If a body cools from 80^ C to 50^ C in the room temperature of 25^ C in 30 minutes, then the temperature of the body after 1 hour is

Step-by-step solution

Let be the temperature of the body at any time t . aligned & d dt ( -25) & d dt =- k ( -25), k >0 aligned Integrating on both sides, we get aligned & | -25|=- kt + c & When t =0, =80^ & 55=0+ c c = 55 & | -25|=- kt + 55 & When t =30, =50^ & 25=-30 k + 55 & k =- 1 30 5 11 & | -25|= t 30 5 11 + 55 aligned When t =1 hour =60 minutes, ... [From (i)] aligned & | -25|= 60 30 5 11 + 55 & ( -25 55 )=2 ( 5 11 ) & -25 55 = ( 5 11 )^2 & -25 55 = 25 121 & =25+ 125 11 =25+11.36=36.36^ C aligned