Question

A body cools from ${50}^{\circ }C$ to ${40}^{\circ }C$ in $5$ minute. Surrounding temperature is ${20}^{\circ }C$. Then what will be its temperature $5$ minutes after reaching ${40}^{\circ }C$?

• A. ${35}^{\circ }C$
• B. ${\frac{100}{3}}^{\circ }C$
• C. ${32}^{\circ }C$
• D. ${30}^{\circ }C$

Answer 1

The correct option is B ${\frac{100}{3}}^{\circ }C$

According to Newton's law of cooling,
$\frac{T_1-T_2}{t}=\alpha (\frac{T_1+T_2}{2}-T_0)$,
where, body cools from temperature $T_1$ to $T_2$ in time $t$ at surrounding temperature $T_0$ and $\alpha$ is heat transfer coefficient.
So, for first $5$ minutes,
$\frac{50-40}{5}=\alpha (\frac{50+40}{2}-20)$
$\Rightarrow \alpha =\frac{2}{25}{\text{min}}^{-1}$
Now, for next $5$ minutes,
$\frac{40-T}{5}=\frac{2}{25}\times (\frac{40+T}{2}-20)$
$200-5T=40+T-40$
On solving it, we get
$T={\frac{100}{3}}^{\circ }\text{C}$