Answer:
11.18 minutes
Explanation:
We shall apply Newton's law of cooling
Rate of cooling ∝ Temperature difference
(T₂ - T₁ ) / t = k ( T₁ + T₂ / 2 - T )
A body cools from temperature of T₂ TO T₁ in time t , K being a constant.
(T₁ + T₂) /2 is the average temperature and T is temperature of surrounding.
Using the data given in the problem ,
For cooling from 425 degree to 300 degree
[tex]\frac{425-300}{5} =k(\frac{425+300}{2}-71)[/tex]
[tex]\frac{125}{5}= k x 291.5[/tex]
For cooling from 425 to 135 in time t we have
[tex]\frac{425 - 135}{t} =k(\frac{425+135}{2}-71)[/tex][/tex]
[tex]\frac{290}{t}[/tex] = 209k
From these two equations we get the value of t as
t = 16.18 s
So time required to cool from 300 to 135 degree isas follows
16.18 - 5 = 11.18 s
