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The excess temperature of a body falls from \( 12^{\circ} \mathrm{C} \) to \( 6^{\circ} \mathrm{C} \) in 5 minutes, then the time to fall the excess temperature from \( 6^{\circ} \mathrm{C} \) to \( 3^{\circ} \mathrm{C} \) is (assume the Newton's cooling is valid)

1. 10 minutes
2. 7.5 minutes
3. 5 minutes
4. 2.5 minutes

Correct answer: 5 minutes

Solution

Newton’s law of cooling gives exponential decay of excess temperature, so the time to halve the excess temperature is constant. Since the excess temperature halves from 12 to 6 in 5 minutes, it takes the same time to halve again from 6 to 3.

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