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(C) According to Newton's law of cooling,the rate of cooling is directly proportional to the temperature difference between the body and its surroundi

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$t_1 < t_2 < t_3$

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(C) According to Newton's law of cooling,the rate of cooling is directly proportional to the temperature difference between the body and its surroundings.Mathematically,$\frac{d heta}{dt} = k \left( \frac{ heta_1 + heta_2}{2} - heta_0 ight)$,where $ heta_0$ is the room temperature.Since the temperature difference decreases as the water cools,the rate of cooling decreases.Therefore,the time taken to cool by the same amount $(5^{\circ} C)$ increases as the temperature of the water approaches the room temperature.Comparing the mean temperatures: $\left( \frac{80+75}{2} ight) > \left( \frac{75+70}{2} ight) > \left( \frac{70+65}{2} ight)$.Thus,the rate of cooling is highest for the first interval and lowest for the third interval.Consequently,$t_1 < t_2 < t_3$.

$A$ 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:

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