A body cools in $7 \text{min}$ from ${60}^{°}\text{C}$ to ${40}^{°}\text{C.}$ What will be its temperature after the next $7 \text{min?}$ The temperature of surroundings is ${10}^{°}\text{C.}$

According to Newton's law of cooling, $\left[\frac{{\theta }_1-{\theta }_2}{t}\right]=K[\left(\frac{{\theta }_1+{\theta }_2}{2}\right)-{\theta }_0]$

So that $\left[\frac{60-40}{7}\right]=K[\left(\frac{60+40}{2}\right)-10]\Rightarrow K=\frac{1}{14}.......\left(i\right)$

Now if after cooling from ${40}^{°}\text{C}$ to $7 \text{min}$ the temperature of the body becomes $\theta ,$ according to Newton's law of cooling, $\left[\frac{40-\theta }{7}\right]=K[\left(\frac{40+\theta }{2}\right)-10]$

Which in the light of Eq. (i), i.e., $K=(1/14),$ gives 

$\begin{array}{l}\left[\frac{40-\theta }{7}\right]=\frac{1}{14}\left[\left(\frac{20+\theta }{2}\right)\right]\\ 160-4\theta =20+\theta ;\theta ={28}^{°}\text{C}\end{array}$