is given by:

Options

A. `C_(v,m) +(R)/((n-1))`
B. `C_(v,m) +(R)/((1-n))`
C. `C_(v, m) +R`
D. `C_(p, m) + (R)/((n-1))`

Answer

B

Explanation

`dU = dp + dw, nC_(v,m).dT = nC_(m)dT -P.dV`,
`C_(m) = C_(v, m) + (P.dV)/(n.dT)` ....(1)
`PV^(n) = K` and `PV = nRT :. KV^(1-n) = nRT`
`K(1-n)V^(-n).dV = nRdT`
`(dV)/(dT) = (nR)/(K(1-n)V^(-n))` .....(2),
From Eqs (1) and (2) `C_(m) = C_(v, m) + (R)/((1-n))`