An ideal gas has an adiabatic exponent `gamma`. In some process its molar heat capacity varies as `C = alpha//T`,where `alpha` is a constant Find :
(a) the work performed by one mole of the gas during its heating from the temperature `T_0` to the temperature `eta` times higher ,
(b) the equation of the process in the variables `p, V`.

Options

A. `a ln eta`
B. `(1)/(aln eta)`
C. `aln eta -((eta-1)/(gamma-1))RT_(0)`
D. `alneta -(gamma-1)RT_(0)`

Answer

C

Explanation

`dW = dQ - dU , dW = nCdT - nC_(v)dT`
`W = int CdT - int C_(v)dT , = int (a)/(T)dT - C_(v) DeltaT`
` = a In ((etaT_(0))/(T_(0))) - ((T_(2)-T_(1))R)/(gamma-1)`
`W = a In eta (-(eta-1)T_(0)R)/(gamma-1)`