Question

A body initially at ${80}^{\circ }$ C cools to ${64}^{\circ }$ C in 5 minutes and to ${52}^{\circ }$ C in 10 minutes. The temperature of the body after 15 minutes will be

• A. C
• B. C
• C. C
• D. C

Answer 1

The correct option is A C

According to Newton law of cooling
$\frac{{\theta }_1-{\theta }_2}{t}=K[\frac{{\theta }_1-{\theta }_2}{2}-{\theta }_0]$



For first process : $\frac{(80-64)}{5}=K[\frac{80+64}{2}-{\theta }_0]$ ....(i)
For second process : $\frac{(80-52)}{10}=K[\frac{80+52}{2}-{\theta }_0]$ ....(ii)
For third process : $\frac{(80-\theta )}{15}=K[\frac{80+\theta }{2}-{\theta }_0]$ ....(iii)
On solving equation (i) and (ii) we get $K=\frac{1}{15}$ and ${\theta }_0={24}^{\circ }C$ . Putting these values in equation (iii) we get $\theta ={42.7}^{\circ }C$