Question

A body cools from ${50}^{\circ }C$ to ${40}^{\circ }C$ in $5$ minutes. The surrounding temperature is ${20}^{\circ }C$. In what further time (in minutes) will it cool to ${30}^{\circ }C$

• A. $5$
• B. $25/3$
• C. $15/2$
• D. $10$

Answer 1

The correct option is B $25/3$

From newton's law of cooling
$\frac{\Delta \theta }{\Delta t}=-K[\overline{\theta }-{\theta }_0]$
$\frac{50-40}{5}=-k[\frac{50+40}{2}-20]$
$\frac{10}{5}=-k[45-20]...\left(i\right)$
$\frac{40-30}{t}=-k[\frac{40+30}{2}-20]$
$\frac{10}{t}=-k[35-20]...\left(ii\right)$
Divide (i) by (ii)
$\frac{t}{5}=\frac{25}{15}$
$t=\frac{25}{3}$ minute
Hence, option (B) is correct.