Chapter 5.3, Problem 33P

An inventor proposes to make a heat engine using water/Ice as the working taking advantage of the fact that water expands as it freeze. A weight to be lifted is placed on top of a piston over a cylinder of water at 1°C. The system is then placed in thermal contact with a low–temperature reservoir –1°C until the water freezes into ice, lifting the weight. The weight is then removed and the ice is melted by putting it in contact with a high–temperature reservoir at 1°C. The inventor is pleased with this device because it can seemingly perform an unlimited amount of work while absorbing only a finite amount of heat. Explain the flaw in the inventor’s reasoning, and use the Clausius–Clapeyron relation to prove that the maximum efficiency of this engine is still given by the Carnot formula, $1-T_c/T_h$.