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A heat engine that has maximum efficiency starts working by using 1 kg of water with...

A heat engine that has maximum efficiency starts working by using 1 kg of water with initial temperature Ti = 373K as a hot reservoir, and 1 kg of ice at T0 = 273K as its cold reservoir. As the engine goes through cycles, the water cools, and the ice melts. At some point, all of the ice will be melted.

(a) What is the temperature of the water reservoir at that time?

(b) What is the maximal amount of work that you can extract from the engine by the time all ice melts? Heat capacity of water c = 4.2 kJ/kg can be assumed independent of temperature. Latent heat of melting for ice is q = 334kJ/kg.

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