Cooliette

Meet Cooliette, a hot cup left on the desk. She cools fast at first, then ever more slowly.

Newton's law of cooling says the rate at which an object's temperature changes is proportional to the difference between its temperature and its surroundings. The bigger the gap, the faster heat flows out. The constant k bundles the object's surface area, heat capacity and how well heat leaves its surface.

Solving the equation gives an exponential: the temperature difference shrinks by the same fraction in each equal interval of time. If a drink loses half its excess warmth over the room in ten minutes, it loses half of what remains in the next ten, and so on, approaching room temperature but never quite reaching it in the model.

Forensic scientists use cooling curves as one clue when estimating time of death, and engineers use the same model for cooling electronics.

Honest limits: the law works best for convective cooling with modest temperature differences. Radiation, evaporation and changing air flow make real cooling depart from a pure exponential, especially for very hot objects.