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Global Warming by Backradiation does not violate the Second Law of Thermodynamics
The Second law of Thermodynamics is not violated in global warming as solar radiation after being absorbed by the Earth is re-radiated and absorbed by carbon dioxide in the atmosphere only to undergo backradiation that further warms the Earth
Global warming claims that solar radiation absorbed in the Earth’s surface is re-radiated back in the IR and absorbed by CO2 in the atmosphere only to be conserved by the emission of EM radiation as “backradiation”
In the global warming controversy, skeptics claim backradiation requires heat to be transferred from the CO2 in the cold atmosphere to the warm surface of the Earth, and therefore the Second Law that requires heat to only flow from hot to cold surfaces is violated. Based on this reasoning, global warming skeptics then argue that because the Second Law is violated, backradiation is unphysical and does not occur, and therefore the economic costs of regulating CO2 emissions are unjustified. See "Slaying the Sky Dragon - Death of the Greenhouse Gas Theory," by J. O'Sulivan, et al. and “Mathematical Physics of Blackbody Radiation,” by C. Johnson at http://www.csc.kth.se/~
The problem is backradiation does not violate the Second law. Indeed, the CO2 molecule does absorb the IR radiation from the Earth, but conservation proceeds by the emission of EM radiation at the vibration frequencies of the CO2 molecule. What this means is backradiation has nothing to do with the temperature of the CO2 molecule itself, and therefore violation of the Second Law based on heat flow from cold CO2 molecules to the warm Earth may be safely dismissed.
By QM, the absorption of IR radiation in the atmosphere is conserved by EM emission at the vibration frequencies of the CO2 molecule, the EM emission not depending on temperature. QM stands for quantum mechanics. Classical physics differs in that the atoms of the CO2 molecule are assumed to have heat capacity, and therefore the temperature of the CO2 would depend on the absorption of IR radiation and be subject to Second Law restrictions. However, QM governs the heat capacity of the atom and not classical physics. By QM, the CO2 atoms remain at atmospheric temperature upon absorbing IR radiation, but conservation by BB radiation from the cold atmosphere to the warm Earth is precluded by the Second Law. Instead, conservation by EM emission occurs without violating the Second Law.
Vanishing heat capacity of the atom by QM need not be limited to the CO2 molecule in global warning. Any structure comprised of a continuum of atoms is subject to the same QM restriction on heat capacity, provided the structure is nanoscopic, e.g., heat transfer in nanostructures. See ASME Conference “QED Induced Heat Transfer” at http://www.nanoqed.org/
The controversy about the Second Law in global warming is the same as that between classical physics and QM personified by Maxwell and Planck over a century ago.
Maxwell vs. Planck
In 1865, Maxwell based on classical physics formulated his famous “Maxwell’s equations” for EM waves. However, Planck and others found they could not explain BB radiation as light by classical physics. BB stands for blackbody. Notably, the Rayleigh-Jeans law for light based on the equipartition theorem of statistical mechanics led to the "Ultraviolet catastrophe"
Later in 1900, Planck to avoid the “Ultraviolet catastrophe”
Unphysical claims by global warming skeptics of violations of the Second Law may be traced back to classical physics that allows atoms to have the heat capacity to conserve the absorption of IR radiation by an increase in temperature, instead of by EM emission from the CO2 molecules as required by QM. The global warming problem is the same as the explanation of BB radiation in the “Ultraviolet catastrophe”
1. Global warming by backradiation from CO2 in the atmosphere does not violate the Second Law.
2. Backradiation occurs as absorbed IR radiation from the Earth is conserved by the EM emission at the vibrational frequencies of the CO2 molecule independent of temperature.
3. Second Law aside, the costs of regulating carbon emissions should be viewed as an investment in the future of the Earth to avoid the costs of climate change by global warming.
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Classically, thermal EM radiation conserves heat by an increase in temperature. But at the nanoscale, temperature increases are forbidden by quantum mechanics. QED radiation explains how heat is conserved by the emission of nonthermal EM radiation.