Question

A body kept in air with temperature 25 deggre celsius cools from 140 degree Celsius to 80 deggre celsius in 20 minutes. Find when the body cools down to 35 deggre celsius?


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Answer 1

Answer:

in 15 minutes body cools down to 35 deggre celsius.

Answer 2

Answer: The body cools down to 35° C in 66.26 minutes

Step-by-step explanation:

Using Newton's law of cooling :

$T(t) = T_s + (T_o - T_s)e^{-kt}$

T(t) ⇒ Temperature of body at a given time t

$T_s$  ⇒  Surrounding temperature

$T_o$ ⇒ Initial temperature of body

k  ⇒ constant

T(t) = 25 + ( 140 - 25)$e^{-kt}$

T(t) = 25 + 115$e^{-kt}$

At t = 20 min , T(t) = 80

Therefore,

⇒ 80 =  25 + 115$e^{-k20}$

⇒ 80 -25 = 115$e^{-k20}$

⇒ 55 =  115$e^{-k20}$

⇒ $e^{20k}$ = 115/55

⇒  $e^{20k}$ = 2.09

⇒ 20k = ㏑(2.09)

⇒ k = 0.0368

Let the temperature of body be 35° C at time t

T(t) = 25 + 115$e^{-kt}$

35 = 25 + 115$e^{-kt}$

10 = 115$e^{-kt}$

 $e^{kt}$ = 115/10 = 11.5

kt = ㏑(11.5)

t = ㏑(11.5)/k

t = 66.26

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