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A liquid cools from 80 degC to 50 degC in 5 minutes. The surroundings are at 20 degC. Using the exact (logarithmic) form of Newton's law of cooling, how long does it take to cool from 60 degC to 30 degC?

1. 5 min
2. 7.5 min
3. 10 min
4. 12.5 min

Correct answer: 10 min

Solution

From 80->50 degC: ln(60/30) = k*5 gives k = ln2/5; for 60->30 degC, t = ln(40/10)/k = ln4/(ln2/5) = 10 min.

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