Computational BlackBody Radiation offers a new proof of the Planck-Stefan-Boltzmann Law PSB based on electromagnetic wave resonance under deterministic finite precision computation, taking the form
- $Q = \sigma (T_A^4 - T_B^4),$ (1)
where $Q$ is (normalised) radiative transfer of heat energy between two blackbodies A and B with temperatures $T_A$ and $T_B$ Kelvin, and $\sigma$ is the SB constant. If $T_A>T_B$ then the heat transfer is from A to B.
This is to be compared with the 1900 proof by Planck based on particle/quanta statistics typically expressed on the following form involving only one blackbody of temperature $T$:
- $Q = \sigma T^4.$ (2)
Comparing (1) and (2) we see that (1) expresses the radiative heat transfer between two bodies in resonance, while (2) is supposed to express the radiative heat transfer from one body independent of surrounding bodies and thus without resonance.
In particular, (1) expresses that heat transfer from A requires the presence of a receptor B with lower temperature. On the other hand (2) appears to express that a body can radiate (spit out quanta/photons) without receptor, or assuming the presence of "empty space" at 0 Kelvin acting as receptor. In this case the body at higher temperature will spit most and so win the combat.
This leads to the following questions:
- Does radiative heat transfer from one body need a receptor at lower temperature?
- Does radiative heat transfer involve a resonance phenomenon between bodies?
The new proof of PSB suggests that the answer is YES, while the standard proof suggests NO. What does physics and observation say? YES or No? Is radiative heat transfer carried by electromagnetic waves or particles/photons? An answer that it is both is no good. The questions concern basic physics and must be answered.
Compare with resonance between two tuning forks:
To be compared with a particle model with both forks spitting out particles/phonons?
PS Read about Planck's struggle to prove (2) in Quantum Mechanics at the Crossroads starting with Schrödinger Against Particles and Quantum Jumps by M. Bitbol and continuing with Max Planck's Compromises on the Way to and from the Absolute by J. L. Heilbron.
Yes, it is not a good idea to resort to compromises in science, which is the essence of politics. Planck was not happy with his particle/quanta statistics and neither was Schrödinger, yet it has come to serve as a fundamental part of quantum mechanics following Born-Bohr. Real Quantum Mechanics in the spirit of Schrödinger presents a new realist deterministic approach based on waves instead of particle statistics.
Inlägg
Hi, Claes.
SvaraRaderaSo I'm looking for a new forum... one based upon scientific reality. Seems that every time I present my proof that the fundamental physical laws are inviolable, that energy doesn't flow spontaneously unless there is an energy density gradient, the forum moderator goes loco and buys into some unscientific drivel.
I had one who, after I presented mathematical evidence of the above, started spouting off that Earth started really small and continues to grow, which is why dinosaurs had such huge rear legs... they hopped everywhere in Earth's early lower gravity.
Jo Nova sided with the warmists and outright personally attacked me.
Joe Postma just bought into an Idealist Illuminist theological belief system which states that the Big Bang wasn't so much a bang as an internal, mathematical reshuffling... it's still a singularity, we exist in zero dimensions within that singularity, and it is sentient 'monads' (from the 9th century Islamic Asharite Occasionalism, modified by Leibniz to remove the miracles and physical impossibilities, then modified by the anonymous group posing as "Mike Hockney" to update the language to incorporate quantum theory (while otherwise bashing quantum theory as "nonsensical") which create the illusion of time and space. We, according to this belief system, are illusions... all of reality is. The only real things are the singularity (which remains a singularity) and the sentient monads. Postma's bought into to such an extent he wants to start a religion based upon it.
I'm not sure why that keeps happening... I suspect that most people NEED there to be some randomness in the universe so they can escape the consequences of their own actions throughout life... but they want that randomness to be directed so there isn't chaos, and thus the invent a god or gods to direct that randomness.
Anyway, from what I've read of your writings, your beliefs exactly coincide with mine. So I'll hang out here for awhile and contribute... please don't go unhinged like the others.
So this is the basis of what I state... do let me know if I've made any errors.
SvaraRaderahttps://i.imgur.com/QErszYW.gif
Idealized Blackbody Object (assumes emission to 0 K and ε = 1):
q_bb = ε σ (T_h^4 - T_c^4) Ah
= 1 σ (T_h^4 - 0 K) 1 m^2
= σ T4
Graybody Object (assumes emission to > 0 K and ε < 1):
q_gb = ε σ (T_h^4 - T_c^4) Ah
The 'Ah' term is merely a multiplier, used if one is calculating for an area larger than unity [for instance: >1 m^2], which converts the result from radiant exitance (W m-2, radiant flux per unit area) to radiant flux (W).
Temperature is equal to the fourth root of energy density divided by Stefan's Constant (ie: the radiation constant).
e = T^4 a
a = 4σ/c
e = T^4 4σ/c
T^4 = e/(4σ/c)
T = 4^√(e/(4σ/c))
T = 4^√(e/a)
Since we're using the Kelvin temperature scale, which has its base at 0 K, we can calculate temperature (and thus energy density) as above. Energy density at 0 K is zero, thus temperature at zero energy density is, of course, 0 K.
q = ε σ (T_h^4 - T_c^4)
∴ q = ε σ ((e_h / (4σ / c)) – (e_c / (4σ / c))) A_h
Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = W m-2 K-4 * (Δ(J m-3 / (W m-2 K-4 / m sec-1)))
∴ q = σ / a * Δe = W m-2
Canceling units, we get
W m-2 = (W m-2 K-4 / J m-3 K-4) * ΔJ m-3
∴ q = (ε c (e_h - e_c)) / 4
One can easily see from the equation above that the S-B equation is all about subtracting the energy density of the cooler object from the energy density of the warmer object.
Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = (m sec-1 (ΔJ m-3)) / 4
For graybody objects, it is the energy density differential (ie: the energy density gradient) between warmer object and cooler object which determines warmer object radiant exitance. The climate alarmists misinterpret the S-B radiant exitance equation for graybody objects (intentionally so to bolster their narrative).
Warmer objects don't absorb radiation from cooler objects (a violation of 2LoT in the Clausius Statement sense and Stefan's Law); the lower energy density gradient between warmer and cooler objects (as compared to between warmer object and 0 K) lowers radiant exitance of the warmer object (as compared to its radiant exitance if it were emitting to 0 K). The energy density gradient is brought about because each surface's energy density manifests a proportional radiation pressure, that EM field gradient extending into the space between objects.
Thus, the climastrologists cling to the long-debunked Prevost Principle (whether they know it or not... and if they don't know it, then they really have no business being anywhere near anything related to science) when they claim that energy can radiatively flow without regard to energy density gradient... and that leads to all manner of unscientific drivelry... 'backradiation', 'Global Warming Potential', 'carbon footprint', the incorrect usage of the S-B equation in the K-T (Kiehl-Trenberth) diagram and even in instruments such as pyrgeometers and FTIR spectrometers, and ultimately in their core narrative: CAGW.
The S-B equation for graybody objects isn’t meant to be used to subtract a fictive ‘cooler to warmer’ energy flow from the incorrectly-calculated and thus too high ‘warmer to cooler’ energy flow, it’s meant to be used to subtract cooler object energy density (temperature is a measure of energy density, the fourth root of energy density divided by Stefan’s constant) from warmer object energy density. Radiant exitance of the warmer object is predicated upon the energy density gradient.
Ok, the basics out of the way, let us look at why energy only flows down an energy density gradient, why it will not flow if there is no energy density gradient, and why it will absolutely not flow against an energy density gradient with higher chemical potential than the photon's.
SvaraRaderaTake a look at the S-B equation:
https://i.imgur.com/QErszYW.gif
It's pretty easy to see from the animated .GIF above that at thermodynamic equilibrium, radiant existance of a graybody object is going to be zero. But how and why does this happen?
Remember that idealized blackbody objects have their emissivity and absorptivity pegged to 1 all the time by definition... they maximally emit (and absorb).
But for graybody objects, as two objects approach thermodynamic equilibrium with each other, emissivity and absorptivity of the objects tend toward zero.
Thus, while an idealized blackbody object emits when its temperature is > 0 K, a graybody object emits when its temperature is > 0 K above its ambient. This is plainly evident in the animated graphic above.
The definition of emissivity: The ratio of the total emissive power of a body to the total emissive power of a perfectly black body at that temperature.
The definition of absorptivity: The ratio of the absorbed to the incident radiant power.
Do remember that temperature is a measure of energy density, equal to the fourth root of energy density divided by Stefan’s Constant.
As Δe → 0, ΔT → 0, q → 0. As q → 0, the ratio of graybody object total emissive power to idealized blackbody object total emissive power → 0. In other words, emissivity → 0. At thermodynamic equilibrium for a graybody object, there is no energy density gradient and thus no impetus for photon generation.
As Δe → 0, ΔT → 0, photon chemical potential → 0, photon Helmholtz Free Energy → 0. At zero chemical potential, zero Helmholtz Free Energy, the photon can do no work, so there is no impetus for the photon to be absorbed. The ratio of the absorbed to the incident radiant power → 0. In other words, absorptivity → 0.
α = absorbed / incident radiant power
ρ = reflected / incident radiant power
τ = transmitted / incident radiant power
α + ρ + τ = 100%
For opaque surfaces τ = 0% ∴ α + ρ = 100%
If α = 0%, 0% + ρ = 100% ∴ ρ = 100% … all incident photons are reflected at thermodynamic equilibrium for graybody objects.
This coincides with standard cavity theory… applying standard cavity theory outside a cavity, for two graybody objects at thermodynamic equilibrium, no absorption or emission takes place. The photons remaining in the intervening space set up a standing wave, with the wavemode nodes at the object surfaces by dint of the boundary constraints. Nodes being a zero-crossing point (and anti-nodes being the positive and negative peaks), no energy can be transferred in or out of the objects. Photon chemical potential is zero, they can do no work. Photon Helmholtz Free Energy is zero, they can do no work. Should one object change temperature, the standing wave becomes a traveling wave with the group velocity proportional to the energy density gradient and in the direction of the cooler object.
Do remember that photons, each a quanta of energy, are considered the force-carrying gauge bosons of the EM interaction.
SvaraRaderaGoing back to dimensional analysis:
We start with Energy:
Energy: [M1 L2 T−2]
And we subtract Force:
Force: [M1 L1 T-2]
Over Distance:
Distance: [M0 L1 T0]
[M1 L2 T−2]
[M1 L1 T-2]
[M0 L1 T0]
We are left with nothing on the 'transmitting' end... [M0 L0 T0]. In other words, that Energy is used for apply a Force over a Distance.
That Force applied over a Distance gives us (on the 'receiving' end):
Force: [M1 L1 T-2]
Length: [M0 L1 T0]
Work: [M1 L2 T-2]
You'll note that Energy and Work have the same units:
Work: [M1 L2 T-2]
Energy: [M1 L2 T−2]
There's a reason for that. Free Energy is defined as that energy capable of performing work. I use Helmholtz Free Energy in my post above (and in this post, below).
Object 1 Energy: [M1 L2 T−2] = Object 2 Energy: [M1 L2 T−2], Free Energy is zero, no work can be done. No energy can flow.
Object 1 Energy: [M1 L2 T−2] > Object 2 Energy: [M1 L2 T−2], Free Energy is non-zero, work can be done by Object 1 upon Object 2. Energy must flow from Object 1 to Object 2.
Object 1 Energy: [M1 L2 T−2] < Object 2 Energy: [M1 L2 T−2], Free Energy is non-zero, work can be done by Object 2 upon Object 1. Energy must flow from Object 2 to Object 1.
This is reflected in the equation for Helmholtz Free Energy (represented here as a single object and its environment):
F = U – TS
Where:
F = Helmholtz Free Energy (J)
U = internal energy (J)
T = absolute temp (K)
S = system final entropy (J K-1)
TS = energy the object can receive from the environment (J)
If U > TS, F > 0… energy must flow from object to environment.
If U = TS, F = 0… no energy can flow to or from the object.
If U < TS, F < 0… energy must flow from environment to object.
Of course, in a system comprising only two objects and no environment other than those two objects, the equation for Helmholtz Free Energy would be:
SvaraRaderaF = U_1 - U_2
Now, compare that to what I wrote above:
==========
https://i.imgur.com/QErszYW.gif
∴ q = (ε c (e_h - e_c)) / 4
One can easily see from the equation above that the S-B equation is all about subtracting the energy density of the cooler object from the energy density of the warmer object.
Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = (m sec-1 (ΔJ m-3)) / 4
==========
You'll see that the S-B equation is all about subtracting the energy density of the cooler object from the energy density of the warmer object because Free Energy is all about subtracting the energy density of the cooler object from the energy density of the warmer object.
Hence the climastrologists misuse the S-B equation by treating real-world graybody objects as if they are idealized blackbody objects, by using the form of the S-B equation meant for idealized blackbody objects:
q = σ T^4
... and slapping emissivity onto that (sometimes... they didn't in the Kiehl-Trenberth graphic):
q = ε σ T^4
This presupposes emission to 0 K, and thus inflates radiant exitance for all graybody objects, necessitating that the climastrologists carry those incorrect values through their calculation and cancel them on the back end, essentially subtracting a wholly fictive 'cooler to warmer' energy flow from the real (but calculated for emission to 0 K and thus too high) 'warmer to cooler energy flow.
Their doing so implies that energy can flow 'cooler to warmer' and thus violates 2LoT.
Further, their assumption means they must claim graybody objects > 0 K emit and absorb radiation, which leads to double the energy density in a cavity space than what we calculate from Stefan's Law... so it also violates Stefan's Law.
Even further, their assumption that graybody objects > 0 K emit and absorb means they are forced to claim that radiative energy transfer is an idealized reversible process, because at thermodynamic equilibrium, entropy doesn't change... but energy can only flow without entropy changing if that energy flow is an idealized reversible process... but we know radiative energy flow is a temporal, entropic and irreversible process... so their methodology also violates the Principle of Entropy Maximizaton.
They should be using the form of the S-B equation for graybody objects:
q = ε σ (T_h^4 - T_c^4)
They do not do so for a reason... misusing the S-B equation is the only way they can get their doomsaying climate alarmism to mathematically reconcile.
Even worse is that they then further misuse the S-B equation by converting it into what they call a “forcing formula” (used in IPCC AR6):
4 ε σ T^3
… which builds-in a warming trend:
----------
For 288 K, a 1 K negative temperature change, ε=0.93643 (ref: NASA ISCCP program):
4 ε σ T^3 = 5.07369679087621 W m-2
For 288 K, a 1.00525093764635 K negative temperature change, ε=0.93643 (ref: NASA ISCCP program):
q = ε σ T^4 = 5.07369679087621 W m-2
----------
For 288 K, a 1 K positive temperature change, ε=0.93643 (ref: NASA ISCCP program):
4 ε σ T^3 = 5.07369679087621 W m-2
For 288 K, a 0.99474906235365 K positive temperature change, ε=0.93643 (ref: NASA ISCCP program):
q = ε σ T^4 = 5.07369679087621 W m-2
----------
So their equation gives the result for a warming of 0.99474906 K while claiming it's a warming of 1 K, and gives the result for a cooling of 1.00525093 K while claiming it's a cooling of 1 K.
And that's likely why they altered the S-B equation... to hide the fact that they continue to treat real-world graybody objects as idealized blackbody objects, and to build-in whatever warming trend they possibly could in order to help sustain their alarmist narrative.
I'm actually amazed that Planck was able to arrive at the conclusions he did, given his weird notion of photons.
SvaraRaderaFrom my prior writings:
"Planck (a former student of Kirchhoff and his successor as lecturer at Berlin’s Friedrich Wilhelms University) erred in confusing ‘temperature’ and ‘heat’ in The Theory of Heat Radiation [5, § 46], and in failing to properly validate Kirchhoff’s Law (from which he derived his equation). His attempt at validating Kirchhoff’s Law in his book is filled with errors… he had to redefine blackbodies to be predicated upon transmissivity (except idealized blackbodies by definition are opaque, zero transmissivity); he ignored absorptivity at the interface of the blackbody (he claimed that the state of photons on the surface and inside the material were identical, and that as a photon traversed through a material, it was successively absorbed); he used polarized light in his experiments (whereas thermal radiation is never polarized) and thus misused Brewster’s Law; and he, like Kirchhoff, cheated a bit by using a small chunk of graphite or carbon as a thermalizer (what he called a ‘catalyst’) in a perfectly reflecting cavity (which cannot otherwise exhibit a blackbody spectrum because the radiation field can do no work upon the walls nor the walls upon the radiation field). In short, Planck held a weird view of what photons were and how they interacted with matter. His definition of a blackbody didn’t even coincide with Kirchhoff’s definition (nor with the standard definition). Planck also erred in clinging to a long-debunked radiative model (Prevost Theory of Exchanges and its core tenet, Prevost's Principle), and his follow-on assumptions stemming from that led to his treating real-world (graybody) objects as though they radiatively emit willy-nilly without regard to the energy density gradient."
Planck held the notion that photons were akin to worms burrowing through dirt and being successively ablated as they went. That's why he ignored absorptivity at the interface of an object, claiming that the photon state at the surface and inside the object were the same.
It is via Planck's clinging to the long-debunked Prevost Principle that we have the warmist CAGW problem to contend with today, to wit and again from my prior writings:
SvaraRadera"Planck correctly stated:
“Conduction of heat depends on the temperature of the medium in which it takes place, or more strictly speaking, on the non-uniform distribution of the temperature in space, as measured by the temperature gradient.”
Do remember that temperature is equal to the fourth root of energy density divided by Stefan's Constant... temperature is a measure of energy density. In other words, Planck correctly stated that energy can only flow (the definition of ‘heat’) via conduction if there is a temperature (and therefore an energy density) gradient.
Where Planck erred is in his clinging to the Prevost Theory Of Exchanges (and its core tenet, the Prevost Principle) in regard to radiative energy, which led him to eschew scientific reality (that energy only flows if there is an energy density gradient), to wit:
“But the empirical law that the emission of any volume-element depends entirely on what takes place inside of this element holds true in all cases (Prevost’s principle).”
The immediate corollary to Prevost’s Principle is that E = e… that the actual emission is equal to the disposition to emit, which is false, implying that an object must emit all energy it absorbs (the definition of idealized blackbody objects, which do not and cannot exist).
A further corollary to Prevost’s Principle is that A = I * a… that the actual absorption is equal to the intensity of the incident beam times the disposition to absorb, which is again false, implying that excited quantum states have the same disposition to absorb as do unexcited quantum states (again, the definition of idealized blackbody objects, which do not and cannot exist).
Of course, Prevost, in 1791, didn’t know of quantum states, so he couldn’t have known that the corollaries to Prevost’s Principle were incorrect."
For those averse to signing up or providing an email address, you can still access all the texts mentioned in the OP via:
SvaraRaderahttps://sci-hub.se/10.1007/978-3-540-32665-6
Claes, if you could explain the below, it'd be much appreciated. It's difficult to properly format on a forum, so I've got a PDF of all of this, if you want it.
SvaraRaderaOk, here's where we get deep... I constructed a model dry atmosphere consisting of 16 atomic and molecular species, with the percentages of each adjusted to total 100% (most of the atmospheric concentration data you find online exceeds 100%).
From that, I calculated the number of electrons per mol of atmosphere:
8707690981705880560000000 electrons / 6.02214076e23 mol-1_particles = 14.45946106 mol_electrons mol-1_particles
IOW, there is an average of 14.45946106 electrons per atmospheric particle (atom, molecule), or 14.45946106 moles of electrons per mole of atmospheric particles.
1.602176634e-19 J electron-1 * 8707690981705880560000000 electrons mol-1_particles = 1395125.902698168329362683504 J mol-1_particles
Checking our math: 14.45946106 mol_electrons mol-1_particles * 96485.3321233100184 J mol-1 = 1395125.902698168329362683504 J mol-1_particles
From that, I derived the radiant exitance three different ways...
Using Faraday’s Constant [F(Ah)]:
26.801481145363894 Ah mol-1 * 14.45946106 moles of electrons per mole of atmospheric particles = 387.53497297171342482296764 W m-2
Using the S-B equation:
σ = (2 π^5 K_B^4)/(15 h^3 c^2) = 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4
Where:
σ = Stefan-Boltzmann Constant (5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4)
kB = Boltzmann Constant (1.380649e−23 J K−1)
h = Planck Constant (6.62607015e−34 J Hz−1)
c = light speed (299792458 m sec-1)
(287.52445649918761281451967994314 K)^4 * σ = 387.53497297171342482296764 W m-2
Assuming 1 hour (to cancel Wh) and assuming each mole of particles forms a 1 m^2 surface:
SvaraRadera1395125.902698168329362683504 J mol-1particles / (1 J sec-1 W-1 * 3600 sec hour-1) = 387.53497297171342482296764 Wh / 1 hr * 1 m-2 = 387.53497297171342482296764 W m-2
23 decimal places... each of those is exact with the others to 23 decimal places. That can't be a mere coincidence.
Where does 3600 come from?
By combining the 2nd and 3rd equations, the relation can be seen more easily here:
1395125.902698168329362683504 J mol-1_particles / ((287.52445649918761281451967994314 K)^4 * σ) = 3600
So that’s the SI unit of energy per mole of material, divided by the temperature to the fourth power times the Stefan-Boltzmann Constant. And out of that comes time. It would appear that time is baked-in to the thermodynamic equations.
∴ J mol-1 / (K^4 * σ) = J mol-1 / (F(Ah) * moles of electrons per mole of particles) = 3600
∴ (K4 * σ) = (F(Ah) * moles of electrons per mole of particles) = radiant exitance (W m-2)
Why did I do all of the above? Because another poster noticed a correlation between the number of moles of electrons per mole of atmospheric particles (atoms, molecules) and the temperature.
In fact, I was able to derive the average humidity from the above, and determine that the average number of atoms per molecule in a mol of atmosphere seems to drive whether warming or cooling will occur... when the average dips below 2 (extremely low humidity), the atmosphere warms... it needs the polyatomic H2O to drive the average above 2 to cause radiative cooling to exceed warming.
The majority of the dry atmosphere (~99%) consists of homonuclear diatomics (N2, O2), with two atoms per molecule. In an atmosphere consisting of solely homonuclear diatomics, the ‘atoms per particle’ ratio would be 2. Obviously, monoatomics (especially Ar) and polyatomics (especially H2O) skew the ‘atoms per particle’ ratio a bit (1.991069298).
If we take the molar mass of the atmosphere (28.96599225582808 g mol-1) and divide it by the average number of atoms per particle (atom or molecule) in a mole of atmosphere (1.991069298), we get 14.547957866119474461405712459537.
Not quite the 14.45946106 moles of electrons per mole of atmospheric particles that we calculated, but very close. What makes up the difference?
Well, if we displace N2, O2 and Ar in the atmosphere with water vapor, and solve for 14.45946106, it gives 1.1512951958965% water vapor, when dividing the total molar mass of the atmosphere by the atoms per particle of the dry atmosphere.
The above ties into my contention that the actual 'greenhouse gases' are the monoatomics and homonuclear diatomics. Think about how an actual greenhouse works... by hindering convection.
SvaraRaderaNow, in an atmosphere consisting solely of monoatomics and homonuclear diatomics, they could gain energy via conduction by contacting the surface (just as the polyatomic radiative molecules can do), they could convect (just as the polyatomic radiative molecules can do), but once in the upper atmosphere they could not as effectively radiatively emit (because monoatomics have no vibrational mode quantum states and thus cannot emit nor absorb IR; and because the homonuclear diatomics have a net-zero magnetic dipole and thus cannot emit (nor absorb) IR unless that net-zero magnetic dipole is perturbed via collision)... the upper atmosphere would warm, which would lend less buoyancy to parcels of air attempting to convect, and that would hinder convection.
And from there, I was able to derive a molar heat capacity lapse rate equation, rather than the usual mass heat capacity lapse rate equation... and in so doing, I discovered that both forms of the lapse rate equation aren't fit for purpose... they both treat all particles (atoms, molecules) as if they can dump energy to space, they both assume that once that energy leaves the surface, it's gone and out of the system... which most certainly isn't the case for monoatomics and homonuclear diatomics (which cannot effectively emit IR).
So, Claes, if you could help me to flesh out my knowledge of the above, and to develop a new lapse rate equation that takes into account whether or not an atmospheric particle (atom, molecule) is a radiative molecule or not, again, it'd be greatly appreciated... I'm at the limits of my knowledge here.
So...
SvaraRaderaRadiant Exitance =
= ε σ (T^4_h - T^4_c) Ah
= (ε c (e_h - e_c)) / 4
= σ / a * Δe
= Faraday’s Constant (Ah) * (Molar Mass of Atmosphere / Ratio of Atoms Per Particle)
= Faraday’s Constant (Ah) * Moles of electrons per Mole of atmospheric particles
= (((Faraday's Constant (J electron-1) * Number of Electrons per Mole of Atmosphere) / 3600) / Stefan-Boltzmann Constant)^0.25
= (((Faraday's Constant (J mol-1) * Moles of Electrons per Mole of Atmosphere) / 3600) / Stefan-Boltzmann Constant)^0.25
There’s no way that’s a mere coincidence. Why is it like that? That's what I'm hoping Claes can help explain.
One can analogize thermodynamics to electrical theory... which may provide a clue to the equations above which use Faraday's Constant:
SvaraRaderaFalstad.com Circuit Simulator:
https://tinyurl.com/yzo8hak9
The bottom circuit in the circuit simulator is how reality works... objects interact. That interaction through radiation pressure determines radiant exitance of each object. So while the climate alarmists claim that there's no way a photon could possibly 'know' the temperature of the object upon which that photon supposedly incides, it absolutely does 'know' because that photon must pass through the EM field (the photon being nothing but a quantum of EM energy) between objects, and thus the energy density gradient between objects.
You'll note that the top two circuits in the circuit simulator are how the climate alarmists calculate radiant exitance... (ie: they put each object into its own separate system that doesn’t interact with other objects, and they essentially claim all objects emit to 0 K, equivalent in electrical terms to discharging to ground). That's not how reality works.
And from the above, we can deduce that removing CO2 will not only not cause cooling, it will cause rampant warming (because the prevalent atmospheric radiative coolant in the upper atmosphere is CO2... removing it will cause the upper atmosphere to warm, reducing the energy density gradient, reducing buoyancy of convecting air parcels, hindering convective (and thus evaporative) removal of surface energy, and thus causing warming).
SvaraRaderaNo, if the warmists actually wanted to cool the atmosphere, the quickest route would be to remove Ar, a monoatomic which dilutes the molar concentration of polyatomics and thus reduces the ability of any given mole parcel of air to radiatively emit.
This wouldn't affect flora (as would removing CO2) and thus wouldn't affect agriculture, nor would it affect fauna (as would removing CO2... blood chemistry relies upon a certain concentration of CO2 being present, and removing enough CO2 from the atmosphere kills flora which fauna eat).
In fact, given that Ar is a gas used in industry for many purposes, removing it from the atmosphere would provide industry plentiful quantities of the gas, while at the same time reducing global temperature by increasing the molar concentration of polyatomic radiative molecules and thus increasing radiant exitance from each mole of atmosphere, thus increasing radiant exitance to space, thus increasing energy loss from the system known as 'Earth', thus causing cooling.
Hi Kook's
SvaraRaderaSome nice stuff in there. This site is full of great stuff. Thank you for the heads up.
Yes, finding a place to converse with a moderator who strictly hews to mathematical reality and the Scientific Method is paramount to advancing our knowledge.
RaderaThe last forum we inhabited has descended into superstition, nonary mathematics and religious arguments justified via hand-wavium.
I've invited Christopher Monckton to join us here to work on the new lapse rate equation... I'm hoping he does. The sheer mathematical brute force of Claes and Christopher and myself and yourself would be a force to be reckoned with.
Claes, I'd like to introduce you to Jopo... the quirky-brained genius who started me on this epic quest of figuring out how, exactly, the atmosphere 'works'. He's the one who noticed the correlation between the number of moles of electrons in a mole of atmospheric particles (atoms, molecules) and the atmospheric temperature... which means that CO2 is not, cannot be, the 'temperature control knob' and is, in fact, a net atmospheric radiative coolant.
SvaraRaderaOk, let us go a bit deeper... into the realm of constraint forces and virtual work.
SvaraRaderaFirst, the definitions:
Constraint forces determine the object's displacement in the system, limiting it within a range. They eliminate all displacements in directions where there is zero work, that is, the velocity in the direction of the constraint is limited to 0, so that the constraint forces do not perform work on the system.
Virtual work is an application of the Principle of Least Action... the Principle of Virtual Work states that at equilibrium the virtual work of the forces applied to a system is zero.
Now apply that to thermodynamic equilibrium... all action requires an impetus. At thermodynamic equilibrium, there is no energy density gradient and thus no impetus for photon generation, nor is there any impetus for photons to be absorbed (the photons have a chemical potential of zero, a Helmholtz Free Energy of zero).
It is the energy density gradient which drives all physical processes... in the case of water spontaneously flowing downhill (ie: down a pressure gradient), it is that pressure gradient which is the impetus.
In the case of energy spontaneously flowing down an energy density gradient, it is that energy density gradient which is the impetus.
Pressure and energy density both have the same units:
Pressure: [M1 L-1 T-2]
Energy Density: [M1 L-1 T-2]
Pressure gradient and energy density gradient both have the same units:
Pressure Gradient: [M1 L-2 T-2]
Energy Density Gradient: [M1 L-2 T-2]
That's because energy density is a pressure, and energy density gradient is a pressure gradient... for energy.
Thus, just as we speak of water only spontaneously flowing down a pressure gradient (ie: downhill), we speak of energy only spontaneously flowing down an energy density gradient.
That is 2LoT in the Clausius Statement sense, in a nutshell.
If the climate alarmists were claiming that water could spontaneously flow uphill (ie: against a pressure gradient), they'd rightfully be laughed off the internet. There is no reason they shouldn't likewise be laughed off the internet for having based a multi-brillion dollar CAGW scam based upon energy spontaneously flowing up an energy density gradient.
By all rights, the IPCC and all alarmist climastrologists should not only be fired and their organizations disbanded with prejudice, they should be jailed for fraud and forced to repay the taxpayers for the billions of dollars they've stolen to fund this unscientific, unphysical scam.
Hi Kooks and Claes. On this page of Claes I was reminded of the make up of Plancks Constant. https://claesjohnson.blogspot.com/search/label/Wien%27s%20displacement%20law
SvaraRaderaWhere I recalled that h= kB.C.eV
Thus h= R.C.eV / Na
So R= Na.h / C.eV
So the Ideal Gas Law PV=n.R.T could be re-written as:
PV=n.Na .h.T / C.eV
Thus T= P.V.C.eV / n.Na.h
I just cannot see how on Earth Co2 fits into this
It fits in, but plays a very small part... and the part it plays is diametrically opposite to what the CAGW kooks claim.
SvaraRaderaBut no matter how much mathematical proof we produce that CAGW violates several fundamental physical laws, we make no headway because it's a technical field, and most people can't wrap their heads around it. We need analogies to concepts they can readily grasp. Hence my analogization of water and energy, energy density and pressure, and energy density gradient and pressure gradient. We need more analogies like that.
So Joe's site has descended into nonary (base-9) math, counting letters, converting it to base-9 math, reducing that and drawing incorrect conclusions from that to find "hidden messages" in text (change the alphabet or the base (both randomly chosen) and the conclusion changes... a sure sign that the methodology is not arriving at correct conclusions) and creating a religious hymn to 'hijack the frequency mind control mechanisms of hymnal music' to control people's minds, or somesuch. Still no definitive proof of any of what he states... likely because he's got none. He's got equations from empirical science which he attempts to apply to Idealist Illuminism (which bashing empirical science... a hypocrisy of such magnitude that it boggles the mind), but that's it.
I fear that Joe's undergoing a break from reality, and that his credibility will suffer for it. He sounds a bit unhinged, maniacally laughing when listening repeatedly to a not-very-good Oompah-band-sounding 'hymn' with a goofy voice and a not-very-good melody and declaring it to be superb.
Claes, you know him... can you determine if he's in a proper frame of mind, and if not, get him help?
At the very fundament of Joe's new 'religion' is the claim that 'nothing' can exist... that 'nothing' has a material existence, rather than it being a concept denoting the lack of or non-existence of 'something'.
SvaraRaderaThus he's able to then claim that 'nothing' can become 'something' through 'motion', which they've claimed is also identical to light, to thought and to space.
Yes, they literally claim light = thought = motion = space.
I guess they forgot that light is 'something'. LOL
It makes no logical sense, but every time I point out the inconsistencies, Joe censors me.
Having a blackbody (BB) that somehow knows about its surroundings, exchanging energy with it through waves, is harder to believe than a BB that simply radiates according to its internal energy state and irrespective of the environment.
SvaraRadera