If at instant t = 0 the temperature difference is ∆T0, show that at a later instant t the temperature will equal ∆T = ∆T0and^-At

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Hot or cold objects are observed to cool down or warm up, respectively, to reach
the temperature of the environment. If the temperature difference ∆T between the object and its neighborhood
(∆T = Tobjeto - Tvizinha¸ca) is not large, the cooling or heating rate of the object will be
approximately proportional to the temperature difference, i.e,
d ∆T/dt = -A (∆T) ,
where A is a positive constant. This is Newton's law of cooling.

a. Why is there a minus sign in the equation?
b. What factors does A depend on and what are its dimensions?
c. If at instant t = 0 the temperature difference is ∆T0, show that at a later instant t the temperature will equal
∆T = ∆T0and^-At

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