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Newton's law of cooling
Intermediate
Cooling rate is proportional to temperature difference.
dT/dt = −k(T−T₀)The cooling rate is proportional to the temperature difference with the surroundings: T(t) = T_s + (T₀ − T_s)e^{−kt}.
Coffee at 90 °C in a 20 °C room halves its excess in minutes.
Valid for small differences.
In more detail
Newton's law of cooling states that the rate of heat loss is proportional to the temperature difference between an object and its surroundings. Hot objects cool quickly at first and then more slowly.
Real-world uses
- Forensic scientists estimate time of death from body temperature.
- Coffee cools faster when it is hotter.
- A cup of hot tea cools quickly at first and then slowly as it approaches room temperature, following Newton's law of cooling.
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Frequently asked questions
Is it exact?
It is an approximation, valid for small temperature differences.
Does the rate depend on the surroundings?
Yes, the temperature of the surroundings sets the final equilibrium.
Is Newton's law of cooling exact?
It is a good approximation for small temperature differences. For large ones, radiation and other effects make the cooling rate depend on temperature in a more complex way.
Related topics in Heat & Thermodynamics
Convection · Radiation · Stefan–Boltzmann law · Wien's displacement law · Blackbody radiation · Ideal gas laws