5 ms·
Small correction, not the ration of the energy to the entropy but the derivate of the energy by the entropy - that is, the rate at which the energy increases as
by jgeralnik 14y ago
Small correction, not the ration of the energy to the entropy but the derivate of the energy by the entropy - that is, the rate at which the energy increases as the entropy increases.
(Of course, it's slightly more confusing since it's actually the inverse of the temperature that's defined as dS/dE, which is the rate at which the entropy increases as the energy increases, a much more understandable definition. And as the physics professor who taught this to a room of students from various departments said of the transition from
1/T = dS/dE
to
T = dE/dS
"The mathematicians in the crowd will be in an uproar now. But we can do stuff like that in physics")
- rfurmani 14y agoIt's fine mathematics too, it's just like the chain rule (or interpreting the d notation via infinitesimals/limits)
- jgeralnik 14y agoThe problem is in the assumption that the inverse derivative exists, which is true for most functions in the real world but not for all (non-smooth) mathematical functions.
- deleted 14y ago[deleted]
- cygx 14y agoKeep in mind that the relations T = ∂E/∂S and 1/T = ∂S/∂E are normally associated with different levels of abstraction: T = ∂E/∂S is implied by the fundamental relation of (phenomenological) thermodynamics, whereas 1/T = ∂S/∂E gets derived from a microscopic theory via statistical mechanics.