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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
`C_(m) = (dq)/(dT)= (dU)/(dT) - (dW)/(dT), C_(V) + P (dV)/(dT)`
`PV = RT, PV^(a) = K rArr (K)/(V^(n)).V = RT`
`KV^(n-1)= RT`,
`K(1-n). V^(-n) .(dV)/(dT) = R, (dV)/(dT) = (R )/((1-n))P`
`rArr C_(m) =C_(v) + P.(R )/((1-n)P) = C_(V) + (R )/(1-n)`
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