Thermal Properties of Matter - Result Question 48
49. A beaker full of hot water is kept in a room. If it cools from $80^{\circ} C$ to $75^{\circ} C$ in $t_1$ minutes, from $75^{\circ} C$ to $70^{\circ} C$ in $t_2$ minutes and from $70^{\circ} C$ to $65^{\circ} C$ in $t_3$ minutes, then
[1995]
(a) $t_1=t_2=t_3$
(b) $t_1<t_2=t_3$
(c) $t_1<t_2<t_3$
(d) $t_1>t_2>t_3$
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Answer:
Correct Answer: 49. (c)
Solution:
- (c) Let $\theta_0$ be the temperature of the surrounding. Then
$\frac{80-75}{t_1}=k(\frac{80+75}{2}-\theta_0)$
or, $\frac{5}{t_1}=k(77.5-\theta_0)$
or, $\quad t_1=\frac{5}{k(77.5-\theta_0)}$
Similarly, $t_2=\frac{5}{k(72.5-\theta_0)}$
and $t_3=\frac{5}{k(67.5-\theta_0)}$
From (1), (2) & (3), it is obvious that $t_1<t_2<t_3$
