Nat R.
asked • 03/04/20Freshly cooked porridge starts at a temperature
T(0)=100 degrees Celcius. Assume that, in the room in which the porridge sits, the temperature is 21 degrees Celcius. Assume that porridge cools according to Newton's Law of Cooling with an unknown constant of proportionallityk. Solve the resulting InitialValue Problem for T(t).
Tom K. answered • 03/05/20
Knowledgeable and Friendly Math and Statistics Tutor
100 - 21 = 79
T(t) = 21 + 79 e -kt
Tom K.
The baby bear's porridge should be the coldest, as it has the highest ratio of surface area to volume, hence the greatest cooling coefficient, but this is not the case.03/06/20
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Nat R.
wondering if you know how to do the part b to this question? b) Goldilock's observation seems to be inconsistent with Newton's law of cooling. Describe the inconsistency. your answer should make reference to the ration A/V (surface area/volume) that appears in the constant of proportionality k. Make some simple assumptions about the bowls (stated explicitly) for the sake of illustrating with equations how your idea relates the bowl size to its temperature through time. k= (hA)/(PVcp ) where h is the heat transfer coefficient A is surface area of object P is density of objects material cp is mass-specific heat capicity of material V is volume of object03/05/20