Question

A liquid cools down from $70^{\circ }C$ to $60^{\circ }C$ in $5min$. 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
$\frac{d{Q}_1}{dt}=k\left(\frac{70+60}{2}-{\theta }_0\right)$
$=\left(65-{\theta }_0\right)$
$\frac{d{Q}_2}{dt}=k\left(\frac{60+50}{2}-{\theta }_0\right)$
$=\left(55-{\theta }_0\right)$
As $\frac{d{Q}_2}{dt}<\frac{d{Q}_1}{dt}$
As rate of cooling is decreased, therefore liquid will take more than $5\min$ to cool from $60^{\circ }C$ to $50^{\circ }C$.