A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is 22°C. How long will it take to cool from 75°C to 69°C?
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A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is 22°C. How long will it take to cool from 75°C to 69°C?

G1 Physics · Accepted Answer

Using Newton's law of cooling over small intervals, rate ∝ average excess temperature. First interval: 12/2 ∝ [(98+86)/2 - 22] = 70. Second: 6/t ∝ [(75+69)/2 - 22] = 50. Thus (6/t)/6 = 50/70, giving t = 1.4 min.