Answer:
Explanation:
we can use Newton's law of cooling, which says that the rate of change of temperature of an object is directly proportional to the difference in temperature between the object and its surroundings.
Let's denote the initial temperature of the coffee as T0
The temperature of the freezer is Tr
The temperature of the coffee at any given time(t)as T(t)
The constant of proportion as k
According to Newton's law of cooling, we have the following equation:
(dT/dt) = k * (T - Tr)
Given that the initial temperature of the coffee is 104°F and the temperature of the freezer is 0°F, we substitute the value of k:
(k) = (dT/dt) / (T - Tr)
(k) = (51.3°F - 0°F) / (104°F - 0°F)
(k) = 51.3°F / 104°F
(k) ≈ 0.49375
Now, with the value of k determine the temperature of the coffee 11 minutes after it is placed in the freezer. Let's denote this temperature as T(11).
(dT/dt) = k * (T - Tr)
(dT/dt) = 0.49375 * (T - 0°F)
Separating variables and integrating, we have:
∫ dT / (T - 0°F) = ∫ 0.49375 dt
|T| = 0.49375t + C
Using the initial condition T(8) = 51.3°F, we can find the value ofC:
|51.3| = 0.49375 * 8 + C
C = ln |51.3| - 0.49375 * 8
Substituting the value of C, t = 11, and solve for T(11):
|T(11)| = 0.49375 * 11 + ln |51.3| - 0.49375 * 8
|T(11)| = e^(0.49375 * 11 + ln |51.3| - 0.49375 * 8)
T(11) ≈ 30.16°F
Therefore, the temperature of the coffee 11 minutes after it is placed in the freezer will be approximately 30.16°F when rounded to the nearest degree