MHT CET202012 Oct 2020Morning ShiftMathematicsDefinite IntegrationActual
If the body cools from 135^ C to 80^ C at room temperature of 25^ C in 60 minutes, then the temperature of body after 2 hours is
Options
- A(52.5)^ C
- B(10.5)^ C
- C(52.75)^ C
- D(10.75)^ C
Correct answer
A. (52.5)^ C
Step-by-step solution
Let ^ C be the temperature of the body at time t min. Room temp is given 25^ C Then by Newton's law of cooling, we write aligned & d dt ( -25) d dt =- k ( -25) & d -25 = - kdt & ( -25)=- kt + c ...(1) Initially when t =0, =135 & (135-25)=0+ c c = 110 & ( -25)=- kt + 110 & ( -25 110 )=- kt ...(2) aligned Now when t=60, =80 array l w when t=60, =80 ( 55 110 )=-60 k k=- 1 60 ( 1 2 ) array From (2) ( -25 110 )= t 60 ( 1 2 ) At t=120 , we get ( -25 110 )=2 1 2 ( -25 110 )= ( 1 4 ) -25 110 = 1 4 4 -100=110 4 =210 =52.5^