If the boundary of system moves by an infinitesimal amount, the work involved is given by $\mathrm{dw}=-{\mathrm{P}}_{\text{ext }}\mathrm{dV}$

for irreversible process $\mathrm{w}=-{\mathrm{P}}_{\text{ext }}\mathrm{\Delta V}\text{ (where }\mathrm{\Delta V}={\mathrm{V}}_{\mathrm{f}}-{\mathrm{V}}_{\mathrm{i}}\text{ ) }$

for reversible process ${\mathrm{P}}_{\text{ext }}={\mathrm{P}}_{\text{int }}\pm \mathrm{dP}\simeq {\mathrm{P}}_{\text{int }}$

so V for reversible isothermal process $\mathrm{w}=-\mathrm{nRTln}\frac{{\mathrm{V}}_{\mathrm{f}}}{{\mathrm{V}}_{\mathrm{i}}}$

2 mole of an ideal gas undergoes isothermal compression along three different paths: 

different paths: 
(i) reversible compression from ${\mathrm{P}}_{\mathrm{i}}=2\text{ bar and }{\mathrm{V}}_{\mathrm{i}}=8\mathrm{L}\text{ to }{\mathrm{P}}_{\mathrm{f}}=20\text{ bar }$ 
(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 ${\mathrm{P}}_{\text{gas }}={\mathrm{P}}_{\text{ext }},$ followed by compression against a constant pressure of 20 bar until ${\mathrm{P}}_{\mathrm{gas}}={\mathrm{P}}_{\mathrm{ext}}$.