The equation of state for a gas is given by `PV = eta RT + alpha V`, where `eta` is the number of moles and `alpha` a positive constant. The initial pressure and temperature of 1 mol of the gas contained in a cylinder is `P_(0)` and `T_(0)`, respectively. The work done by the gas when its temperature doubles isobarically will be

Options

A. `(P_(0)T_(0)R)/(P_(0) - alpha)`
B. `(P_(0)T_(0)R)/(P_(0) + alpha)`
C. `P_(0)T_(0)R In 2`
D. None of these

Answer

A

Explanation

`DeltaW = PDeltaV [PV=mu RT+alphaV]`
`P_(0)[(muRDeltaT)/(P_(0)-alpha)]=:. PDeltaT = mu RT+alphaDeltaT`
or `DeltaV = (muRDeltaT)//(P-alpha)]`
`i.e., DeltaW = (P_(0)RT_(0))/(P_(0)-alpha) [mu-1]`.