consider a 38 degree F object placed in 68 F room write a differential equation for T thetemperature of the object at time t using k>0 for the constant of proportionality and write your equation in terms of T k and t

Question

Braylon Johnston

Physics

14 March, 07:37

consider a 38 degree F object placed in 68 F room write a differential equation for T thetemperature of the object at time t using k>0 for the constant of proportionality and write your equation in terms of T k and t

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Answers (1)

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Harmon · Answer 1

dY/dt = k (Y - Ys).

Explanation:

Okay, this question based on the law known as the Newton's law of cooling. According to Newton's law of cooling, when an object is placed into a specific or particular environment, the object's temperature will definitely be lower than the temperature of the surrounding or the environment.

So, we are given that the temperature of the object = 38 degree F = Y (o) of the object and the temperature of the environment = 68 degree F = Ys

Hence, dY/dt = k (Y - Ys).

dY / (Y - Ys) = kdt.