A metal sphere cools from 80^ C to 60^ C in 10 minute. The time taken (in minute) by it to cool from 60^ C to 40^ C if the room temperature is 30^ C , is

Step-by-step solution

Using Newton's law of cooling in approximation form: T₁ - T₂ t = K ( T₁ + T₂ 2 - T₀ ) For the first interval: 80 - 60 10 = K ( 80 + 60 2 - 30 ) 2 = K (70 - 30) 2 = 40 K K = 1 20 For the second interval: 60 - 40 t = K ( 60 + 40 2 - 30 ) 20 t = K (50 - 30) 20 t = 20 K Substituting the value of K : 20 t = 20 1 20 20 t = 1 t = 20 minute Answer: 20