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)
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)
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