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A water cooler holds 120 litres of water and removes heat at a constant rate of P watts. In a closed loop, this water cools an external device that continuously dissipates 3 kW of heat. The water sent to the device must stay at or below 30 deg C, the whole 120 litres starts at 10 deg C, and the system is perfectly insulated. Find the minimum P (in watts) so the device can run for 3 hours. (Specific heat of water = 4.2 kJ/kg/K, density of water = 1000 kg/m³.)

1. 1600
2. 2067
3. 2533
4. 3933

Correct answer: 2067

Solution

Energy balance over 3 hours: 3000 * t = P * t + (heat to raise 120 kg by 20 K); solving gives P about 2067 W.

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