Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from (p i, V i ) to (p f, V f ). With the help of a PV, plot compares the work done in the above case with that carried out against a constant external pressure pf.

Consider a cylinder having 1-mole gas with no weight and no friction having area of cross-section A. Total volume is V_i and the initial pressure is p.

Let p_ext is the external pressure and if p_ext> p, piston move down until p_ext = p, Now the final volume is V_f. The distance moved by piston be ∆l

Therefore ∆V = ∆l × A (eq-1)

∆V = V_f - V_i

Force = pressure ×area

Therefore

F = p_ext× A (eq-2)

If w is work done on the system

W = force × displacement

= p_ext × A ×∆l

From eq-1

W = p_ext×(-∆V)

W = -p_ext∆V

W = -p_ext( v_f – v_i)

If v_f> v_i work is done by the system and w is negative

If v_f< v_i work is on the system and w is positive