Question

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

• A. $5$ minutes
• B. Lesser than $5$ minutes
• C. Greater than $5$ minutes
• D. Lesser or greater than $5$ minutes depending upon the density of the liquid

Answer 1

The correct option is C Greater than $5$ minutes

According to Newton's law of cooling ,
Rate of cooling $\propto$ Mean temperature difference.
Initially, mean temperature difference $=(\frac{70+60}{2}-{\theta }_0)=(65-{\theta }_0)$
Finally, mean temperature difference $=(\frac{60+50}{2}-{\theta }_0)=(55-{\theta }_0)$
In the second case , mean temperature difference decreases, so rate of fall of temperature decreases, so it takes more time to cool through the same range.