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EMISSIVITY, ABSORBENCY AND TOTAL EMITTANCE OF CARBON DIOXIDE (CO2)
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EMISSIVITY, ABSORBENCY AND TOTAL EMITTANCE OF CARBON DIOXIDE (CO2).
By Nasif Nahle Sabag

Published on ©1 September 2007. Updated: 8 September 2007. Grammar revision on July 20, 2008

To quote this article copy and paste the next two lines. Please, fill in the spaces of day, month and year:

Nahle, Nasif. Total Emittance of Carbon Dioxide. Biology Cabinet. 27 April 2007. Obtained on  _____(month)  _____(day), _____(year); from http://biocab.org/Heat_Stored.html

INTRODUCTION

The whole idea of global warming is based on the capacity of absorption and emissivity of carbon dioxide. The gases that have an influence on the atmosphere temperature are water vapor, carbon dioxide, nitrogen dioxide and methane. Heat Transfer science demonstrates that the effect known like "global warming" is caused by the Solar Irradiance, Interstellar Cosmic Radiation and land and oceans. The influence of carbon dioxide is negligible, as I will demonstrate it in the next paragraphs.

The values of emissivity, total emittance and absorbency of carbon dioxide obtained experimentally by Hottel (H. C. Hottel. Heat Transmission. 1954) have been confirmed recently by different investigators. The temperature introduced in the calculations is 300.15 K (27 °C):

Eb or black body total emittance = σ (T ^4) = 460.165 W/m^2
Eg or gray body total emittance = e σ (T ^4) (e is the emissivity of the studied system)
Absorbency (α) = Eg/Eb

Partial pressures of gases in the atmosphere:

Pp of Oxygen (O2) = 0.21 atm*m
Pp of Nitrogen (N2) = 0.78 atm*m
Pp of Carbon Dioxide (CO2) = 0.00034 atm*m
Pp of Argon (Ar) = 0.009 atm*m
Pp of other gases = 0.00066 atm*m

TABLE ON EMISSIVITY, ABSORBENCY AND TOTAL EMITTANCE OF CARBON DIOXIDE

CLICK ON THE TABLE TO SEE A LARGER IMAGE

From the table, the emissivity of carbon dioxide decreases with height and its partial pressure. In addition, the total emittance of CO2 with a partial pressure (Pp) of 1 atm*m would not exceed 0.9 W/m^2. At its current partial pressure, the CO2 has a total emittance of 0.423 (second line in blue characters) For this reason the value for the total emittance (€) given by some authors from the IPCC -5.35 W/m^2- is not the actual value, but an adaptation to make the numbers agree with pre-assumed and subjective numbers. The IPCC team of experts has changed the radiative forcing so many times that the IPCC team have had to admit that the numbers are not real. The real values for the emittance or "radiative forcing" have been provided by the heat transfer science and thermodynamics.

Now the IPCC team has found that the radiative forcing changes erratically, induced by the climate changes. The last assertion from the IPCC team is an assumption without scientific support, and it contradicts the physics of heat transfer because the radiative forcing capability of any system depends of its physical characteristics, like specific heat, mass, enthalpy, etc. not in the state of climate. The climate is not driven by the radiative forcing of the elements in the atmosphere, but by the Sun and the oceans.

Knowing the real values of emissivity, total emittance and absorptivity of the carbon dioxide obtained by other scientists by experimentation and observation of nature, the formula derived from the Stephan-Boltzmann's equation adopts the following form, introducing values from the real world:

ΔT = (0.423 W/m^2) [ln ([CO2] current / [CO2] standard)] / 4 (5.6697 x 10^-8 W/m^2*K^4) (300.15) ^3

For example, the real radiative equilibrium temperature of Earth is 300.15 K (27 °C), and we want to know the anomaly caused by carbon dioxide, which concentration in the atmosphere was 381 ppmv. If the standard concentration of CO2 in the atmosphere is 280 ppmv (another subjective number because the real one was fixed by scientific associations and boards, and its value is 350 ppmv), the anomaly in the temperature of the lower troposphere (the layer of air just above the ground and in contact with the surface with not more than one meter thick) caused by CO2 (Partial Pressure from 381 ppmv [CcdL] = 0.00034 atm-m) under a total atmospheric pressure of 1 atm is:

ΔT = (0.423 W/m^2) [ln (δ CO2 current / δ CO2 standard)]/4 (5.6697 x 10^-8 W/m^2* K^4) (T^3)

ΔT = (0.423 W/m^2) [ln (0.000681 Kg/m^3 / 0.0005 Kg/m^3)] / 4 (5.6697 x 10^-8 W/m^2* K^4) (300.15 K) ^3

= (0.423 W/m^2)(0.308) / 4 (5.6697 x 10^-8 W/m^2*K^4) (27040520.253 K^3) = 0.130284 W/m^2 / 6.13 W/m^2*K = 0.02 K

Thus, the anomaly of the lower troposphere temperature caused by the increase of CO2, on June 15, 2007 at 18:05 hrs. (UT) was 0.02 K, which is equal to 0.02 °C. The maximum efficiency of the whole atmosphere was 1-[[Tatm/Tbb)^2] = 1 - [311.75 K/300.15 K)^2] = 0.08. A really low efficiency for a heat engine.

Thus, carbon dioxide is not able to cause the global warming experienced again in the last two centuries. In addition, the warmest year of the last century up to present was 1934, not 1998. The real data are “being fitted” and being corrected by NOAA because the team of experts there had flawed the records of the temperature anomalies.

Let's see what could happen if carbon dioxide concentration increases up to the double from the "standard" value:

The assumed value given to the "standard" concentration of CO2 by the team of IPCC is 280 ppmv. Doubling this concentration means an increase of 560 ppmv. Introducing magnitudes in the formula with the value for alpha of 5.35 W/m^2 and the equilibrium temperature of a black body is 300.15 K:

ΔT = (5.35 W/m^2) ln[(560 ppmv/280 ppmv)] / 4 (5.6697x 10^-8 W/m^2*K^4) (300.15 K)^3 =
= 3.71 W/m^2 / 6.13 W/m^2*K = 0.6 K.

The change of temperature by doubling the concentration of the atmospheric CO2 is not as high even when we introduced an excessive value for the total emitancy of CO2.

The real emittancy for CO2 if the carbon dioxide was increased to 560 ppmv is at a partial pressure of 0.0005 atm*m, that is 0.443 W/m^2. Introducing the total emittancy in the formula, we obtain a change of temperature of:

ΔT = (0.443 W/m^2) ln[(560 ppmv/280 ppmv)] / 4 (5.6697x 10^-8 W/m^2*K^4) (300.15 K)^3 =

= 0.307 W/m^2 / 6.13 W/m^2*K = 0.05 K.

Carbon dioxide is a conveyor of energy through convection and radiation more than an accumulator of heat.

Author: Nasif Nahle Sabag
August 30, 2007

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FURTHER READING

http://www.nap.edu/catalog.php?record_id=10787

http://www.stat.washington.edu/peter/7IMSC/Normals.pdf

Bakken, G. S., Gates, D. M., Strunk, Thomas H. and Kleiber, Max. Linearized Heat Transfer Relations in Biology. Science. Vol. 183; pp. 976-978. 8 March 1974.

Boyer, Rodney F. Conceptos de Bioquímica. 2000. International Thompson Editores, S. A. de C. V. México, D. F.

Haworth, M., Hesselbo, S. P., McElwain, J. C., Robinson, S. A., Brunt, J. W. Mid-Cretaceous pCO2 based on stomata of the extinct conifer Pseudofrenelopsis (Cheirolepidiaceae). Geology; September 2005; v. 33; no. 9; p. 749-752.

Manrique, José Ángel V. Transferencia de Calor. 2002. Oxford University Press. England.

Maoz, Dan. Astrophysics. 2007. Princeton University Press. Princeton, New Jersey.

McGrew, Jay L., Bamford, Frank L and Thomas R. Rehm. Marangoni Flow: An Additional Mechanism in Boiling Heat Transfer. Science. Vol. 153. No. 3740; pp. 1106 - 1107. 2 September 1966.

Petit, J.R., J. Jouzel, D. Raynaud, N.I. Barkov, J.-M. Barnola, I. Basile, M. Benders, J. Chappellaz, M. Davis, G. Delayque, M. Delmotte, V.M. Kotlyakov, M. Legrand, V.Y. Lipenkov, C. Lorius, L. Pépin, C. Ritz, E. Saltzman, and M. Stievenard. Climate and Atmospheric History of the Past 420,000 Years from the Vostok Ice Core, Antarctica. Nature, Vol. 399, June 3, 1999 pp.429-43.

Pitts, Donald and Sissom, Leighton. Heat Transfer. 1998. McGraw-Hill.

Potter, Merle C. and Somerton, Craig W. Thermodynamics for Engineers. Mc Graw-Hill. 1993.

Schwartz, Stephen E. 2007. Heat Capacity, Time Constant, and Sensitivity of Earth's Climate System. Journal of Geophysical Research. [Revised 2007-07-16]

Van Ness, H. C. Understanding Thermodynamics. 1969. McGraw-Hill, New York.

Wagner, Friederike, Bohncke, Sjoerd J. P., Dilcher, David L., Kürschner, Wolfram M., Geel, Bas van, Visscher, Henk. Century-Scale Shifts in Early Holocene Atmospheric CO2 Concentration. Science; 18 June 1999: Vol. 284. No. 5422, pp. 1971 - 1973

Wagner, F., Aaby, B., and Visscher, H. Rapid atmospheric CO2 changes associated with the 8,200-years-B.P. cooling event. Proceedings of the National Academy of Sciences. September 17, 2002; vol. 99; no. 19; pp. 12011-12014.

Wilson, Jerry D. College Physics-2nd Edition; Prentice Hall Inc. 1994.

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