Question

A body cools from 50°C to 49.9°C in 5 s. How long will it take to cool from 40°C to 39.9°C? Assume the temperature of the surroundings to be 30°C and Newton’s law of cooling to be valid. 

(1) 20 s 

(2) 15 s 

(3) 10 s 

(4) 5 s

Answer 1

A body cools from 50°C to 49.9°C in 5 s, then we have to find the time of body when it cools from half the temperature. According to Newton’s law of cooling, the ratio of cooling is directly proportional to the temperature difference. When the temperature difference is halved, the rate of cooling is also halved. So, the time taken is 10 s.

Hence, the correct option is (2).