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(B) 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

$T_1 < T_2 < T_3$

Vedclass · Answer

(B) 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 $(T - T_s)$ between the water and the surroundings decreases.Since the rate of cooling $(-\frac{dT}{dt})$ is proportional to this difference,the rate of cooling decreases over time.Therefore,to lose the same amount of heat (a $5^{\circ}C$ drop),more time is required as the temperature approaches the ambient temperature.Thus,$T_1 < T_2 < T_3$.

Hot water is kept in a thermally insulated closed container. It takes $T_1 \, min$ for the temperature to drop from $75^{\circ}C$ to $70^{\circ}C$,$T_2 \, min$ to drop from $70^{\circ}C$ to $65^{\circ}C$,and $T_3 \, min$ to drop from $65^{\circ}C$ to $60^{\circ}C$. Then:

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