A body cools from 75 , ^circ text{C} to 65 , | vedclass

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(A) According to Newton's law of cooling,the rate of cooling is given by $\frac{dT}{dt} = -k(T - T_s)$,where $T_s$ is the surrounding temperature.For

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$4$

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(A) According to Newton's law of cooling,the rate of cooling is given by $\frac{dT}{dt} = -k(T - T_s)$,where $T_s$ is the surrounding temperature.For the first interval: $\frac{75 - 65}{2} = k \left( \frac{75 + 65}{2} - 30 ight) \implies 5 = k(70 - 30) \implies 5 = 40k \implies k = \frac{5}{40} = \frac{1}{8} \, 	ext{min}^{-1}$.For the second interval: $\frac{55 - 45}{t} = k \left( \frac{55 + 45}{2} - 30 ight) \implies \frac{10}{t} = k(50 - 30) \implies \frac{10}{t} = 20k$.Substituting $k = \frac{1}{8}$ into the second equation: $\frac{10}{t} = 20 	imes \frac{1}{8} \implies \frac{10}{t} = 2.5 \implies t = \frac{10}{2.5} = 4 \, 	ext{min}$.

$A$ body cools from $75 \, ^\circ \text{C}$ to $65 \, ^\circ \text{C}$ in $2 \, \text{min}$ in a room at $30 \, ^\circ \text{C}$. How long will it take to cool from $55 \, ^\circ \text{C}$ to $45 \, ^\circ \text{C}$ in the same room?

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