Question

A bucket full of hot water cools from ${75}^{\circ }C$ to ${70}^{\circ }C$

in time $T_1$ , from ${70}^{\circ }C$ to ${65}^{\circ }C$ in time $T_2$ and

from ${65}^{\circ }C$ to ${60}^{\circ }C$ in time $T_3$, then

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

According to Newton's law of cooling

Rate of cooling ∝ Mean temperature difference

$\Rightarrow \frac{Fallintemperature}{time}\propto (\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0)$

$\because {\left(\frac{{\theta }_1+{\theta }_2}{2}\right)}_1>{\left(\frac{{\theta }_1+{\theta }_2}{2}\right)}_2>{\left(\frac{{\theta }_1+{\theta }_2}{2}\right)}_3$

$\Rightarrow T_1<T_2<T_3$