Please provide very thorough answers for these thermodynamic problems. Using Daniel V Schroeder's book, only if possible! I will leave great reviews, as your help is sincerely appreciated this weekend before midterms. Thank you!!

Heat Engine An inventor proposes to make a heat engine using water/ice as the working substance, taking advantage of the fact that water expands as it freezes. A weight to be lifted is placed on top of a piston over a cylinder of water at 1C. The system is then placed in thermal contact with a lowtemperature reservoir at 1C 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 1C. 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, 1Tc/Th