# A Differential Equation for Heat Transfer According to Newton's Law of Cooling

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Let be the temperature of a building (with neither heat nor air conditioning running) at time and let be the temperature of the surrounding air. Newton's law of cooling states that

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Contributed by: Stephen Wilkerson (March 2011)

(United States Military Academy West Point, Department of Mathematics)

Open content licensed under CC BY-NC-SA

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## Details

This is example 4, Heating and Cooling of a Building from [1], Section 1.1, Modeling with First Order Equations.

Reference

[1] J. R. Brannan and W. E. Boyce, *Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications*, New York: John Wiley and Sons, 2010.

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