Final answer:
The temperature T of the liquid satisfies the differential equation T' = -k(T - 3). The temperature as a function of time is T(t) = 3 + (46 - 3)e^(-kt) and the cooling constant is approximately 0.0579.
Step-by-step explanation:
Using Newton's law of cooling, we are given that T' = -k(T - T0) where T is the temperature of the liquid, T0 is the ambient temperature (in this case, the temperature inside the fridge), and k is the cooling constant. So the differential equation that the temperature T of the liquid satisfies is T' = -k(T - 3)
To find the temperature of the liquid as a function of time, we solve this differential equation. The solution to this is T(t) = T0 + (T(0) - T0)e^(-kt). We know that T(0) is 46°C, so we have T(t) = 3 + (46 - 3)e^(-kt).
Last, we find the liquid cooling constant k. We know that after 10 minutes (or 10/60 hours), the temperature is 16°C. Solving T(t) = 16 for k, we get k = ln((16 - 3) / (46 - 3)) / -10/60. Thus, we find the cooling constant to be approximately 0.0579.
Learn more about Newton's Law of Cooling