Newton's cooling

Newton’s law of cooling states that the temperature difference between a hot body and its surroundings decays exponentially:

$T(t)-T_{\text{amb}}=(T_0-T_{\text{amb}})\,e^{-t/\tau}.$

Example — A cooling coffee

A coffee at $90\,°\text{C}$ in a room at $20\,°\text{C}$ with $\tau=10\,\text{min}$: after $20\,\text{min}$ it is at $20+70/e^2\approx 29{,}5\,°\text{C}$.

Links

Topics: Exponential function
Concepts: Exponential decay · Euler’s number
Functions: Exponential function
Skills: Modelling · Using formulae
People: Isaac Newton