A Modification of the Newton's Cooling Law and Mpemba Effect

Details A Modification of the Newton's Cooling Law and Mpemba Effect A Modification of the Newton's Cooling Law and Mpemba Effect

2010-05-06

arxiv.org/abs/1005.1013v1

Physics

General Physics

4 pages, no figures

Scientific paper

In this work we suggest a simple modification of the Newton's cooling law that can model Mpemba effect. We introduce, in the usual Newton's law, i.e. linear differential equation, an additional term proportional to the quadrate of the geometrical average value of the initial and latter difference between liquid and cooling thermostat (environment) temperature. It, after simple transformations, yields usual Newton's linear differential equation but with modified cooling parameter. This modified cooling parameter represents sum of the usual cooling parameter and an additional term directly proportional to the difference between initial temperature of the liquid and cooling thermostat temperature. Corresponding solution of the modified Newton's cooling equation, i.e. temperature decrease during time, has an additional exponential term with negative argument proportional to mentioned difference between initial temperature of the liquid and temperature of the cooling thermostat. (It can be observed that appearance of such "hysteresis" or "memory" terms can imply some circulation effects by liquid flow but it goes over basic intention of this work.) It admits that liquid with higher initial temperature, after a characteristic time interval, cools faster than the same liquid with lower initial temperature, in full agreement with experimental data on the Mpemba effect.

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