A black body calorimeter filled with hot wate | vedclass

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(B) According to Newton's Law of Cooling,the rate of cooling is proportional to the difference in temperature between the body and its surroundings: $

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$15$

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(B) According to Newton's Law of Cooling,the rate of cooling is proportional to the difference in temperature between the body and its surroundings: $\frac{dT}{dt} = k(T - T_s)$,where $T_s$ is the surrounding temperature.$CASE-1$: The body cools from $60^{\circ}C$ to $50^{\circ}C$ in $4 	ext{ min}$. The average temperature is $\frac{60+50}{2} = 55^{\circ}C$.$\frac{60-50}{4} = k(55 - T_s) \Rightarrow 2.5 = k(55 - T_s)$  $(1)$$CASE-2$: The body cools from $40^{\circ}C$ to $30^{\circ}C$ in $8 	ext{ min}$. The average temperature is $\frac{40+30}{2} = 35^{\circ}C$.$\frac{40-30}{8} = k(35 - T_s) \Rightarrow 1.25 = k(35 - T_s)$  $(2)$Dividing equation $(1)$ by $(2)$:$\frac{2.5}{1.25} = \frac{55 - T_s}{35 - T_s}$$2 = \frac{55 - T_s}{35 - T_s}$$70 - 2T_s = 55 - T_s$$T_s = 15^{\circ}C$Therefore,the temperature of the surrounding is $15^{\circ}C$.

$A$ black body calorimeter filled with hot water cools from $60^{\circ}C$ to $50^{\circ}C$ in $4 \text{ min}$ and from $40^{\circ}C$ to $30^{\circ}C$ in $8 \text{ min}$. The approximate temperature of the surrounding is ........ $^{\circ}C$.

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