Question

A body cools from ${60}^{\circ }\text{C}$ to ${50}^{\circ }\text{C}$ in $10$ minutes. If the room temperature is ${25}^{\circ }\text{C}$ then the temperature of the body at the end of the next $10$ minutes will be

• A. ${38.50}^{\circ }\text{C}$
• B. ${40.25}^{\circ }\text{C}$
• C. ${42.86}^{\circ }\text{C}$
• D. ${45.75}^{\circ }\text{C}$

Answer 1

The correct option is C ${42.86}^{\circ }\text{C}$

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 $10$ minutes,
$\frac{60-50}{10}=\alpha (\frac{60+50}{2}-25)$
$\Rightarrow \alpha =\frac{1}{30}{\text{min}}^{-1}$
Now, for next $10$ minutes,
$\frac{50-T}{10}=\frac{1}{30}\times (\frac{50+T}{2}-25)$
On solving it, we get
$T={42.86}^{\circ }\text{C}$