A pan filled with hot food cools from 94^ C to 86^ C in 2 ~min , when the room temperature is 20^ C . The time taken for the food to cool from 86^ C to 74^ C will be

Step-by-step solution

According to Newton's law of cooling, T₁-T₂ t =K ( T₁+T₂ 2 -T_ s ) ...(i) where, T_ s is the temperature of surrounding. For the first case, T₁=94^ C , T₂=86^ C t=2 =120 ~s , T_ s =20^ C Putting these values in Eq. (i), we get aligned 94-86 120 &=K ( 94+86 2 -20 ) K &= 8 120 70 ...(ii) aligned For the second case, T₁=86^ C , T₂=74^ C From Eq. (i), we get aligned 86-74 t =K ( 86+74 2 -20 ) 12 t = 8 120 70 (60) t =210 ~s aligned