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 ∝ 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 second case mean temperature difference decreases,

so rate of fall of temperature decreases,

so it takes more time to cool through the same range.