3 ms·
Temperature is conventionally defined as the average kinetic energy of a collection of particles. Many thermo and statmech texts will use this phrase as an ope
by aphyr 14y ago
Temperature is conventionally defined as the average kinetic energy of a collection of particles.
Many thermo and statmech texts will use this phrase as an operational definition for temperature in idealized kinetic models, but the conventional thermodynamics definition is actually (as you note) T ~ ∂E/∂S.
Negative-temperature systems are perfectly possible in both theory and the lab; all you need is for an increase in energy to decrease the system's entropy. This is the first gas I've heard of with a negative temperature, but systems like electron spin in crystal lattices can have this property. :)
Amusingly, these systems don't transition from positive to negative temperatures by getting cooler and cooler, crossing through absolute zero. Instead their temperature increases towards positive infinity, flips to negative infinity, and rises asymptotically towards zero. Some folks like to think of temperature as the inverse (∂S/∂E) because this seems so unintuitive!
- cygx 14y agoTemperature is conventionally defined as the average kinetic energy of a collection of particles. More precisely, temperature is related to average energy per degree of freedom via the equipartition theorem. This doesn't only break down in case of negative temperatures, but also if continuity is no longer a good approximation for quantized energy levels. See http://physics.stackexchange.com/questions/33750/is-temperature-an-extensive-property-like-density/33752#33752 http://physics.stackexchange.com/questions/33750/is-temperat...
- frozenport 14y agoDoes stimulated emission hold this property? We increase the energy until the system lases but the entropy decreases as the gain narrows?
- jpdoctor 14y ago> Does stimulated emission hold this property? Yes. > We increase the energy until the system lases but the entropy decreases as the gain narrows? Typical model is the two level system. At abs 0+, all the electrons are in the lower state. at abs 0-, all the electrons are in the upper state.
- frozenport 14y agoSo are the photons in a laser at a negative temperature.
- jpdoctor 14y agoNo. The photon population is not in thermal equilibrium. (They are concentrated at one energy, rather than obeying the Bose-Einstein distribution vs energy.) More generally: A negative absolute temperature is possible only when the distribution of energy states is bounded by some maximum.