Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (the ambient air temperature in most cases). Suppose that the ambient temperature is 70°F and that the rate constant is 0.04 (min) ¹. Write a differential equation for the temperature of the object at any time. Note that the differential equation is the same whether the temperature of the object is above or below the ambient temperature. NOTE: Use u for the temperature of the object in °F and t for time. du dt ||
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (the ambient air temperature in most cases). Suppose that the ambient temperature is 70°F and that the rate constant is 0.04 (min) ¹. Write a differential equation for the temperature of the object at any time. Note that the differential equation is the same whether the temperature of the object is above or below the ambient temperature. NOTE: Use u for the temperature of the object in °F and t for time. du dt ||
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Newton's law of cooling states that the temperature of an object
changes at a rate proportional to the difference between the
temperature of the object itself and the temperature of its
surroundings (the ambient air temperature in most cases).
Suppose that the ambient temperature is 70°F and that the rate
constant is 0.04 (min) ¹. Write a differential equation for the
temperature of the object at any time. Note that the differential
equation is the same whether the temperature of the object is above
or below the ambient temperature.
NOTE: Use u for the temperature of the object in °F and t for time.
du
dt
||
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Transcribed Image Text:Newton's law of cooling states that the temperature of an object
changes at a rate proportional to the difference between the
temperature of the object itself and the temperature of its
surroundings (the ambient air temperature in most cases).
Suppose that the ambient temperature is 70°F and that the rate
constant is 0.04 (min)-¹. Write a differential equation for the
temperature of the object at any time. Note that the differential
equation is the same whether the temperature of the object is above
or below the ambient temperature.
NOTE: Use u for the temperature of the object in °F and t for time.
du
dt
-0.05 (u - 70)
X
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