Question

A body cools from $60^{\circ }C$ to $50^{\circ }C$ in $10$ min. If the room temperature is $25^{\circ }C$ and assuming Newton law of cooling to hold good, the temperature of the body at the end of the next $10$ min will be

• A. $45^{\circ }C$
• B. $42.85^{\circ }C$
• C. $40^{\circ }C$
• D. $38.5^{\circ }C$

Answer 1

Answer: (B)

As the body cools down, its rate of cooling slows down.
From Newtons law of cooling when a hot body is cooled in air, the rate of loss of heat by the body is proportional to the temperature difference between the body and its surroundings.
Given, ${\theta }_1=60{}^{\circ }C,{\theta }_2=50{}^{\circ }C,\theta =25{}^{\circ }C$.
$\therefore$ Rate of loss of heat $=K$
(Mean temp.-Atmosphere temp.)
where $K$ is coefficient of thermal conductivity.
$\frac{{\theta }_1-{\theta }_2}{t}=K\left(\frac{{\theta }_1+{\theta }_2}{2}-\theta \right)$
$\frac{60-50}{10}=K\left(\frac{60+50}{2}-25\right)$
$\Rightarrow K=\frac{1}{30}$
Also putting the value of $K$, we have
$\frac{50-{\theta }_2}{10}=\frac{1}{30}\left(\frac{50+{\theta }_2}{2}-25\right)$
$\Rightarrow {\theta }_3=42.85^{\circ }C$
Note: For Newtons law of cooling to hold good, temperature difference between the body and its surroundings should not be large.