Newton's law of cooling states that the rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of the air. If the temperature of the air is 290 K. We can write it as 
= – k (T – 290), k > 0 constants. where T is temperature of substance. On the basis of above information, answer the following question
(i) The substances cools from 370 K to 330 K in 10 min., then
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Ans.
(i)
Sol. 
= – k(T – 290).
⇒ 
= – kdt
⇒ λ n(T – 290) = – kt + c
Initially, T = 370k and t = 0, then λ n(80) = c
From Equation (i), λ n(T – 290) = – kt + λ n80
λ n 
= – kt
= e –kt
T = 290 + 80 e –kt
(ii)
Sol. For t = 10 min, T = 330
then, 330 – 290 = 80 e – 10k
= e –10k
e 10k = 2 ⇒ 10k = λ n2
k = λ n2/10
(iii)
Sol. Time can never be negative
Number of solution = 2
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