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A Carnot engine operates between a source at 91^ C and a sink consisting of a large block of ice at 0^ C . The engine produces 16.8 kJ of work per cycle. The mass of ice melted per cycle due to the heat rejected by the engine is: (Given: Latent heat of fusion of ice = 3.36 10^5 J/kg )

Options

  1. A50 g
  2. B150 g
  3. C200 g
  4. D0 g

Correct answer

B. 150 g

Step-by-step solution

The temperatures of the source and sink in Kelvin are: T₁ = 91 + 273 = 364 K T₂ = 0 + 273 = 273 K The efficiency of the Carnot engine is: = 1 - T₂ T₁ = 1 - 273 364 = 1 - 3 4 = 1 4 The efficiency is also given by the ratio of work done to heat absorbed: = W Q₁ Q₁ = W = 16.8 1 4 = 67.2 kJ The heat rejected to the sink per cycle is: Q₂ = Q₁ - W = 67.2 - 16.8 = 50.4 kJ = 50400 J This rejected heat melts the ice. Using the latent heat formula Q₂ = m L : m = Q₂ L = 50400 3.36 10^5 = 0.15 kg Converting the mass to grams:

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