The rate of heat transfer between Reservoir A at \(200^{\circ} \mathrm{F}\) and Reservoir B at \(180^{\circ} \mathrm{F}\) is \(1,000 \mathrm{Btu} / \mathrm{hr}\).

(a) Compute the lost work.

(b) Adjust the temperature of Reservoir A to \(10^{\circ} \mathrm{F}\). For the same heat duty and lost work, compute the temperature of Reservoir B. How does the approach temperature, \(\Delta T_{\mathrm{AB}}\), compare with the original value of \(20^{\circ} \mathrm{F}\) ?