A body cools according to Newton's law of cooling from 100^ C to 60^ C in 15 minutes. If the temperature of the surrounding is 20^ C , then the temperature of the body after cooling down for one hour is

Step-by-step solution

Let be the temperature of the body at any time t . aligned & d dt ( -20) & d dt =- k ( -20), k 0 aligned Integrating on both sides, we get aligned & | -20|=- kt + c & When t =0, =100^ & 80=- k (0)+ c & c = 80 aligned array ll & | -20|=- kt + 80 & When t =15, =60^ & 40=-15 k + 80 & k = -1 15 1 2 array aligned & | -20|= t 15 1 2 + 80 [ From ( i )] & When t =1 hour =60 minutes, & | -20|= 60 15 1 2 + 80 & ( -20 80 )=4 1 2 & -20 80 = ( 1 2 )^4 & =5+20=25^ C aligned