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A 0.5 kg metal cylinder is heated by a 12 W electric heater in a room kept at 15°C. Its temperature rises to 25°C in 5 minutes and eventually levels off at a steady 45°C. Assuming Newton's law of cooling (heat-loss rate proportional to excess temperature over surroundings), which statement is correct?

1. The rate of loss of heat of the cylinder to surrounding at 20°C is 2 W
2. The rate of loss of heat of the cylinder to surrounding at 45°C is 2 W
3. Specific heat capacity of metal is 240 / ln(3/2) J/kg°C
4. None of these

Correct answer: The rate of loss of heat of the cylinder to surrounding at 20°C is 2 W

Solution

At steady state, power lost = 12 W at excess 30°C, so k = 12/30 = 0.4 W/°C. At 20°C, excess = 5°C, loss = 0.4*5 = 2 W.

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