The molar heat capacity of a perfect gas at constant volume is `C_v`. The gas is subjected to a process `T =T_0e^(AV)`, Where `T_0` and A are constant. Calculate the molar heat capacity of the gas a function of its volume

Answer

`C_v+(R)/(AV)`

Explanation

`dW = PdV`
But,` T=T_(0)e^(AV)`
`therefore dW =(PdT)/(AT_(0)e^(AV))=(PdT)/(AT)=(RTdT)/(ATV)=(RdT)/(AV)`
Also, `dQ =dU + dW
`CdT = C_(v)dT+(RdT)/(AV)` therefore `C= C_(v)+(R)/(AV)`