Q. A liquid cools down from $70℃$ to $60℃$ in $5\ minutes$. The time taken to cool it from $60℃$ to $50℃$ 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
Explanation
(c) According to Newton’s law of cooling
Rate of cooling $\propto$ mean temperature difference
Initially, mean temperature difference
$= \left( \frac{70 + 60}{2} - \theta_{0} \right) = (65 - \theta_{0})$
Finally, mean temperature difference
$= \left( \frac{60 + 50}{2} - \theta_{0} \right) = (55 - \theta_{0})$
In second case mean temperature difference decreases, so rate of fall of temperature decreases, so it takes more time to cool through the same range
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.