An ideal gas is made to undergo a termodynamic process given by `V prop T^(2)` , find the molar heat capacity of the gas for the above process.

Options

A. `(R)/((gamma-1))`
B. `(gammaR)/((gamma-1))`
C. `((2gamma-1)/(gamma-1))R`
D. `((2gamma-1)/(gamma+1))R`

Answer

C

Explanation

Given: `VpropT^(2)`
`V=KT^(2)` where `k` is constant.
Differentating both sides, of the above equation, we have
`dV=2kTdT or P=(nR)/(kT) dW=PdV`
`=(nR)/(kT)2kTdT=2nRdT(dW)/(ndT)=2R`
The molar heat capacity of the gas for the process will be
`C=C_(v)+W=(R)/(gamma-1)+2R=((2gamma-1)/(gamma-1))R`