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,compare the work done in the above case with that carried out against a constant external pressure $P_f$.

(N/A) $(i)$ Total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from $(P_i, V_i)$ to $(P_f, V_f)$ is represented by the area under the curve between $V_i$ and $V_f$.
$(ii)$ Work done against constant external pressure $P_f$ is represented by the rectangular area under the line at $P_f$ between $V_i$ and $V_f$.
$(iii)$ Comparing the two,the area under the reversible curve is greater than the area under the constant pressure line,therefore,reversible work is greater than the work done against constant external pressure $P_f$.