In 5minutes , a body cools from 75 ° C to 65 ° C at room temperature of 25 ° C . The temperature of body at the end of next 5minutes is C ∘ .

Question

Quantrex Academy · Accepted Answer

Correct answer: 57

By newton's law of cooling (with approximation),
$\dfrac{\DeltaT}{\Deltat} = - C\left({T}_{ag} - {T}_{s}\right)$

${1}^{st}\dfrac{- 10 ° C}{5min} = - C\left(70 ° C - 25 ° C\right)$

$⇒ C = \dfrac{2}{45}\min^{- 1}$

${2}^{nd}\dfrac{T - 65}{5min} = - C\left(\dfrac{T + 65}{2} - 25\right) = - \left(\dfrac{2}{45}\right)\left(\dfrac{T + 15}{2}\right)$

$⇒ 9 ( T - 65 ) = - ( T + 15 )$
$⇒ 10T = 570$
$⇒ T = 57 ° C$

In 5minutes , a body cools from 75 ° C to 65 ° C at room...