Question

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

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

Answer 1

The correct option is B ${42.85}^{\circ }C$

Given
$T_1={60}^{\circ }C$
$T_2={50}^{\circ }C$
$T_0={25}^{\circ }C$
$t=10minutes$

$\left|\frac{T_2-T_1}{t}\right|=K(\frac{T_1+T_2}{2}-T_0)$

When body cools from ${60}^{\circ }C$ to ${50}^{\circ }C$ in $10$ minutes

$\frac{60-50}{10}=K(\frac{60+50}{2}-25)\dots \left(i\right)$

In next $10$ minutes

$\frac{50-\theta }{10}=K(\frac{50+\theta }{2}-25)\dots \left(ii\right)$

On dividing, We get

$\frac{10}{50-\theta }=\frac{60}{\theta }\Rightarrow {42.84}^{\circ }C$