Newton’s law of cooling

Definition

Newton’s law of cooling describes the rate at which an exposed body changes temperature through radiation. The rate of change of the temperature is proportional to the difference between its own temperature and the ambient temperature.

5 Must Know Facts For Your Next Test

1. The differential equation for Newton's law of cooling is $\frac{dT}{dt} = -k(T - T_{env})$, where $T$ is the object's temperature, $T_{env}$ is the ambient temperature, and $k$ is a positive constant.
2. This law assumes that the surrounding environment maintains a constant temperature.
3. The solution to the differential equation is $T(t) = T_{env} + (T_0 - T_{env}) e^{-kt}$, where $T_0$ is the initial temperature of the object.
4. It can be used to model real-life processes like cooling beverages or predicting time of death in forensic science.
5. The concept can be extended to exponential decay problems where factors other than temperature are involved.

Review Questions

• What does Newton’s law of cooling state about the rate of change in an object's temperature?
• Write down and solve the differential equation for Newton's law of cooling given initial conditions.
• How does Newton’s law of cooling apply to real-life scenarios such as forensic science?

Related terms

Exponential Decay: A process where a quantity decreases at a rate proportional to its current value.

$e$ (Euler's Number): $e$ is approximately equal to 2.71828 and is the base of natural logarithms. It commonly appears in continuous growth or decay models.

Differential Equation: An equation involving derivatives which represents how a quantity changes over time.