Water at 100^ C cools in 15 minutes to 75^ C in a room temperature of 25^ C . Then the temperature of water after 30 minutes is

Step-by-step solution

Let ^ C be the temperature of water at time t min. Room temperature is given 25^ C . then by Newton's law of cooling -d d t ( -25) d dt =- K ( -25) where K >0 d -25 =- K dt d -25 =- K dt ( -25)=- Kt + c (1) When t =0, =100^ 75= c from (1) ( -25)=- K t+ 75 ( -25 75 )=- Kt (2) When t=15, =75^ aligned & ( 50 75 )=-15 ~K K = -1 15 ( 2 3 ) & ( -25 75 )= t 15 ( 2 3 ) ...[from 2] When t =30^ & ( -25 75 )= 30 15 ( 2 3 ) & ( -25 75 )=2 ( 2 3 )= ( 2 3 )²= ( 4 9 ) & -25 75 = 4 9 = 525 9 = ( 175 3 )^ C aligned