 Solution

To obtain the maximum work from two finite heat reservoirs, operate a reversible heat engine between the bodies until their temperatures coincide. Include the work store in the isolated total system: no heat enters from outside, while the bodies can transfer energy to that store. With the stated constant heat capacities, reversibility requiresNumerically, $T_f=450^{5/8}273^{3/8}=373.094\mathrm{K}$. The decrease of the bodies' internal energy isDirect thermal equilibration without an engine would instead reach the arithmetic heat-capacity-weighted temperature $383.625\mathrm{K}$ and deliver no work. entropy production can only raise the final common temperature above the value for zero entropy production and reduce extractable work.