A cup of coffee cools from 9 0 ∘ C to 8 0 ∘ C in t minutes when the room temperature is 2 0 ∘ C . The time taken by the similar cup of coffee to cool from 8 0 ∘ C to 6 0 ∘ C at the same room temperatu

Question

A cup of coffee cools from 9 0 ∘ C to 8 0 ∘ C in t minutes when the room temperature is 2 0 ∘ C . The time taken by the similar cup of coffee to cool from 8 0 ∘ C to 6 0 ∘ C at the same room temperature is :

TestHub · Accepted Answer

By using average form of Newton's law of cooling
$\frac{90 - 80}{t} = k (\frac{90 + 80}{2} - 20) \frac{80 - 60}{t ^{'}} = k (\frac{80 + 60}{2} - 20)$
$(i)/(ii) \frac{10 \times t ^{'}}{t \times 20} = \frac{65}{50} t^{'} = \frac{65}{50} \times 2 t = \frac{65}{25} t = \frac{13}{5} t$

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