A bowl filled with very hot soup cools from 98$^\circ$C to 86$^\circ$C in 2 minutes when the room temperature is 22$^\circ$C. How long it will take to cool from 75$^\circ$C to 69$^\circ$C?
Solution
From Newton's law of cooling.
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$\frac{d T}{d t}=-k\left(T-T_{s}\right)$
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Case $\mathrm{I}: d T=12^{\circ} \mathrm{C}, d t=2 \min$
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$\frac{12}{2}=-k\left[92-22^{\circ}\right]=-k 70$
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Case II : $d T=6^{\circ} \mathrm{C}$
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$\frac{6}{d t}=-k[72-22]=-k 50$
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From (1) and (2)
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$d t=1.4 \mathrm{~min}$
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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