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 . How much time will it take to cool down from 62^ C to 32^ C ? (Given In 2=0.693 , In 5=1.609 )

Step-by-step solution

From Newton's law of cooling, t= 1 k _e ( ₂- ₀ ₁- ₀ ) From question and above equation, 5= 1 k _e (40-30) (80-30) And, t= 1 k _e (32-30) (62-30) Dividing equation (2) by (1), t 5 = 1 k _e (32-30) (62-30) 1 k _e (40-30) (80-30) On solving we get, time taken to cool down from 62^ C to 32^ C , t=8.6 minutes.