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Q & A: what does temperature mean?

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Most recent answer: 02/16/2013
Sir,Is temperature a microscopic or macroscopic concept?
- Aqib (age 18)
The usual definition of temperature is T= dU/dS|V where U is the internal energy of an object, S is its entropy, and "|V" means "at constant volume". This doesn't quite make sense for a microscopic object, for which specifying U may specify what state the object is in, and thus force S=0. So we usually think only of macroscopic objects as having a temperature.

There is a microscopic version of this meaning, however. Over time a microscopic system that can exchange energy with the outside will sample various different states with different energies. So you can define an average U and and S based on the probabilities of the different states. If these probabilities follow the right sort of pattern then you can talk about T of the time-averaged microscopic object.

Mike W.

(published on 02/16/2013)

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