Rankers Physics

Thermal Physics: Practice Problem & Solution

A beaker full of hot water is kept in a room. If it cools from $80^\circ\text{C}$ to $75^\circ\text{C}$ in $t_1$ minutes, from $75^\circ\text{C}$ to $70^\circ\text{C}$ in $t_2$ minutes and from $70^\circ\text{C}$ to $65^\circ\text{C}$ in $t_3$ minutes, then: (1995)
$t_1 < t_2 < t_3$
$t_1 > t_2 > t_3$
$t_1 = t_2 = t_3$
$t_1 < t_2 = t_3$

Solution Explained:

To solve this problem, we apply the core principles of Thermal Physics. Understanding the underlying formula is key to arriving at the correct answer below:

According to Newton's law of cooling, the rate of cooling is directly proportional to the temperature difference between the body and surroundings. As the water cools, the temperature difference decreases, slowing the rate of cooling. Thus, successive intervals take more time, giving $t_1 < t_2 < t_3$.

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