John von Neumann (1903-1957) was a very clever mathematician who offered the following advice:
- No one really knows what entropy really is, so in a debate you will always have the advantage (by pretending that you know).
This is still true, and causes a lot of confusion. If you want to improve your understanding then you could consult Computational Thermodynamics, which presents the 2nd Law of Thermodynamics resulting from the Euler equations for a compressible gas subject to finite precision computation in the following integrated form, with the dot signifying time differentiation (see the previous post):
- $\dot K+\dot P = W-D$
- $\dot E = -W + D$,
where $K$ is kinetic energy, $P$ potential energy, $W$ work, $E$ heat energy and $D\ge 0$ is turbulent dissipation with $W > 0$ under expansion and $W < 0$ under compression. The sign of $D$ sets the direction of time with always transfer of energy from $K+P$ to $E$ from turbulent dissipation.
Here turbulent dissipation is the same as entropy production or the other way around:
Here turbulent dissipation is the same as entropy production or the other way around:
- Entropy production is the same as turbulent dissipation.
This removes the mystery from entropy and you can now win any debate, by really knowing what entropy is!
For application an application see the recent post on Basic Atmospheric Thermodynamics and the 2nd Law.
Inlägg
Entropy production is the same as turbulent dissipation.
SvaraRaderaBut this would imply that that an isochoric (no volume work) process excludes entropy production? That can't be right since it contradicts empiric observations.
Doesn't the Neumann quote touch upon the fact that entropy, same as it's close companion energy, can't be explained with a more fundamental concept than itself? Nobody really knows what energy is either...
No, entropy production is the same as turbulent dissipation. Think of that!
SvaraRaderaJokes aside, whatever way you look at it, entropy has to be a measure of progression towards thermodynamic equilibrium. The Second Law of Thermodynamics tells us that entropy increases until an isolated system reaches thermodynamic equilibrium, whereupon entropy is then at a maximum attainable value within the constraints of the system.
SvaraRaderaHence the statement of the Second Law and the concept of entropy are mutually consistent.
No, entropy production is the same as turbulent dissipation.
SvaraRaderaI don't agree. A statement like that misses cases where there is no turbulent dissipation but still entropy production (radiation absorption and emission will become a total mess with this view).
Still worse, a system sufficiently small so that turbulent dissipation is a meaningless concept would then not have any entropy production at all (hurray, we are saved from the second law ;) ). Relate with the Hellman-Feynman theorem if you like, all forces are electrostatic in nature, there is no friction.
Equating entropy production and dissipation from turbulence are rather stupid since it obscures and completely murks the underlying physics. That can not be good and is most probably why it isn't a part of modern physics.
The Second Law of Thermodynamics tells us that entropy increases until an isolated system reaches thermodynamic equilibrium, whereupon entropy is then at a maximum attainable value within the constraints of the system.
SvaraRaderaOf course true.
Still, isolated systems are not really that interesting. The fun begins with open and closed systems...
One should think of turbulent dissipation as a general form of production of heat energy occuring in radiative heat transfer which thus can be included in the 2nd law I suggest to use.
SvaraRadera