Table of Contents
What Is Newton's Law of Cooling?
Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in temperature between the body and its surroundings. This exponential decay model works well when the temperature difference is not too large and natural convection is the dominant heat transfer mechanism.
The law was formulated by Sir Isaac Newton and is widely used in forensic science (estimating time of death), food safety (cooling curves), thermal engineering, and climate science. The cooling constant k depends on the thermal properties of the object, its surface area, and the heat transfer coefficient.
Formula
Where T(t) is temperature at time t, Tenv is ambient temperature, T0 is initial temperature, k is the cooling constant, and t is time.
Examples
| Scenario | Typical k (per min) |
|---|---|
| Coffee in ceramic mug | 0.02-0.05 |
| Metal part in still air | 0.005-0.02 |
| Body in room temp | 0.01-0.03 |
| Water in insulated container | 0.002-0.005 |
Frequently Asked Questions
How do I find the cooling constant k?
Measure the temperature at two different times. Using the formula: k = -ln((T2-Tenv)/(T1-Tenv))/(t2-t1). Alternatively, plot ln(T-Tenv) vs time; the slope gives -k.
Does Newton's law apply to heating?
Yes. The same equation applies when an object is colder than its environment. The object warms up exponentially toward ambient temperature using the same formula. The temperature difference decreases exponentially regardless of whether the object is cooling or heating.