Question

A bucket full of hot water cools from ${75}^{\circ }\text{C}$ to ${70}^{\circ }\text{C}$ in time $t_1$, from ${70}^{\circ }\text{C}$ to ${65}^{\circ }\text{C}$ in time $t_2$ and from ${65}^{\circ }\text{C}$ to ${60}^{\circ }\text{C}$ 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

The correct option is C $t_1<t_2<t_3$

According to Newton's law of cooling
Rate of cooling $\propto$ Mean temperature difference
$\Rightarrow \frac{\text{Fall in temperature}}{\text{Time}}\propto (\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0)$
$\because {\left(\frac{{\theta }_1+{\theta }_2}{2}\right)}_1>{\left(\frac{{\theta }_1+{\theta }_2}{2}\right)}_2>{\left(\frac{{\theta }_1+{\theta }_2}{2}\right)}_3$
$\Rightarrow t_1<t_2<t_3$