Question

A cup of tea cools from $65.5^{\circ} C$ to $62.5^{\circ} C$ in 1 minute in a room at $22.5^{\circ} C$. How long will it take to cool from $46.5^{\circ} C$ to $40.5^{\circ} C$ in the same room ?

• A. 4 minutes
• B. 2 minutes
• C. 1 minute
• D. 3 minutes

Answer 1

Answer: (A)

4 minutes

Answer 2

$\frac{dT}{dt} = k (\theta =\theta _0)$
I $\frac{3}{1} = k (64 - 22.5)|$
$\frac{3}{1} = k(41.5)\,\,\,\,\,\,\dots(1)$
ii $\frac{6}{t} = k (43.5 - 22.5)$
$\frac{6}{t} = k (21)\,\,\,\,\,\dots(2)$
$\frac{(1)}{(2)} \Rightarrow \frac{3}{1} \times \frac{t}{6} = \frac{41.5}{21}$
$t = 4\, min$