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. $T_1=T_2=T_3$
• B. $T_1>T_2>T_3$
• C. $T_1<T_2<T_3$
• D. $T_1>T_2<T_3$

Answer 1

Answer: (C)

According to Newton's law of cooling
$\text{Rate of cooling}\propto Meantemperaturedifference$
$\Rightarrow \frac{\text{ Fall in temperature }}{\text{ Time }}\propto \left(\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0\right)$
$\because {\left(\frac{{\theta }_1+{\theta }_2}{2}\right)}_1>{\left(\frac{{\theta }_1+{\theta }_2}{2}\right)}_2>{\left(\frac{{\theta }_1+{\theta }_2}{2}\right)}_3$
$\Rightarrow T_1<T_2<T_3$