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Question:

The equation of state for a gas is given by PV=nRT+αV, where n is the number of moles and α is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are T₀ and P₀ respectively. The work done by the gas when its temperature doubles isobarically will be

PoToRPo+α

PoToRln2

PoToRPo−α

PoToR

Solution:

Isobaric process means pressure will be constant. For one mole gas, n=1
If Vᵢ is the initial volume, P₀Vᵢ=RT₀+αVᵢ, Vᵢ=RT₀/(P₀−α)
If Vf is the final volume, P₀Vf=R⋅2T₀+αVf, Vf=2RT₀/(P₀−α)
The work done = ∫VfVi P₀dV = P₀[Vf−Vᵢ] = P₀(2RT₀/(P₀−α) − RT₀/(P₀−α)) = P₀RT₀/(P₀−α)