Global Warming Skeptics Misinterpret the Second Law of Thermodynamics

May 1, 2012 - PRLog -- Introduction
Global warming claims solar radiation absorbed in the Earth is re-radiated back in the IR and absorbed by the CO2 greenhouse gases in the atmosphere, only to be conserved by the emission of EM radiation as “backradiation” that further warms the Earth. IR stands for infrared and EM for electromagnetic. The Earth therefore warms more by backradiation than otherwise, the consequence of which is CO2 emissions need to be regulated to avoid climate change in a warming Earth.

However, skeptics [1-3] 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. The argument assumes the CO2 molecules are BBs allowing radiative heat transfer in backradiation to proceed by the SB equation as derived from QM. BB stands for blackbody, SB for Stefan-Boltzmann, and QM for quantum mechanics. And since the Second Law is violated, backradiation cannot occur, and therefore the economic costs of regulating CO2 emissions are not justified.



Background
Rebuttal [4] of the skeptics’ argument argues the CO2 molecules dispersed in the atmosphere are not BBs as required in the SB equation, and therefore backradiation does not violate the Second law. Upon the CO2 molecule absorbing IR radiation from the Earth, conservation proceeds by the emission of EM radiation at the vibration frequencies of the CO2 molecule some of which undergoes backradiation that further warms the Earth. 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.

Discussion

Planck In 1900, Planck to avoid the “Ultraviolet catastrophe” departed from classical physics to explain BB radiation by QM as quanta called photons. Unlike classical physics, QM as given in the Einstein-Hopf relation for atom as a harmonic oscillator requires the heat capacity of the atom to vanish at high frequencies. In effect, Planck showed the failure of classical physics was caused by the equipartition theorem of statistical mechanics that allows the atom to have heat capacity at all frequencies; whereas, QM allows the atom to only have heat capacity at low frequencies. Instead of frequency, the difference between QM and classical physics as a size effect is best understood by expressing the Einstein-Hopf relation for the heat capacity of the atom in terms of the EM confinement wavelength as shown in the thumbnail.

In global warming by Einstein-Hopf, individual greenhouse gas molecules like CO2 with microscopic EM confinement wavelengths have vanishing heat capacity and cannot conserve absorbed BB radiation from the Earth by an increase in temperature. Instead, the CO2 molecule conserves the absorbed BB radiation [4] by molecular vibration. Backradiation is therefore independent of the CO2 molecule temperature and not subject to the Second Law. By assuming the CO2 molecules in the atmosphere are blackbodies at a cold temperature, the skeptics have misinterpreted backradiation as a violation of the Second Law when in fact molecular vibration is independent of the Second Law..

Johnson  In Johnson’s theory [2] of EM radiation, continual reference is made to Planck’s “\act of despair" inventing the idea of photons, which Nature assembles according to laws of statistics with high frequency photons being unlikely. Johnson could not have known “Planck viewed quanta to be merely a mathematical trick to resolve a scientific deadlock of classical wave mechanics, a trick without real physical meaning.” Hence, Johnson was simply demeaning Planck’s accomplishment. Science usually advances by imagination and not necessarily by rational thinking. Unlike Johnson, Feynman’s view [5] of Planck’s accomplishment as “the first quantum-mechanical formula ever known, or ever discussed as it was the beautiful culmination of decades of puzzlement” stands for itself

Perhaps, Johnson seeks to replace Planck’s QM with Finite Precision Computation (FPC). If so, Johnson will have significant hurdles to overcome, not the least of which is including the size effect of QM in the FPC. The Abraham-Lorentz recoil force needs to describe loss of radiative or viscous EM energy in terms of the effect of EM confinement of the atom as given in the Einstein-Hopf relation avoiding if possible the equipartition theorem of statistical mechanics.

With regard to global warming, Johnson’s misinterprets the Second Law as applicable to greenhouse gases as blackbodies evidenced by his comment that algebraic manipulation of the temperature terms in the SB equation suggests hea flows from the cold atmosphere to the warm Earth. Instead, backradiation is caused by a QM effect and has nothing to do with the cold temperature of the atmosphere.
       
Cotton Similar to Johnson, Cotton [3] misinterprets the greenhouse gases as heat transfer from the colder CO2 to the warmer Earth when he states: ”just as a vacuum flask does not further warm the coffee, neither does any additional temporary thermal energy trapped by the atmosphere warm the surface.”

Individual greenhouse gases are discrete molecules that by QM lack heat capacity to conserve absorption of EM radiation by an increase in temperature, and therefore are not subject to Second Law restrictions. The vacuum flask differs in that the atoms in the solid walls do not respond individually but rather as a macroscopic body that having temperature is subject to restrictions by the Second Law.

CO2 Absorption By QM, backradiation by CO2 molecular vibrations cannot occur unless the CO2 molecule does indeed absorb BB radiation from the Earth. Wien’s law at 300 K gives the peak of Earth’s emission at 9.66 microns with an emissive power of about 30 W/m2-micron. But the Earth’s BB radiation is broadband [6] and about 75% of the peak power or 22.5 W/m2-micron is available at 14 microns.  Of this, about 40% is absorbed [7] by water vapor, leaving about 10 W/m2-micron for backradiation to the Earth. Whether this is significant to justify the costs of carbon legislation requires more study..          

Conclusions

1.  Global warming by backradiation is misinterpreted by skeptics as blackbody radiation from cold CO2 in the atmosphere to the warm Earth..

2.  Backradiation occurs as CO2 molecules conserve absorbed BB radiation from the Earth by EM emission at their vibrational frequencies. Corrected for a 40 % reduction by water vapor absorption, the CO2 molecule by backradiation does indeed further warm the Earth by about 10 W/m2-micron, but how significant this is in global warming requires further study.  

References.
[1] J. O'Sulivan, et al., "Slaying the Sky Dragon - Death of the Greenhouse Gas Theory,"
Kindle, 2011.
[2] C. Johnson, “Mathematical Physics of Blackbody Radiation” See www.csc.kth.se/~cgjoh/ambsblack.pdf
[3] D. Cotton, “Radiated Energy and the Second Law of Thermodynamics,” by D. Cotton, http://principia-scientific.org/publications/psi_radiated...
[4] T. Prevenslik, “Global Warming by Backradiation does not violate the Second Law of Thermodynamics,” See http://www.prlog.org/11842623-global-warming-by-backradia...
[5] R. P. Feynman, et al., See Lectures in Physics, The Brownian Movement, Equipartition and the quantum oscillator, Vol. 1, Chp. 41-3 (1971)
[6] T. Prevenslik, “Blackbody Radiation absorbed by Atmospheric Carbon Dioxide,”
http://www.nanoqed.org/ at “Global Warming and the Second Law of Thermodynamics,” 2012.
[7] A.G. Biggs, “An Alternative Theory of Climate Change,” http://members.iinet.net.au/~alexandergbiggs/An%20alternative%20theory%20of%20climate%20change%203.pdf