An object kept in a large room having air temperature of 25^ C takes 12 minutes to cool from 80^ C to 70^ C . The time taken to cool for the same object from 70^ C to 60^ C would be nearly

Step-by-step solution

Key Idea From Newton's law of cooling, the time taken (t) by a body to cool from T₁ to T₂ when placed in a medium of temperature T₀ can be calculated from relation T₁-T₂ t = 1 K ( T₁+T₂ 2 -T₀ ) When the object cool from 80^ C to 70^ C in 12 minutes, then from Newton's law of cooling, array r 80-70 12 = 1 ~K ( 80+70 2 -25 ) [ T ₀=25^ C ] 5 6 = 1 ~K 50 array Similarly, when object cool from 70^ C to 60^ C we get gathered 70-60 t = 1 ~K ( 70+60 2 -25 ) 10 t = 1 ~K 40 gathered Divide Eq. (i) and (ii), we get gathered 5