A cup of coffee cools from 90°C to 80°C in t minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is: [2025]

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Solution

Q.
A cup of coffee cools from 90°C to 80°C in t minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is: [2025]

1 $\frac{13}{5} t$

2 $\frac{10}{13} t$

3 $\frac{13}{10} t$

4 $\frac{5}{13} t$

Ans.
(1)

By using average form of Newton's law of cooling

$\frac{90 - 80}{t} = c (\frac{90 + 80}{2} - 20)$ ... (i)

and $\frac{80 - 60}{t_{1}} = c (\frac{80 + 60}{2} - 20)$ ... (ii)

From (i) and (ii)

$t_{1} = \frac{13}{5} t$

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