A clever inventor makes a heat engine that uses water/ice as the working substance, taking advantage of the fact that water expands as it freezes. A load is placed on a piston containing "warm" water at 1C; the water is then placed in thermal contact with the ambient air (and ground) at -1C until the water freezes, lifting the weight. The weight is then removed and the ice is melted back (by taking heat energy from a "warm" 1C reservoir) and the cycle is repeated. Take the piston to be a cylinder with a cross-section area of 2m2 containing a 10cm height of water. The volume of ice is 9.1% larger than that of water (Vliquid = 1L/kg) and the enthalpy of fusion is DHfus = 334 kJ/kg. Neglect the heat capacities cp of ice and water, as well as any effect of pressure on the volumes of water and ice. 

(a) Suppose the piston effectively lifts a 2000-ton (2 x 106kg) mass (perhaps by using an ingenious system of pulleys to lift a 2-ton mass over 1000 times the piston's displacement). 

How much mechanical work is done by the ice freezing? Use g = 9.8m/s2.

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Answer 1 Initial volume of water at 1C ... View the full answer