Question

A liquid cools down from $70^{\circ} C$ to $60^{\circ} C$ in $5 min$. The time taken to cool it from $60^{\circ} C$ to $50^{\circ} C$ will be

• A. 5 min
• B. lesser than 5 min
• C. greater than 5 min
• D. lesser or greater than 5 min depending upon the density of the liquid

Answer 1

Answer: (C)

According to Newton's law of cooling, Rate of cooling $\propto$ mean temperature difference
$\frac{d Q_{1}}{d t}=k\left(\frac{70+60}{2}-\theta_{0}\right)$
$=\left(65-\theta_{0}\right)$
$\frac{d Q_{2}}{d t}=k\left(\frac{60+50}{2}-\theta_{0}\right)$
$=\left(55-\theta_{0}\right)$
As $\frac{d Q_{2}}{d t}<\frac{d Q_{1}}{d t}$
As rate of cooling is decreased, therefore liquid will take more than $5\, \min$ to cool from $60^{\circ} C$ to $50^{\circ} C$.