From the course: Complete Guide to Differential Equations Foundations for Data Science
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Cooling and heating
From the course: Complete Guide to Differential Equations Foundations for Data Science
Cooling and heating
- [Narrator] So far you have worked with opposites that are related such as growth and decay. Let's look at another set of opposites with cooling and heating. This begins by exploring Newton's law of cooling. Newton's law of cooling is essential to cooling and heating processes. Newton's law of cooling states the rate of change of the temperature of an object is proportional to the difference in the temperature between the object and its environment. This law is generally seen as a consequence of Fourier's law, also known as the law of heat conduction. The formula for Newton's law of cooling is given by D capital T, DT equals negative K multiplied by capital T minus capital TE. Note that this is where K is greater than zero and the rate of change of the object's temperature is given by D capital T over DT. The other variables in this formula are the temperature decay constant, which is represented by K, the temperature of the object at time T, which is represented by capital T and the…
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