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 Vi and the initial pressure is p.

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


Therefore ∆V = ∆l × A (eq-1)


∆V = Vf - Vi


Force = pressure ×area


Therefore


F = pext× A (eq-2)


If w is work done on the system


W = force × displacement


= pext × A ×∆l


From eq-1


W = pext×(-∆V)


W = -pext∆V


W = -pext( vf – vi)


If vf> vi work is done by the system and w is negative


If vf< vi work is on the system and w is positive



1