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Question

A body cools from 50oC to 45oC in 5 min and to 40oC in another 8 min. The temperature of the surrounding is

A
34o
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B
30o
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C
43o
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D
37o
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Solution

The correct option is C 37o
Newton's cooling law dθdt=k(θθ0)
putting the given values of the situation in the formula we get:-
(5045)5=k(50T)
=>1=k(50T) -----(1)

Now, cooling body at takes 8 min to reach 400C form 450C
(4540)8=k(45T)
58=k(45T) ------(2)

Dividing the two equations, we get:
8(45T)=5(50T)
3608T=2505T
T=110/3=36.670C

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