A body cools from 60⁰C to 50⁰C in 10 min. If room temperature is 25⁰C. Temperature of body at the end of next 10 min, will be

Newton's cooling law is given as

$\frac{{\theta }_1-{\theta }_2}{t}=k\left(\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0\right)$

Given,   ${\theta }_0=25°\mathrm{C},{\theta }_1=60°\mathrm{C},t=10\min \text{ and }{\theta }_2=50°\mathrm{C}$

$\therefore \frac{60-50}{10}=k\left(\frac{60+50}{2}-25\right)$

We get,  $k=\frac{1}{30}\text{ units and }{t}_2=10 \min$

Again,  ${\theta }_2=\theta ,{\theta }_1=50°\mathrm{C},{\theta }_0=25°\mathrm{C}$

$\therefore \left(\frac{50-\theta }{10}\right)=\frac{1}{30}\left(\frac{50+\theta }{2}-25\right)$

$\Rightarrow \theta =42.85°\mathrm{C}$