And for newcomers to statistical thermodynamics, the principle of
equipartition of energy allows successful prediction of properties like the specific heat capacity of a gas.
You see, I don't remember matter being able to continually shed energy (continuous radiation) without a lose of temperature, energy will never transfer unless it should and then it must by temperature gradients always keeping in mind that we are speaking in an LTE environment along with
the equipartition of the degrees of available freedom, that I will call these microstates for brevity.
A drought / deluge / drought sigmoid is much less advantageous than
equipartition of an equal amount of precipitation over time, in particular if we do not know the lengths of droughts and deluges to expect.
It is
equipartition of the total energy of a each of the molecules.
So radiative transport is the reason the evolved isothermal atmosphere departs from
a equipartition of energy distribution?
This is why, for example, one can have non-equilibrium reactions AND
equipartition of energy all together.
That's it; it doesn't say any gobbledegook about
equipartitions of energy or gravity, or Einstein's theory of relativity; either special or general, or QED, or Maxwell's equations, or even the big bang.
Not exact matches
Directly testing this «
equipartition theorem» requires the velocity
of a particle to be measured, but Einstein predicted that its rapidly changing speed and direction would make that impossible.
This allowed them to obtain a measure
of the velocity every 5 microseconds and demonstrate that the
equipartition theorem holds (Science, DOI: 10.1126 / science.1189403).
You can look at this in terms
of equipartition.
Have you ever heard
of the
equipartition theorem?
Still, that little work to throw off
equipartition has shown it likely, by a probability
of something like 7 / 8ths, that significant warming has occured in those unmeasured expanses filling some sixth
of the planet surface.
The little work that has been done to overcome the assumption
of equipartition with regard to this lack, such as in Cowtan and Way, falls all too short
of what could be achieved had, for example, companies who use words like «exploration» and «discovery» in their advertising and lobbying, in the Luntzian sense, put a tiny amount toward maintaining weather stations for real exploration and real discovery.
Sadly, Tom assumes LTE, energy
equipartition, time symmetrical equations invariant under time reversal, and then caveats «the dynamics
of the Earth - atmosphere system» as well as «relaxation time».
In this case, enery is
equipartitioned (almost, it's slightly more complicated) which means there is an equal amount
of energy in three translational degrees
of freedom (for all species), two rotational degrees
of freedom for linear molecules only and three rotational degrees
of freedom in non-linear molecules, and 3n -(5 or 6) degrees
of vibrational freedom for (linear or non-linear) molecules IF those rotational or vibrational degress
of freedom are «accessible».
Actually the whole point
of LTE and energy
equipartition law is to make sure that all degrees
of freedom
of material particles interact sufficiently so that all energy forms are «well mixed».
Several commenters (including myself) have pointed out that
equipartition is not an invariable law and is not valid under conditions
of radiative pumping for example.
Not «Can CO2 heat N2 under conditions
of LTE, time symmetry and energy
equipartition?»
I don't know whether any
of the assumptions
of LTE,
equipartition, or Boltzmann statistics actually hold at the altitudes you are interested in.
Ed Fix The
equipartition law, like all such empirical laws, is a statistical approximation that becomes less and less accurate as the population
of gas molecules becomes smaller.
Over a sufficiently long period
of time, it follows from the
equipartition theorem and other principles
of statistical mechanics that every molecule in a gas will have the same average kinetic energy, the same average potential energy, and the same total energy, as any other molecule.
of the added heat energy goes directly into the usual increased kinetic energy
of the ideal gas, which is still precisely described by
equipartition and still has a local MB distribution
of velocities in any slice
of the gas large compared to the MFP and small compared to, so that my detailed balance argument is not, actually asymptotically incorrect.
and not
of the collegial variety [«If what you say is true, then how does the theory
of equipartition hold in the presence
of a temperature gradient with no work being done on the gas?»]
To re-balance horizontal and vertical KE and maintain equilibrium under
equipartition, a portion
of horizontal KE must be converted to vertical KE.
The average gravitational potential energy
of every molecular species is given by
equipartition theorem as kT / 2 per molecule.
Physics folk tend to think in terms
of «energy
equipartitioning»: that is, systems with 1 / f noise have no preferred scale at which to dissipate their energies.
But GHE is such a misnomer to me, IMHO it is roughly the local radiative resonance that keeps the air about any point in the atmosphere in radiative and LTE stasis (
equipartition across the available degrees
of freedom) and therefore maintains maximum warmth and it is performed mainly by GHGs radiation and to a smaller degree, conduction.
That is a whole lot
of words that I normally would not delve into for thermal equalization,
equipartition between the degrees
of freedom, and Fourier heat transfer handles all
of that in the tropopause case with a whole lot
of less words.