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

Options

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

Answer

B

Explanation

`dU=dq+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`
`therefore" "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)`