A Carnot engine operates between a source at 546^ C and a sink consisting of an ice-water mixture at 0^ C . The engine performs 66.8 kJ of work per cycle. The heat rejected by the engine is entirely used to melt the ice in the sink. The mass of ice melted per cycle is: (Given: Latent heat of fusion of ice L = 334 kJ/kg )

Step-by-step solution

The temperatures of the source and sink in Kelvin are: T_H = 546 + 273 = 819 K T_C = 0 + 273 = 273 K The efficiency of the Carnot engine is given by: = 1 - T_C T_H = 1 - 273 819 = 1 - 1 3 = 2 3 Efficiency is also the ratio of work done to heat absorbed: = W Q_ in 2 3 = 66.8 Q_ in Q_ in = 3 2 66.8 = 100.2 kJ The heat rejected to the sink per cycle is: Q_ out = Q_ in - W = 100.2 - 66.8 = 33.4 kJ This rejected heat melts the ice. Using the latent heat formula Q_ out = mL : 33.4 = m 334 m = 33.4 334 = 0.1 kg Converting