A body cools according to Newton's law from 100^ C to 60^ C in 20 minutes. The temperature of the surrounding being 20^ C then the temperature of the body after one hour is

Step-by-step solution

Let ^ C be the temperature of the body at time t. The temperature of surrounding is 20^ C . According to Newton's law of cooling d d t ( -20) d d t =-K( -20), where K>0 d -20 = -K d t | -20|=-K t+c We have =100 and t=0 |100-20|=0+c c= 80 | -20|=- Kt + 80 | -20 80 |=- Kt When t=20, =60 K= -1 20 ( 1 2 ) Thus ( -20 80 )= t 20 ( 1 2 ) When t=60 ( -20 80 )=3 ( 1 2 )= ( 1 8 ) -20 80 = 1 8 =30^