Consider one mole of an ideal gas whose volume changes with temeperature as `V=(alpha)/(T)`, where `alpha` is a constant. Heat is supplied to the gas to raise its temperature by `DeltaT`. If `gamma` adiabatic constant then choose the correct options.

Options

A. The work done in the process is `RDeltaT`
B. The work done in the process is `-RDeltaT`
C. Change in internal energy of gas is `(RDeltaT)/(gamma-1)`
D. Change in internal energy of gas is `-(RDeltaT)/(gamma-1)`

Answer

B, C

Explanation

`PV=nR((alpha)/(V))`
`P=(Ralpha)/(V^(2))`
`W=intPdv=int_(V_(1))^(V_(2))(Ralpha)/(V^(2))dv`
`=-Ralpha((1)/(V^(2))-(1)/(V_(1)))=-R(T_(2)-T_(1))=-RDeltaT`
`DeltaU=(nR(T_(2)-T_(1)))/(gamma-1)=(RDeltaT)/(gamma-1)`