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 50°F and that the rate constant is 0.07 (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 50°F and that the rate constant is 0.07 (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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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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 50°F and that the rate
constant is 0.07 (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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