Home page for accesible maths 6 Chapter 6 contents 6.10 Further example 6.12 Solution to differential equation

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6.11 Newton’s law of cooling revisited

If the independent variable $t$ denotes time, then $\frac{dz}{dt}$ denotes the rate of change of $z$ with respect to time. For applications in physics, economics, biology or engineering, the rate of change can very often depend on both $z$ as well perhaps as $t$ .

Example.

Newton’s Law of Cooling The rate of change of the temperature $T$ of an object is proportional to the difference between its temperature and the temperature $\tau$ of its surroundings.

Assuming $\tau$ is constant, we can express this via the differential equation:

\frac{dT}{dt}=-\lambda(T-\tau)

where $\lambda$ is a positive constant.