Again with the high quality graphics, the Temperatures of Earth, (yes, I know there is a degree or so off here or there.)

**Note: This is a work sheet I am leaving public. I know most of this has been done before, I am just using a different frame of reference to attempt to better define the variables.**

RHC, Relativistic Heat Conduction, is not required to solve any particular thermodynamic problem, but it does simplify solution of complex problems cover millions of years of heat transfer.

**d{dF}t/d{dT)t or the change of the change in flux per the change of change in temperature, both with respect to time. It is like all energy flow wants to accelerate, but may be limited by its media of transport. Light appears to have a mass because it cannot accelerate beyond the speed of light because space is not a perfect media.**

~~Unfortunately, it appears that the appearent mass of a photon has to approach zero, from its all ready near infintesimally small mass, for this to work. That would mean the speed of light is a relative constant, it would approach an infinity. A little scary when you look at it as a whole, but it makes sense. Whether this totally agrees with the concept of VLS, I don't know yet.~~

**Note: Light having a mass is a bone of contention with some. The way I look at it, as the energy of a photon increases, its mass is converted into energy, when the energy decreases, the mass increases as energy is converted to mass. E=MC^2 and all that. So my hypothesis is that a photon is an assembly of sub atomic particles, each with a specific quantum of energy and the equivalent of shells for orbits. The combination of possible orbital occupations would be the quantum energy of the photon. Interaction with electrons in matter produces the Phonon effect. The Phonon is the missing element in the RHC equation for the atmosphere. It really should be simple.**

Would this play hell with Coulomb's Law? I don't think so. It would tend to more firmly relate fields. Not a bad thing. It should not be too hard to figure out what the basic quatum is?

http://youtube/tEL3Amxf8eI

So a photon may have 1x10^35 quantum states from relativistic masses of 2.21x10-42kg to 2.21x10-7kg. That's just rough estimate of course. The mass of an electron is 9.10938x10^-31kg. Since the relative mass of a photon is obviously not going to be equal to that of an electron, angular momentum, gravity and charge would have to be allowed for to determine the effective rest mass of the photon, which is likely on the order of 2.21x10^-42kg. The overlap of potential relative masses would indicate possible interaction in a mixed gas environment, but there is work still to be done.

Would this play hell with Coulomb's Law? I don't think so. It would tend to more firmly relate fields. Not a bad thing. It should not be too hard to figure out what the basic quatum is?

http://youtube/tEL3Amxf8eI

So a photon may have 1x10^35 quantum states from relativistic masses of 2.21x10-42kg to 2.21x10-7kg. That's just rough estimate of course. The mass of an electron is 9.10938x10^-31kg. Since the relative mass of a photon is obviously not going to be equal to that of an electron, angular momentum, gravity and charge would have to be allowed for to determine the effective rest mass of the photon, which is likely on the order of 2.21x10^-42kg. The overlap of potential relative masses would indicate possible interaction in a mixed gas environment, but there is work still to be done.

I will be working on this from time to time to define simple RHC boundaries. One of the more interesting is the deep ocean 4C barrier. This is density barrier, above 4C sea water density varies with energy flow. Below the 4C barrier, temperature is relatively constant as heat flow is slow, tens of millinia and mirco Watts per meter squared. The effect is the appearance of near perfect conduction of heat, thermal equilibrium on a much longer time scale, that is a much tigher, denser, probability cloud, i,e, if it is easier to locate a packet of energy, its rate of change is less.

**What is The 4C Thermal Boundary?**

Selecting a frame of reference is more than just a choice of a point in space, it is a choice of space and time. The 4C boundary in the deep ocean is the point of maximum density of our saline ocean. From this boundary upward is the ocean atmopshere mixing layer. Heat is transfer is much greater speed than below the 4C layer. Below the 4C layer is the ocean crust mixing layer. Its heat transfer time scale is on the order of tens of millinia.

This is analogous to the tropopause, we the rate of heat transfer can be much greater than the rate of transfer of energy from the surface mixing layer to the tropopause.

Most studies of thermodynamic full cover thse issues with coefficients of heat transfer across a thermal barrier. Part of the description of the coefficient of heat transfer is the time restraints, but in normal applications, the time constraints can be simplified. In studying the Earth system, these time constrains are only negligable between one boundary per estimate. The relative impacts of the time constraints between two or more thermal boundariers has to be consider for correct estimates.

4C boundary time constant tens of millinia

**upper ocean time constant roughly a millinium**

This layer is from the 4C density boundary to the surface. There are several layers in this layer. The 100m layer, defined by shorter short wave radiant energy, green to ultraviolet, and the 10 meter layer defined by the longer short wave energy, yellow moving to near infrared, and the skin layers, millimeters to micro meters.

**surface air mixing layer time constant roughly months**

This is the most interesting boundary to me. Radiant heat from the surface of the oceans is limited by the coefficient of heat transfer from water to air. Changes in wind change the rate of flow. Changes in density change the flow. Changes in the composition of the gases change the flow. Once radiant energy is transferred, the photons enter a supercharge version of nature's pinball machine from Hell. Greenhouse gases can readily absorb photions but the much higher rate of collisional heat transfer to emission by relaxation is phenominal. Conductive heat transfer is more coherent in the direction of temperature drop while emissions are totally random. The absorption the collision de-excitation can enhance conductivity like crazy. The wavelength of the photon from one form of de-excitation can change in nanoseconds. Each of these relaxations that change wavelength can be less efficient than the last or more efficient than the next. This is thermal chaos! Going from near zero to light speed and back billions of times in fractions of seconds.

This is the main reason for my considering relativistic heat conduction and the possibility of variable light speed. While the speed of light may not vary, it would definitly appear to vary. It is like the doppler effect on steroids. Yeah, I think it is kind of exciting :)

The probability density approach is the only way to come close to solving this layer. Once that is estimated, the probability density changes with density of the media, ratio of the mixed gases and the rate of temperature decrease with density. This is where the Kimoto equation becomes a major tool to simplify the calculations. Using surface temperature, potential temperature and "effective" emissivity, a reasonable approximation may be possible. Approximation though, is all it will ever be. There is no equilibrium, just probability density.

**Tropopause time constant roughly microsecs**

In the Tropopause, you have up welling infrared with downwelling infrared with incoming solar at wide angles and scattered/reflected solar from below. A lot of different fluxes from all directions. The spectral window is very clear for some wavelengths and opaque for others. This is the one spot in the atmosphere that a sandard radiative model could get totally lost. More ice, water vapor or water would play hell in getting a good number. All it takes is a few molecules combined to change the radiant spectrum of the small amounts of water. Measurement of the changes would be complicated becaue of the available angles of emission and absorption not inline with the instrumentation. Getting it close is quite a feat. This is were RHC can really come in handy. The complicate relationships of heat flux can be simplified to temperature, pressure, potential temperature, which is a function of temperature and pressure, to get an estimate of the "effective" emissivity*. That may sound complicated, but the change in temperature with altitude is a direct indication of the net flux. Change in the rate of change of temperature is an indication of the magnitude and sign of the net flux. So the temperature relationship between the mid-troposphere temperature and the lower stratosphere can give you and indication of the flux relationships in the tropopause.

Now that the weird energy changes and actual change in the speed of light are ruled out, the relative motion of the of the photons is the impedance to radiant flux, which changes with density. Near the tropopause the side windows are more open, which expalins the dramatic changes possible in the tropopause. So it will be much easier to explain why the change in rate of change has such an impact. Resistance to flow through the stratosphere changes slowly with respect to the side windows, allowing radiant flux relief, if you will, for larger changes in flux from the surface.

What does this mean for the mid-tropo/strat Watt-meter? That larger areas of the stratopshere will be needed to get the full signal of the change in flux from the surface.

Now that the weird energy changes and actual change in the speed of light are ruled out, the relative motion of the of the photons is the impedance to radiant flux, which changes with density. Near the tropopause the side windows are more open, which expalins the dramatic changes possible in the tropopause. So it will be much easier to explain why the change in rate of change has such an impact. Resistance to flow through the stratosphere changes slowly with respect to the side windows, allowing radiant flux relief, if you will, for larger changes in flux from the surface.

What does this mean for the mid-tropo/strat Watt-meter? That larger areas of the stratopshere will be needed to get the full signal of the change in flux from the surface.

* At the surface, emissivity of the surface times transmittance of atmosphere times the change in transmittance with respect to density. Roughly at this point in the calculations.

The confusing part is the "Effective" emissivity. In a straight line, electromagnetic radiation would follow all the classic rules. The mixture of wavelengths, energies and angles appears to be simplified as a single "effective" unit, with this special case of RHC. How accurately, I am still working on that. It looks pretty close and would be closer with two accurate estimates at two different denisities. The more points you get right, the more you can get right.

In any case, the change in the rate of change is very important.

**TOA time constant with space roughly nano seconds**

As at the tropopause, but much simpler. With less banging around, the photons are more coherent. There is still some, "resistance" to flow so there will be a change in the rate of change of interaction entering relatively constant emissivity of space. Space still has a "resistance" so there is still entropy. So there is roughly an order of magnitude change in the rate of collisions between the stratosphere and space.

This is the concept of Relativistic Heat Conduction,

**as I see it**, the change in the rate of change for all forms of energy is related to entropy, so all forms of energy flux share common transmission properties.

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