A bucket full of water cools from 75^{circ}C | vedclass

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(C) According to Newton's Law of Cooling,the rate of cooling is proportional to the difference between the average temperature of the body and the sur

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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 proportional to the difference between the average temperature of the body and the surrounding temperature.Mathematically,$\frac{d	heta}{dt} \propto \left( \frac{	heta_1 + 	heta_2}{2} - 	heta_0 ight)$.Since the average temperature of the water decreases as it cools,the rate of cooling decreases over time.For the given intervals:Average temperature $1$: $\frac{75+70}{2} = 72.5^{\circ}C$Average temperature $2$: $\frac{70+65}{2} = 67.5^{\circ}C$Average temperature $3$: $\frac{65+60}{2} = 62.5^{\circ}C$Since the average temperature is highest for the first interval,the rate of cooling is fastest,meaning $T_1$ is the smallest time.Therefore,$T_1 < T_2 < T_3$.

$A$ bucket full of 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 is correct?

Similar Questions

Newton's law of cooling is based upon which of the following principles?

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