Meaning of Temperature
Most recent answer: 10/22/2007
- Anonymous
hyderabad
T=dU/dS (taken at constant volume), where U is the total energy of some system and S is the entropy (a measure of how many quantum states are available to it) in conventional units. Now that derivative doesn’t make any sense for really microscopic systems, at least at any particular time. In fact, if you specify what quantum state a system is in (a reasonable thing to do for an atom, for example), S=0 by definition. So T is really a meaningful quantity only for macroscopic systems. However, for a microscopic system exchanging energy with the outside over time one can describe the probabilities of the system being in its different states. If those probabilities follow the Boltzmann distribution, then one can speak of the T of the microscopic system. The reason for them to follow that distribution, however, is the energy exchange with the macroscopic environment. So something macroscopic ends up involved either way.
Mike W.
(published on 10/22/2007)
Follow-Up #1: meaning of temperature
- Byron
USA
Mike W.
(published on 03/07/2010)
Follow-Up #2: Energy, entropy, and temperature
- Francis F. Kish (age 89)
FLORE. ACT. Australia
I'm not sure I understand the first question. The definition of T involves the quantity of energy, but with the assumption that this energy has the quality of having being randomly distributed among the modes of the system.
It's of course easy for two systems to have different energies and the same T. Consider a little block of copper and a big block at the same T. Probably you're thinking of something less trivial. An example would be a kg of ice at 0°C and a kg of water at 0°C. There's more energy in the water but they're at the same T. This effect is possible at first-order phase transitions (like the liquid-solid transition here) where there's a coincidence in which the free-energies (which also include an entropy term) of two different forms happen to be equal.
Mike W.
(published on 07/25/2012)