A Body Cools From 91oC To 89oC In 5 Minutes When The Room Temperature Is 20oC. Then It Will Cool From 71oC To 69oC In:   

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Question

A body cools from 91oC to 89oC in 5 minutes when the room temperature is 20oC. Then it will cool from 71oC to 69oC in:   

Solution

Correct option is

7 minutes

 

Room temperature = 20oC. 

In the first interval of 5 minutes:   

Mean temperature =    

Mean temperature excess = 90 – 20 = 70oC  

Average rate of loss of heat   

                 

Now, average rate of loss of heat ∝ mean temperature excess

         

Let t be the time taken to cool from 71oC to 69oC.

Then, for the second stage:

   

Mean temperature excess = 70 – 20 = 50oC.   

Average rate of loss of heat   

Dividing eq. (1) by (2),

                   

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Q10

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