Question

A body cools from ${60}^{\circ }C$ to ${50}^{\circ }C$ in 10 minutes when kept in air at ${30}^{\circ }C$. In the next 10 minutes, its temperature will be

• A. $below{40}^{\circ }C$
• B. ${40}^{\circ }C$
• C. $above{40}^{\circ }C$
• D. $cannotbepredicted$

Answer 1

The correct option is C $above{40}^{\circ }C$

Let $\theta$ be the temperature of the body after next 10 min.
From cooling law,
$\frac{m\times s\times [60-50]}{10}=K\left[\frac{60+50}{2}\right]$
Or $ms=K\times 25$ . ...(1)
Further, $m\times s\times [50-\theta ]=K[\frac{50+\theta }{2}-30]$ ....(2)
Dividing (1 ) by (2)
$\frac{ms}{ms[50-\theta ]}=\frac{K\times 25}{[25+\frac{\theta }{2}-30]}$
$\frac{\theta }{2}-5=1250-25\theta or25.5\theta =1255,\theta ={49.2}^{\circ }C$