Transmission Of Heat Question 184

Question: Hot water kept in a beaker placed in a room cools from $ 70^{o}C $ to 60°C in 4 minutes. The time taken by it to cool from $ 69^{o}C $ to $ 59^{o}c $ will be

[JIPMER 1999]

Options:

A) The same 4 minutes

B) More than 4 minutes

C) Less than 4 minutes

D) We cannot say definitely

Show Answer

Answer:

Correct Answer: B

Solution:

Rate of cooling $ =\frac{-d\theta }{dt}\propto ( \frac{{\theta _{1}}+{\theta _{2}}}{2}-{\theta _{0}} ) $ In second case average temperature will be less hence rate of cooling will be less.

Therefore time taken will be more than 4 minutes.