W a JRA project: "We should build an engine that exploits the fact that water expands in the transition from liquid to s

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W A Jra Project We Should Build An Engine That Exploits The Fact That Water Expands In The Transition From Liquid To S 1 (88.31 KiB) Viewed 46 times

W a JRA project: "We should build an engine that exploits the fact that water expands in the transition from liquid to solid. We could have a cylinder filled with water in touch with a "hot" thermal reservoir just above the melting temperature at atmospheric pressure, Th 0°C, closed by a light movable piston. We then put a mass m on the piston. We then put the cylinder at thermal contact with a "cold" thermal reservoir at Te = -1°C. The water will make a phase transition to ice, increasing its volume and therefore doing work by lifting the mass m. Finally, (after removing the mass m), we bring the engine back to its initial state putting it back into contact with the hot thermal reservoir. The volume expansion is independent of the mass m, so, for very large values of m we do a very large amount of work, only spending a fixed amount of latent heat L". 1. You are the referee of this proposal. You should immediately be suspicious that such an engine could lift a mass regardless of the value of m. What laws of thermodynamics would be violated by if a very large (possibly infinite) mass m could be lifted by a finite height using a finite amount of heat? 2. If the surface of the piston is S, what is the amount of work that the engine does, if it lifts a mass m following an expansion AV in the water to ice transition? Express the answer in terms of m, S, AV. 3. The student is neglecting an important physical effect. Do you see the problem in the proposal's reasoning? What is the student neglecting? 4. By making use of the Clausius-Clapeyron relation, show that there is a maximum mass that can be lifted by this engine. Also show that the efficiency in such conditions does not exceed the Carnot efficiency.