Question

A body cools down from \(75^\circ C\) to \(65^\circ C\) in 10 minutes. It will cool down from \(65^\circ C\) to \(55^\circ C\) in a time

• A. 10 minutes
• B. Less than 10 minutes
• C. More than 10 minutes
• D. Less than or more than 10 minutes depending on its mass

Hint:

When the temperature gap decreases, the cooling rate drops — so it takes longer to cool through the same interval.

Answer 1

The Correct Option is C

According to Newton’s Law of Cooling, the rate of cooling is proportional to the difference between the object's temperature and the surrounding temperature. \[ \frac{dT}{dt} \propto (T - T_{\text{env}}) \] As the object cools down, the temperature difference with the surroundings decreases, so the rate of cooling becomes slower. Therefore, cooling from \(65^\circ C\) to \(55^\circ C\) will take more time than cooling from \(75^\circ C\) to \(65^\circ C\), assuming constant surrounding temperature.