A beaker full of hot water is kept in a room. | vedclass

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(B) According to Newton's Law of Cooling,the rate of cooling $\frac{dT}{dt}$ is directly proportional to the temperature difference between the body a

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$t_1 < t_2 < t_3$

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(B) According to Newton's Law of Cooling,the rate of cooling $\frac{dT}{dt}$ 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 $(T - T_s)$ between the water and the room decreases.Since the rate of cooling decreases as the temperature difference decreases,the time taken to cool by the same amount $(5\,^{\circ}C)$ will increase.Therefore,$t_1 < t_2 < t_3$.

$A$ 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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