question_answer

A hot body, obeying Newton’s law of cooling is cooling down from its peak value 80°C to an ambient temperature of 30°C. It takes 5 minutes in cooling down from 80°C to 40°C.                                  [JEE ONLINE 11-04-2014]

How much time will it take to cool down from 62°C to 32°C?

(Given In 2 = 0.693, In 5 = 1.609)

A)  3.75 minutes

B)       8.6 minutes

C)  9.6 minutes      

D)       6.5 minutes

Correct Answer: B

Solution :

[b] From Newton’s law of cooling,

From question and above equation,

(1)

and                          (2)

Dividing equation (2) by (1),

On solving we get, time taken to cool down from 62°C to 32°C, t = 8.6 minutes.