If the boundary of system moves by an infinitesimal amount, the work involved is given by dw = –P ext dv

For irreversible process W = –P ext Δ V

(where Δ V = V f –V i )

For reversible process P ext = P int ± d p ≈ P int

So for reversible isothermal process

W = – nRT λ n

2 mole of an ideal gas undergoes isothermal

Compression along three different paths :

(i) Reversible compression from P i = 2 bar and V i = 8L to P f = 20 bar

(ii) A single stage compression against a constant.

External pressure of 20 bar, and

(iii) A two stage compression consisting initially of

compression against a constant external pressure of 10 bar until P gas = P ext , followed by compression against a constant. pressure of 20 bar until P gas = P ext .

(i)Work done (in bar-L) on the gas in reversible

isothermal compression is –