Question 100: Properties of Matter

Question

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?

Accepted Answer

From Newton's law of cooling.
$$
\frac{d T}{d t}=-k\left(T-T_{s}\right)
$$
Case $\mathrm{I}: d T=12^{\circ} \mathrm{C}, d t=2 \min$
$$
\frac{12}{2}=-k\left[92-22^{\circ}\right]=-k 70
$$
Case II : $d T=6^{\circ} \mathrm{C}$
$$
\frac{6}{d t}=-k[72-22]=-k 50
$$
From (1) and (2)
$$
d t=1.4 \mathrm{~min}
$$

Answer

2 minutes

Answer

0.5 minute

Answer

1.4 minutes

Answer

1 minute

Properties of Matter

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

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