A body cools from 60 ° C to 40 ° C in 6 minutes. If, temperature of surroundings is 10 ° C . Then, after the next 6 minutes, its temperature will be ______ ° C .

Step-by-step solution

From Newton’s law of cooling d T d t = k T a v g - T 0 , here, T 0 is surrounding temperature. For case 1 : 60 - 40 6 = k 60 + 40 2 - 10 20 6 = k 50 - 10         . . . 1 For case 2 : 40 - T 6 = k 40 + T 2 - 10         . . . 2 From equation 1 , we have k = 1 12 Putting in equation 2 40 - T 6 = 1 12 40 + T 2 - 10 ⇒ 10 + T 2 = 80 - 2 T ⇒ 2 T + T 2 = 70 ⇒ T = 140 5 = 28 ° C