Question

One mole of an ideal gas is expanded isothermally from (T1, P1, V1) to (T2,

P2, V2) in two stages. First stage uses constant opposing pressure P’ and

second stage uses constant opposing pressure P2. Show that the maximum

value of work produced is given by 2RT{1- square root of (P2/P1) }

and P’= Square root of (P1,P2)

Answer 1

For an irreversible process:

W = P₂(V₂ – V₁) =

= RT/V₂ (V₂ – V₁) =

= RT(1-V₁/V₂)

As P₁V₁ = P₂V₂ then:

V₁/V₂ = P₂/P₁

So W = RT(1 – P₂/P₁)