Question

A body takes 5 min to cool from $80^{\circ }C$ to $70^{\circ }C$. To cool From $80^{\circ }C$ to $60^{\circ }C$, it will take
(Room temperature = $40^{\circ }C$)

• A. 5 min
• B. 10 min
• C. 12 min
• D. 14 min

Answer 1

Answer: (C)

According to Newton's law of cooling
$\frac{{\theta }_1-{\theta }_2}{t}=K\left[\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0\right]$
$\therefore$ $\frac{80-70}{5}=K\left[\frac{80+60}{2}-40\right]$
$\Rightarrow K=\frac{2}{35}$
Again $\frac{80-60}{t}=\frac{2}{35}\left[\frac{80+60}{2}-40\right]$
$\approx 11.55\approx 12min$