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For polytropic process PV^(n) = constant...

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

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))`

Text Solution

Verified by Experts

The correct Answer is:
B
`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)`
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