A bucket full of hot water cools from 75^{cir | vedclass

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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

Vedclass · Accepted Answer

$T_1 < T_2 < T_3$

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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: $-\frac{dT}{dt} = k(T - T_s)$.As the temperature of the water decreases,the temperature difference between the water and the surroundings decreases.Consequently,the rate of cooling decreases,meaning the time taken to cool by a specific temperature interval increases.Since the initial temperature is highest for the first interval ($75^{\circ}C$ to $70^{\circ}C$),the rate of cooling is fastest,resulting in the shortest time $T_1$.As the water cools further,the temperature difference becomes smaller,leading to slower cooling and longer time intervals.Therefore,the relationship between the times is $T_1 < T_2 < T_3$.

$A$ 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 $T_3$. Which of the following relations is correct?

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