Question

A liquid cools down from to in 5 minutes. The time taken to cool it from to 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

Answer: (C)

Greater than 5 minutes

Answer 2

According to Newton's law of cooling. Rate of cooling ∝ mean temperature difference.

Initially, mean temperature difference

$= \left( \frac { 70 + 60 } { 2 } - \theta _ { 0 } \right) = \left( 65 - \theta _ { 0 } \right)$

Finally, mean temperature difference

$= \left( \frac { 60 + 50 } { 2 } - \theta _ { 0 } \right) = \left( 55 - \theta _ { 0 } \right)$

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.