Question

A liquid cools down from ${70}^{o}C$ to ${60}^{o}C$ in 5 minutes. The time taken to cool it from ${60}^{o}C$ to ${50}^{o}C$ 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 $\mu$ mean temperature difference. Initially, mean temperature difference
$=(\frac{70+60}{2})=(65-{\theta }_0)$
Finally, mean temperature difference
$=(\frac{60+50}{2})=(55-{\theta }_0)$
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.