Question

A body cools from 80°c to 60°c in 2minutes. in how much time it cools from 60° to 40°c ? the temperature of the surrounding is 10°c ​

Answer 1

Answer:

2 minutes

Explanation: the difference between 80 and 60 is 20 Whereas, difference between 60 and 40 is also 20. So the answer is 2 minutes.

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Answer 2

AnSwer :-

1st Case :

Mean temperature of the body

$\sf = \dfrac{80 + 69}{2}= 70° C$

Mean excess temperature = 70 - 10 = 60°C

$\sf \dfrac{d \theta}{dt} = K(\theta - \theta_0) </p><p>$

$\sf\dfrac{20}{2} = K(60) \: \: \: \: .......(1)$

2nd case :

Mean temperature of the body

$\sf = \dfrac{60+40}{2} = 50°C$

Mean excess temperature = (50 - 10) = 40°C

Let 't' minutes be the time to cool down from 60°C to 40°C

$\sf then \: \dfrac{20}{t} = K(40) \: \: \: \: \: .......(2)$

Dividing eq (1) and (2)

$\sf \dfrac{ \dfrac{20}{2} }{ \dfrac{20}{t} } = \dfrac{K(60)}{K(40)}$

$\sf \dfrac{t}{2} = \dfrac{60}{40}$

.i.e.,

$\sf t = 3mins$