Can a Cold Radiator with High Emissivity Transfer Radiant Energy to a Warmer Radiator with Low Emissivity? Yes Indeed.
1. The review was anonymous, an unscientific policy disapproved by legitimate science and technical reviewers. I was not given an opportunity to refute it.
2. Reviewer changed definitions of my algebraic symbols, then concluded they disproved my conclusions. This old trick was entirely false and reprehensible.
3. Reviewer confuses conduction and convection thermal energy transfer through matter, or heat, with radiant energy transfer between matter, not heat (except infrared radiation is easily converted to heat). I am taking X-ray radiation for cancer. No heat involved, only cancer cell destruction by chemical reaction.
In Chemical Engineering practice, the term heat is reserved for thermal energy transfer, which is measured by temperature differences, the kinetic energy of motion of matter particles. To reduce confusion as displayed by the reviewer, I replaced heat with more meaningful radiant energy transfer.
4. The mechanisms and rate laws for thermal and radiant energy transfer are quite different. Thermal energy transfer driving force from one radiator to another is their temperature gradient or difference through matter, Qt, joule/min sq mtr = kA(Th – Tc) in the direction from h to c where Th > Tc.
Only when Th = Tc is Qt = 0 from this thermal rate law. k is the thermal conductivity of the radiating material; A is its area of transfer. Reviewer and I agree on this. Therefore, we agree thermal energy transfer is always from the hotter to cooler body, never the other way. It is mathematically built into the thermal rate law definitions.
5. Net radiant energy transfer driving force between intense radiator 1 and less intense radiator 2 is energy intensity difference, I2 – I1 > 0, from 2 to 1. Never from 1 to 2 when this is so. Note we do not assume T2 > T1 here. Otherwise, it is 0 or from 1 to 2. Intensity I2 joule/min – sq mtr = Ze2A2T2**4 by Stephan-Boltzmann Radiation Law: for real nonblack bodies when Kirchhoff’s Law does not apply.
Kirchhoff’s law of thermal radiation – Wikipedia. Radiant energy transfer rate between them is rate emitted from radiator 2 that is absorbed by radiator 1 less the rate emitted from 1 absorbed by 2, is Qr = I2 – I1 = Z(e2a1A2T2**4 – e1a2A1T1**4). Transfer is from 2 to 1 when I2 > I1 or Qr > 0. (1)
6. The steady-state solution of no radiant energy transfer I2 = I1, Qr = 0, gives e2a1A2T2**4 = e1a2A1T1**4 and T2**4 = (e2a1A2/e1a2A1)T1**4 = RT1**4 (2)
7. Unless R = 1, T2 differs from T1. When R > 1, T2 > T1. When the physical properties of the two radiators are such that e2a1A2 > e1a2A1 and R > 1, the steady-state solution is T2**4 > T1**4 or T2 > T1. The radiating temperatures can differ even though Qr = 0. In thi cse there is no radiant transfer from T2 to T1, hotter to cooler.
8. More generally, consider a hot poor emitter and good absorber radiator 2 compared to cool excellent emitter and poor absorber radiator 1. T2 > T1. A2 = A1, e1 = e2 + eo > e2 and a2 = a1 + ao > a1, where eo > 0 and/or ao > 0, gives T2**4 = (e1a2A1/e2a1A2)T1**4 = [(e2 + eo)(a1 + ao)A1/e2a1A2]T1**4. (3) Since numerator with eo and ao is larger than denominator, ratio > 1 and T2 > T1 as assumed.
9. However, Qr = Z(e2a1A2T2**4 – e1a2AcT1**4) = Z[e2a1A2T2**4 – (e2 + eo)(a1 + ao)A1T1**4] < 0 (4) Since the negative second term abs value > first positive term, Qr < 0 and radiant energy transfers from T1 to T2 when T1 < T2. QED
10. Some question this result because it proves radiant transfer from colder T1 to warmer T2 can occur when physical properties are related as assumed, increasng their difference as a violation of Thermodynamics 2nd Law for thermal energy transfer. They forget in the real world, thermal energy transfer from warm T2 to colder T1 increases with increasing difference and counteracts radiant transfer until Qt = Qr and the different T’s remain constant. The equation describing this two-way transfer of simultaneous radiant and thermal is easily developed.
11. Numerical example. Let e2 = 0.2; e1 = 0.2 + 0.1 = 0.3; a1 = 0.4; a2 = 0.4 + 0.2 = 0.6; Z = A1 = A2 = 1. We have Qr = 0.2*0.4*T2**4 – 0.4*0.6*T1**4 = 0.08T2**4 – 0.24T1**4 < 0. (5) So, radiant energy transfers from cool T1 to warm T2 at rate Qr. I have not looked for two real radiators with these properties. If they do not exist, I agree with reviewer; otherwise reviewer should agree with me.
12. Thomas Edison, inventor of the commercial electric light bulb around 1880 searched for filaments that would glow without breaking when a voltage was applied. He realized he needed a high emissivity filament the glowed with sufficient intensity at low enough temperature to prevent damage. Knowledge of radiant energy transfer explains his great discovery. Light does not behave like heat.
13. Reviewer neglects Stephan-Bolzmann Radiation Law. Hence, he gets radiant energy transfer wrong. He cannot explain why different objects at steady state in a room can have different temperatures (metal cooler than wood). Or why outdoor temperatures differ. Or why astronomical nebulae have different radiating temperatures throughout for millions of years. Or why leaves are cooler than air. (Leaves are cooler than surroundings because photosynthesis reaction is endothermic.) He does not explain energy conservation for chemical reacting systems.
14. He gave no references and insufficient mathematics. I did.
15. Reviewer stayed with verbal claims with insufficient, invalid, supporting evidence. I provided standard definitions, logic, three Laws of physics, 10th grade algebra and no assumptions or empiricism to prove my conclusion.
I believe this essay proves critical review by “PSI Staff” does not meet PSI standards of sciencs/math excellence.
I welcome identification of logical, mathematical or scientific errors I have made and suggestions for improvement.
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Lit
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“Can A Cold Radiator With High Emissivity Transfer Radiant Energy To A Warmer Radiator With Low Emissivity”
Nope. The definition of energy in this situation is:
There are, moreover, heat and work—i.e., energy in the process of transfer from one body to another.
https://www.britannica.com/science/energy
Heat is defined as:
“heat, energy that is transferred from one body to another as the result of a difference in temperature. If two bodies at different temperatures are brought together, energy is transferred—i.e., heat flows—from the hotter body to the colder.”
https://www.britannica.com/science/heat
So, no heat is transferred from low to high temperature, and you´re not talking about work. So, there is no “energy” being transferred. There may be some interchange of radiation, but that doesn´t qualify as heat or energy in this situation and it won´t raise temperature. It´s like the motion of electrons in a conductor without voltage, they still move around but there´s no net transfer of energy.
Only heat and work can raise temperature, and you don´t have any of them in this case.
Emissivity doesn´t change that.
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Bevan
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The Earth is estimated to be 4.5 billion years old. The earliest geological era is named the Hadean era after Hades due to the extensive volcanic activity creating sheets of molten lava across the surface. Volcanic activity produces copious amounts of atmospheric CO2 so how could the temperature of the hot surface have fallen to the present-day comfortable level if the ever-present atmospheric CO2 is continuously warming the Earth?
In every minute of every hour of every day, the atmospheric CO2 absorbs and re-radiates heat from the Sun and the Earth’s surface and has been doing so for more than 4 billion years. If this caused warming of the Earth’s surface then surely at least all of the oceans would have evaporated by now. It is simply ridiculous to claim that such warming is taking place and will cause catastrophic conditions in the near future. If true then it would have happened long ago, life on Earth would have ceased and we would not be here to listen to such illogical nonsense.
Like every inert, material entity, the atmospheric CO2 is merely a conduit for the passage of heat energy from hot bodies to colder bodies via conduction, convection or radiation, the normal process of achieving thermal equilibrium. It does not produce any heat so it cannot warm anything.
The fictitious warming claim promoted by the UN IPCC and the World Economic Forum is simply untenable. It is an attempt to instill fear into the population at large, cause an economic collapse and then claim that a ‘One World Government’ is necessary, run by them, of course.
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Herb Rose
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Hi Pierre,
Objects do not equalize energy with other objects and the Laws of Thermodynamics is a misnomer since thermal has to do with kinetic energy ( which is a function of mass and energy) and objects only transfer energy. A more appropriate name is Energydynamics and energy (v^2) always flows from greater to lower.
There are 2 ways to transfer energy, convection (where there is physical contact between matter) and radiation (where there is no contact).
These 2 means of transfer follow different laws. Convection follows the laws of conservation of momentum while radiation follows the law of radiation.
With radiation objects cannot equalize, first because what energy each object absorbs is determined by its structure. The laws of Energydynsamics says that all matter absorbs and radiates energy, not that the matter absorbs all the radiated energy. Second because radiated energy decreases with distance an object can never absorb enough energy from another object to equalize their energy. The emitting object will always be “hotter” because it emits energy in all directions while the “cooler” object will absorb energy from one direction but radiate that absorbed energy in all directions. Objects transfer energy to the energy field they are in and equalize with it. If 2 objects are in an energy field of equal strength their energy will become equal but not by transferring energy to the other object.
The energy of an object will be distributed to all its mass (volume) while the energy is radiated by its area.
If 2 objects have the same energy but different volumes (mass) and areas the mass of the smaller will have more energy but if its area is small enough it will radiate less energy (be cooler) than the larger object.
Think of it as 2 pans of water that are being heated by the same amount of energy. The smaller pan has less water and less surface area losing energy, so it will get hotter faster. The large pan with more water will have energy distributed to more molecules and have a larger surface area losing energy so the molecules will be cooler. The larger pan can radiate more heat (be hotter) even though the water molecules have less energy.
With conduction energy will be transferred from the object with greater velocity to the object with lower velocity regardless of their masses. (See my article in PSI “How Cold Heats Hot.) but because the energy is distributed to and lost by all of the molecules the kinetic energy (temperature) of the objects will not be equal. A high speed gas molecule will transfer energy to the Earth even though its temperature ((1/2mv^2) is lower because of greater mass.
One of the follies of the GHGT is the belief that because the N2 an O2 in the atmosphere do not absorb visible or IR radiation from the sun and they have a lower temperature, that they are being heated by the Earth’s surface. All matter absorbs radiated energy and the N2 and O2 are absorbing 90+% of the UV coming from the sun then converting that UV energy into kinetic energy. (Ozone is a result of the energy from UV splitting an O2 molecule into oxygen atoms.)
The molecules in the atmosphere are heating the surface of the Earth which is why during a solar minimum when less UV is produced the Earth gets colder.
It is a misunderstanding of the difference between radiated energy and convection (which is the way energy is transferred in the troposphere), thinking that thermodynamics has to do with kinetic energy instead of energy, and the flow of energy from higher altitudes to lower altitudes that cause metrology and climatology to be fake science.
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Alan
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“I replaced heat with more meaningful radiant energy transfer” – And there is the fundamental error – radiant energy is not heat, it it electromagnetic energy.
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T. C. Clark
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“There are 2 ways to transfer energy….” No, there are 3 ways to transfer heat energy including conduction. “Metrology”? When you are outside in the sunshine and a cloud comes between you and the sun, you feel cooler because the IR radiation is reduced. Herbphysics is hard to understand.
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Koen Vogel
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Hi Pierre,
while it can be fun to refute each other with theoretical physics, the fact of the matter is:
1) The current phase of global warming is largely due to an Arctic heat anomaly that is 3-4 times larger than the rest of the globe. That’s not my opinion, but everyone’s including the IPCC
2) The Arctic heat anomaly cannot be due to RFGHG, as it occurs in winter in an area that does not emit – and RFGHG cannot capture – radiative heat.
Until you can explain those phenomena the radiative cold-to-hot properties of GHG are irrelevant: you have a much bigger problem to explain, namely how the Arctic is not radiating heat but still warming faster than the rest of the planet.
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Squidly
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Nope, impossible! .. Given two molecules, Ma and Mb, Ma can transfer energy to Mb, if, and only if, Ma is of greater energy state than Mb .. period .. end of story .. doesn’t make any difference their emissivity. Ma must be at greater energy state (high frequency) than Mb .. there is no other way to transfer energy without additional work.
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