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A 1 kg mass of water held in a container is left in sunlight, so it becomes warmer than its surroundings. Sunlight delivers an average power of 700 W m⁻², and this is absorbed by the water over an effective area of 0.05 m². If heat loss to the surroundings obeys Newton's law of cooling, what is the steady-state temperature difference (in deg C) between the water and the surroundings after a long time? (Neglect the container; cooling constant = 0.001 s⁻¹, specific heat capacity of water = 4200 J kg⁻¹ K⁻¹.)

1. 8.33
2. 4.17
3. 16.67
4. 2.08

Correct answer: 8.33

Solution

At steady state the absorbed solar power exactly balances the heat radiated/lost to the surroundings, so the temperature stops rising and a constant difference is maintained.

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