According to anthropogenic global warming (AGW) theory, carbon dioxide increases the potential of water vapor to absorb and emit IR radiation as a consequence of the overlapping absorption/emission spectral bands. I have determined the total emissivity of a mixture of gases containing 5% of water vapor and 0.039% of carbon dioxide in all spectral bands where their absorptivities/emissivities overlap. The result of my calculations is that carbon dioxide reduces the total absorptivity/emissivity of the water vapor, working like a coolant, not a warmer of the atmosphere and the surface.

*Update April 8, 2011. There was an error in calculating the overlapping bands, discovered thanks to criticism from ’Neutrino’. The errors are now shown with lines through them, the correct figures beside them. The ‘adjusted’ calculations give a greater cooling effect from carbon dioxide .*

**Introduction**

Since the popularization of AGW theory in 1988, proponents have argued that carbon dioxide causes an increase in the total absorptivity of the atmosphere^{1, 2, 3}.

For example, at Environmental Defense^{1} it is argued that:

“*As humans emit greenhouse gases like CO2, the air warms and holds more water vapor, which then traps more heat and accelerates warming*.”

And at Science Daily^{2} that:

“*Climate warming causes many changes in the global carbon cycle, with the net effect generally considered to be an increase in atmospheric CO _{2} with increasing temperature — in other words, a positive feedback between temperature and CO_{2}*.”

Masato Sugi and Jun Yoshimura^{3 }claim that:

“*By the overlap effect of CO2 and water vapor absorption bands, the existence of CO _{2} significantly reduces the cooling rate of water vapor…*”

These arguments suggest that by increasing the concentration of carbon dioxide in the atmosphere there will be warming of the atmosphere.

However, according to results from experimentation made by H. C. Hottel^{11}, B. Leckner^{12}, M. Lapp^{13}, C. B. Ludwig^{14}, A. F. Sarofim^{15} and their collaborators^{14, 15} on this matter, the combined effect of overlapping absorption bands causes a reduction on the total absorptivity of a mixture of gases^{4, 5, 6}.

My assessment reinforces the argument made by H. C. Hottel^{11}, B. Leckner^{12}, M. Lapp^{13}, C. B. Ludwig^{14}, A. F. Sarofim^{15} and their collaborators^{14, 15 }because my calculations coincide with the results obtained from the algorithms derived from their experiments.

In 1954, Hoyt C. Hottel conducted an experiment to determine the total emissivity/absorptivity of carbon dioxide and water vapor^{11}. From his experiments, he found that the carbon dioxide has a total emissivity of almost zero below a temperature of 33 °C (306 K) in combination with a partial pressure of the carbon dioxide of 0.6096 atm cm.

Seventeen years later, B. Leckner repeated Hottel’s experiment and corrected the graphs^{12} plotted by Hottel. However, the results of Hottel were verified and Leckner found the same extremely insignificant emissivity of the carbon dioxide below 33 °C (306 K) of temperature and 0.6096 atm cm of partial pressure.

Hottel’s and Leckner’s graphs show a total emissivity of the carbon dioxide of zero under those conditions.

The results of Hottel and Leckner have been verified by other researchers, like Marshall Lapp^{13}, C. B. Ludwig^{14}, A. F. Sarofim^{15}, who also found the same physical trend of the carbon dioxide.

On the other hand, in agreement with observations and experimentation carried out by the same investigators^{11, 12, 14, 15, 16}, the atmospheric water vapor, in a proportion of 5% at 33 °C, has a total emissivity/absorptivity of 0.4.^{5, 6}

The total emissivity/absorptivity of water vapor combined with its high specific heat capacity and its volumetric mass fraction makes water vapor the most efficient absorbent and emitter of Infrared Radiation among all gases forming the Earth’s atmosphere.

In contrast, the carbon dioxide has negligible total emissivities and partial pressures as a component of the atmosphere (the partial pressure of the carbon dioxide at the present atmosphere is 0.0051 atm cm).

So what is the effect of a combination of water vapor and carbon dioxide at current conditions of partial pressure, temperature and mass densities in the atmosphere?

**Methodology**

The whole range of spectral absorption of both gases and an effective path length (*L _{e}*) of 7000

The effective path length is the length of the radiation path through the atmosphere. It differs from the geometrical distance travelled because the radiation is scattered or absorbed on entering and leaving the atmosphere. In a vacuum there is no difference between the effective path length and the geometrical path length. As this assessment deals with the atmosphere, I considered the effective path length in my calculations.

The volumetric mass fraction of water vapor in the atmosphere fluctuates between 10000 *ppmV* and 50000 *ppmV *^{10}. This variability allows the water vapor to show a wide range of high total absorptivities and total emissivities which may vary according to the temperature of the molecule of water vapor. For this reason, I considered the maximum mass fraction of the water vapor in the atmosphere.

The water vapor potential to absorb shortwave infrared radiation from the solar photon stream makes of it the most efficient absorbent of Infrared Radiation. In quantum physics, a photon stream is a current of photons emitted by a source that behave as particles and waves and have a specific directionality i.e. from the source towards the surroundings.

After concluding my analysis, Dr. Charles R. Anderson called my attention to the observation that these calculations constituted further evidence for his theory about the cooling effect of carbon dioxide on the Earth’s surface. When Dr. Anderson and I further examined the calculations, we found that carbon dioxide not only has a cooling effect on the surface, but also on the molecules of other gases in the atmosphere.

The total emissivities of the atmospheric carbon dioxide, water vapor and oxygen were obtained by taking into account the mean free path length of the quantum/waves through those gases, taken individually, and the time lapse rate that a quantum/wave takes on leaving the troposphere after colliding with molecules of carbon dioxide, water vapor and oxygen. This set of calculations will be described in a future article.

**Total Emissivity of a Mixture of Water Vapor and Carbon Dioxide in the Current Atmosphere of the Earth**

On July 3, 2010, at 10:00 hr (UT), the proportion of water vapor in the atmosphere at the location situated at 25º 48´ N lat. and 100 º 19’ W long., at an altitude of 513 m ASL, in San Nicolas de los Garza, Nuevo Leon, Mexico, was 5%. The temperature of the air at an altitude of 1 m was 310.95 K and the temperature of the soil was 330 K. I chose this location, near my office, because it is an open field, far enough from the city and its urban effects.

From this data, I proceeded to calculate the following elements:

1. The *correction factor* for the overlapping emissive bands of H_{2}O_{g} and CO_{2g}.

2. The *correction factor of the total emissivity* of carbon dioxide where the *radiative emission bands* of both gases overlaps, considering that the partial pressure of the carbon dioxide is 0.00039 atm.

3. The *total emissivity* of the mixture of water vapor and carbon dioxide in the atmosphere.

4. The *total normal intensity* of the mixture of water vapor and carbon dioxide in the atmosphere.

5. The *change of temperature* caused by the mixture of water vapor and carbon dioxide in the atmosphere.

**Obtaining the correction factor for the overlapping emissive bands of H _{2}O_{g} and CO_{2g}**

To obtain the total emissivity of the mixture of water vapor and carbon dioxide in the atmosphere, we need to know the *equilibrium partial pressure* of the mixture of water vapor and carbon dioxide. The formula for obtaining the equilibrium *partial pressure* (*ζ*) of the mixture is as follows:

*ζ* = *p*_{H2O} /* (p*_{H2O} + *p*_{CO2) }(*Ref. 5)*

Where *p*_{H2O} is the partial pressure of water vapor in a proportion of 5% in the atmosphere –which is an instantaneous measurement of the water vapor, and *p*_{CO2} is the partial pressure of the carbon dioxide.

*Known values:*

*p*_{H2O }= 0.05 atm

*p*_{CO2} = 0.00039 atm

*Introducing magnitudes:*

*ζ* = *p*_{H2O} /* (p*_{H2O} + *p*_{CO2)} =_{ }0.05 atm / (0.05 atm + 0.00039 atm) = 0.9923

Therefore,* ζ* = 0.9923

*Obtaining the total emissivity of a mixture of water vapor and carbon dioxide in the atmosphere:*

Now let us proceed to calculate the magnitude of the overlapped radiative emission bands of the water vapor and the carbon dioxide. To do this, we apply the following formula:

*Δ**E* = [[*ζ* / (10.7 + 101 *ζ*)] – 0.0089 (*ζ**)^*10.4] (log10 [(*p*_{H2O} + *p*_{CO2}) L] / (*p _{abs}L*)

*Known values:*

ζ = 0.9923

*p*_{H2O} = 0.05 atm

*p*_{CO2} = 0.00039 atm

(*p _{abs}L*)

*L _{e}*

*Introducing magnitudes:*

*ΔE* = [(0.992 / 110.892) – (0.0089 * (0.992)^10.4] * (log_{10} [(0.05 *atm* + 0.00039 *atm*) 7000 *m*] / (1 *atm* *m*)_{0})^2.76 *(Ref. 2)*

*ΔE* = [0.00076] * (2.55 atm m / 1 atm m) = 0.0019; rounding up the cipher, *ΔE* = 0.002

Therefore, the *correction addend* for the overlapping absorption bands is 0.002

Consequently, the *total emissivity of the mixture water vapor and carbon dioxide* is as follows:

*E _{ mixture} *=

*Total Normal Intensity of the energy radiated by the mixture of gases in the air:*

Therefore, the total normal intensity (*I*) (or the spectral radiance over wavelength) caused by the mixture of water vapor and carbon dioxide in the atmosphere is:

*I* = *E _{mix}*

*I* = 0.3997 (5.6697 x 10^-8* *W/m^2 K^4) (310.95)^4 / 3.1416 = 67.44 W/m^2 sr

By way of contrast, the spectral irradiance over wavelength caused by the surface (soil), with a total emissivity of 0.82 (*Ref. 1 and 5*), is as follows:

*I* = *E _{surface}*

*I* = 0.82 (5.6697 x 10^{-8}* *W/m^2 K^4) (330 K) / 3.1416 = 203 W/m^2 sr

Following Dr. Anderson’s recommendation (which I mentioned above in the abstract) I calculated the overlapping bands of a mixture of water vapor (4%), carbon dioxide (0.039%) and Oxygen (21%).

The calculation for a mixture of atmospheric Oxygen (O_{2}), Water Vapor (H2O) and Carbon Dioxide (CO_{2}) is as follows:

*ζ* = *p*_{O2} /* (p*_{O2} + *p*_{CO2)} = 0.21 atm / (0.21 atm + 0.00039 atm) = 4.1675 0.9981

*ζ* = *p*_{O2+CO2} /* (p _{H}*

Consequently, the equilibrium partial pressure of the mixture of oxygen, water vapor and carbon dioxide in the atmosphere is 0.9881 0.9522

And the change of the total emissivity of the mixture is:

*Δ**E* = [[*ζ* / (10.7 + 101 *ζ*)] – 0.0089 (*ζ**)^*10.4] (log10 [(*p*_{H2O} + *p*_{CO2} + p_{O}_{2}) L] / (*p _{abs}L*)

*ΔE* = [[0.9881/ (10.7 + 101 (0.9881)^10.4)] – 0.0089 (0.9881)^10.4] (log10 [(0.26039 atm) 7000 m] / (1* atm*)^2.76 = 0.00989

ΔE = [[0. 9522/ (10.7 + 101 (0.9522)^10.4)] – 0.0089 (0.9522)^10.4] (log10 [(0.26039 atm) 1 m] / (1 atm)^2.76 = 0.008 * 26.11 = 0.2086

And the total emissivity of the mixture of gases in the atmosphere is:

*E _{ mixture} *=

Evidently, the mixture of oxygen, carbon dioxide and water vapor, at current conditions of temperature and partial pressures, causes a sensible decrease of the total emissivity of the mixture of air.

The general conclusion is that by adding any gas with total emissivity/absorptivity lower than the total emissivity/absorptivity of the main absorber/emitter in the mixture of gases makes that the total emissivity/absorptivity of the mixture of gases decreases.

In consequence, the carbon dioxide and the oxygen at the overlapping absorption spectral bands act as mitigating factors of the warming of the atmosphere, not as intensifier factors of the total absorptivity/emissivity of the atmosphere.

**Conclusions**

My assessment demonstrates that there will be no increase in warming from an increase of absorptivity of IR by water vapor due to overlapping spectral bands with carbon dioxide.

On the overlapping absorption spectral bands of carbon dioxide and water vapor, the carbon dioxide propitiates a decrease of the total emissivity/absorptivity of the mixture in the atmosphere, not an increase, as AGW proponents argue ^{1, 2, 3}.

Applying the physics laws of atmospheric heat transfer, the carbon dioxide behaves as a coolant of the Earth’s surface and the Earth’s atmosphere by its effect of diminishing the total absorptivity and total emissivity of the mixture of atmospheric gases.

Dr. Anderson and I found that the coolant effect of the carbon dioxide is stronger when oxygen is included into the mixture, giving a value of *ΔE* = 0.3814, which is lower than the value of *ΔE *obtained by considering only the mixture of water vapor and carbon dioxide.

by Nasif S. Nahle, Director of Scientific Research Division at Biology Cabinet Mexico

Read more from Nasif by scrolling through the articles here: http://jennifermarohasy.com/blog/author/nasif-s-nahle/ .

**Acknowledgments**

I am very grateful to Dr. Charles R. Anderson, PhD, author of the Chapter 20 in the book *Slaying the Sky Dragon-Death of the Greenhouse Gases Theory*, especially page 313 for his valuable help on realizing the cooling role of the Oxygen in the atmosphere.

http://www.amazon.com/Slaying-Sky-Dragon-Greenhouse-ebook/dp/B004DNWJN6

**References**

1. http://www.edf.org/documents/5596_GlobalWarmingWaterVapor_onepager.pdf

2. http://www.sciencedaily.com/releases/2010/01/100127134721.htm

3. http://journals.ametsoc.org/doi/pdf/10.1175/1520-0442(2004)017%3C0238%3AAMOTPC%3E2.0.CO%3B2

4. Manrique, J. A. V. *Transferencia de Calor*. 2002. Oxford University Press. England.

5. Modest, Michael F. *Radiative Heat Transfer-Second Edition*. 2003. Elsevier Science, USA and Academic Press, UK.

6. Pitts, Donald and Sissom, Leighto*n. Heat Transfer*. 1998. McGraw-Hill, NY.

7. Van Ness, H. C. *Understanding Thermodynamics*. 1969. General Publishing Company. Ltd. Ontario, Canada.

8. Engel, Thomas and Reid, Philip. *Thermodynamics, Statistical, Thermodynamics & Kinetics*. 2006. Pearson Education, Inc.

9. Anderson, Charles R. *Slaying the Sky Dragon-Death of the Greenhouse Gas Theory. *2011. Chapter 20. Page 313.

10. http://www.eoearth.org/article/Atmospheric_composition

11. Hottel, H. C. *Radiant Heat Transmission-3 ^{rd} Edition*. 1954. McGraw-Hill, NY.

12. Leckner, B. *The Spectral and Total Emissivity of Water Vapor and Carbon Dioxide*. Combustion and Flame. Volume 17; Issue 1; August 1971, Pages 37-44.

13. http://thesis.library.caltech.edu/2809/1/Lapp_m_1960.pdf

14. Ludwig, C. B., Malkmus, W., Reardon, J. E., and Thomson, J. A. L. Handbook of Infrared Radiation from Combustion Gases. Technical Report SP-3080.NASA. 1973.

15. Sarofim, A. F., Farag, I. H., Hottel, H. C. Radiative Heat Transmission from Nonluminous Gases. Computational Study of the Emissivities of Carbon Dioxide. ASME paper No. 78-HT-55.1978

]]>Central to the theory of Anthropogenic Global Warming (AGW) is the assumption that the Earth and every one of its subsystems behaviors as if they were blackbodies, that is their “emissivity” potential is calculated as 1.0. ^{[}^{1}^{]}

But this is an erroneous assumption because the Earth and its subsystems are not blackbodies, but gray-bodies. The Earth and all of its subsystems are gray-bodies because they do not absorb the whole load of radiant energy that they receive from the Sun and they do not emit the whole load of radiant energy that they absorb. ^{[8] [9] [10]}

Furthermore the role of carbon dioxide is misunderstood. According to AGW hypothesis, carbon dioxide is the second most significant driver of the Earth’s temperature, behind the water vapor, which is considered the most important driver of the Earth’s climate. ^{[2]} Other authors of AGW discharge absolutely the role of water vapor and focus their arguments on the carbon dioxide. ^{[3]}

What is the total emissivity of carbon dioxide? I will consider this question with reference to the science of radiative heat transfer.

*Total Emissivity of the Carbon Dioxide – The Partial Pressures Method*

In 1954, Hoyt C. Hottel undertook an experiment for determining the total emissivity of the carbon dioxide and the water vapor ^{[6]}. He found that the total emissivity was linked to the temperature of the gas and its partial pressure. As the temperature increased above 277 K, the total emissivity of the carbon dioxide decreased, and as the partial pressure (*p*) of the carbon dioxide increased, its total emissivity also increased.

Hottel found also that the total emissivity of the carbon dioxide in a saturated state was very low (*Ɛ** _{cd}* = 0.23 at 1.524 atm-m and

As Hottel diminished the partial pressure of the carbon dioxide, its total emissivity also decreased in such form that, below a partial pressure of 0.006096 atm-m and a temperature of 33 °C, the total emissivity of the carbon dioxide was not quantifiable because it was almost zero. ^{[6] [7] [8]}

After Hottel’s experiment, in 1972, Bo Leckner made the same experiment and corrected and error on the graphs plotted by Hottel. However, Leckner’s results placed the carbon dioxide in a lower stand than that found by Hottel. ^{[6] [7]}

The missing part, however, remained at the real partial pressure of the carbon dioxide in the Earth’s atmosphere and instantaneous temperatures. Contemporary authors, like Michael Modest, and Donald Pitts and Leighton Sissom made use of the following formula to know the total emissivity of the carbon dioxide considering the whole emissive spectrum, at any instantaneous tropospheric temperature and altitude ^{[6] [7] [8]}:

*Ɛ** _{cd}* = [1 – (((

Introducing 7700 meters as the average altitude of the troposphere and the real partial pressure of the atmospheric carbon dioxide (0.00038 atm-m), the resulting total emissivity of the carbon dioxide is 0.0017 (0.002, rounding up the number).

Evidently, the carbon dioxide is not a blackbody, but a very inefficient emitter (a gray-body). For comparison, Acetylene has a total emissivity that is 485 times higher than the total emissivity of the carbon dioxide.

After getting this outstanding result, I proceeded to test my results by means of another methodology that is also based on experimental and observational data. The algorithm is outlined in the following section.

*Total Emissivity of CO _{2} – Mean Free Path Length and Crossing Time Lapse of Quantum/Waves Method*

The mean free path length is the distance traversed by quantum/waves through a given medium before it collides with a particle with gravitational mass. The crossing time lapse is the time spent by the quantum/waves on crossing a determined medium; in this case, the atmosphere is such medium.

As the carbon dioxide is an absorber of longwave IR, we will consider only the quantum/waves emitted by the surface towards the outer space.

The mean free path length of quantum/waves emitted by the surface, traversing the Earth’s troposphere, is *l* = 47 *m*, and the crossing time is *t *= 0.0042 s (4.2 milliseconds).^{ [9] [10]}

Considering *l *= 47 m to know the crossing time lapse of quantum/waves through the troposphere, I obtained the crossing time lapse *t *= 0.0042 s. By introducing *t *into the following equation, we obtain the real total emissivity of the atmospheric carbon dioxide:

*Ɛ** _{cd}* = [1-(

*Ɛ** _{cd}* = [1-(

Therefore, the total emissivity of the atmospheric carbon dioxide obtained by considering the mean free path length and the crossing time lapse for the quantum/waves emitted from the surface coincides with the value obtained from the partial pressures method:

*Ɛ** _{cd }*1

*Ɛ** _{cd }*2 = 0.0024 = 0.0024

The difference is 0.0007, which is trivial in this kind of assessment.

*Conclusions*

In the introduction I asked: What is the total emissivity of carbon dioxide?

In this note I have calculated the real total emissivity of the atmospheric carbon dioxide at its current partial pressure and instantaneous temperature to be 0.002.

Clearly carbon dioxide is not a nearly blackbody system as suggested by the IPCC and does not have an emissivity of 1.0. Quite the opposite, given its total absorptivity, which is the same than its total emissivity, the carbon dioxide is a quite inefficient – on absorbing and emitting radiation – making it a gray-body.

Accepting that carbon dioxide is not a black body and that the potential of the carbon dioxide to absorb and emit radiant energy is negligible, I conclude that the AGW hypothesis is based on unreal magnitudes, unreal processes and unreal physics.

*Acknowledgements *

This blog post was inspired by Chapter 12 of the book ‘Slaying the Sky Dragon.

“This first catechism will be referred to in a later figure as the ‘Cold Earth Fallacy’, and it is based on the erroneous assumption that the earth’s surface and all the other entities involved in its radiative losses to free space all have unit emissivity. The second catechism has already been discussed: the contention that Venus’ high surface temperature is caused by the ‘greenhouse effect’ of its CO2 atmosphere.”

-Dr. Martin Hertzberg. *Slaying the Sky Dragon-Death of the Greenhouse Gas Theory*. 2011. Chapter 12. Page 163. ^{[11]}

http://www.amazon.com/Slaying-Sky-Dragon-Greenhouse-ebook/dp/B004DNWJN6

*References*

[1.] Hertzberg, Martin. *Slaying the Sky Dragon-Death of the Greenhouse Gas Theory. *2011. Chapter 12. Page 163.

[2.] http://www.bom.gov.au/info/GreenhouseEffectAndClimateChange.pdf (Page 6).

[3.] http://www.aip.org/history/climate/co2.htm

[4.] http://www.zypcoatings.com/ProductPages/BlackBody.htm

[5.] http://www.ib.cnea.gov.ar/~experim2/Cosas/omega/emisivity.htm

[6.] Hottel, H. C. *Radiant Heat Transmission-3rd Edition*. 1954. McGraw-Hill, NY.

[7.] Leckner, B. *The Spectral and Total Emissivity of Water Vapor and Carbon Dioxide*. Combustion and Flame. Volume 17; Issue 1; August 1971, Pages 37-44.

[8.] Modest, Michael F. *Radiative Heat Transfer-Second Edition*. 2003. Elsevier Science, USA and Academic Press, UK.

[9.] Lang, Kenneth. 2006. *Astrophysical Formulae*. Springer-Verlag Berlin Heidelberg. Vol. 1. Sections 1.11 and 1.12.

[10.] Maoz, Dan. *Astrophysics in a Nutshell*. 2007. Princeton University Press. Pp. 36-41

[11.] Dr. Hertzberg is an internationally recognized expert on combustion, flames, explosions, and fire research with over 100 publications in those areas. He established and supervised the explosion testing laboratory at the U. S. Bureau of Mines facility in Pittsburgh (now NIOSH). Test equipment developed in that laboratory have been widely replicated and incorporated into ASTM standards. Published test results from that laboratory are used for the hazard evaluation of industrial dusts and gases. While with the Federal Government he served as a consultant for several Government Agencies (MSHA, DOE, NAS) and professional groups (such as EPRI). He is the author of two US patents: 1) Submicron Particulate Detectors, and 2) Multichannel Infrared Pyrometers. http://www.explosionexpert.com/pages/1/index.htm

**************

Read more from Nasif by scrolling here: http://jennifermarohasy.com/blog/author/nasif-s-nahle/

]]>The general belief on the conditions of the deep space, beyond the terrestrial exosphere, is about a completely empty place without temperature.

However, highly accurate measurements made by satellites, like the Wilkinson Microwave Anisotropy Probe (WMAP)^{ }[2], have corroborated that the deep space has a temperature and, additionally, that it is not an absolutely empty space.

WMAP has revealed a deep space temperature of 2.7251 K and a density of 1 particle/cm^3** ^{ }**(density based on protons in the outer space) [3].

The theoretical temperature was confirmed by WMAP measurements. The theoretical basis related to the temperature of the deep space is given by the correlation between the temperature and the kinetic energy of the particle. On this case, the root mean square (*rms*) speed *v _{rms}* of protons in deep space is 260 m/s.

The purpose of this essay is to know the amount of energy emitted by the Earth towards the outer space and the concept of microstates.

*The Earth in the Cold Space*

The formula to calculate the temperature of deep space is as follows:

*T* = (*m***v*^2* _{rms}*) / (3*

Where *m* is the mass of particles, *v _{rms}* is the root mean square velocity of those particles in that medium –because protons speed is highly variable, and

Given that ionized Hydrogen is the main constituent in the outer space, we consider the mass and the root mean square velocity of a proton in deep space to make our calculations.

Known values:

*m* = 1.67 x 10^-27 *kg** *(mass of a proton)

*v _{rms}* = 260

*k* = *Boltzmann’s constant* = 1.38 x 10^-23 *J*/*K*

By introducing magnitudes into the formula *T* = (*mv*^2*rms*)**/**( 3**k*), the theoretical temperature *T* of deep space, taking into account the kinetic energy of protons in deep space gives a result of 2.72686. The* rms* error is 0.00176 K, which is quite insignificant (0.06%), therefore, the theoretical value is in conformity with direct measurements.

The outer space is the environment of the Earth. The question is:

How much power the Earth radiates per unit area toward the deep space? To answer this question, let us resort to the Stephan-Boltzmann Equation:

*P* = *e* (*A*) (*σ*) (*T**Earth*^4 – *T**ds*^4)

Here, a problem arises with respect to the emissivity of the Earth. However, careful examinations and calculations of the Earth’s emissivity give a mean correlation factor of 0.82. [4] Introducing this correlation factor, the power emitted by the Earth, per square meter, during one second, is 329.51 W.

To correct this apparent incongruence with respect to the supposed amount of the incident solar IR radiation on Earth’s surface, some authors resort to iterate the quantity until the resulting power equals to the supposed incident solar IR radiation.

However, we only are allowed to take into account the sphericity of the Earth, so the value changes to *e _{sph}* =

The result after introducing the new correlation factor of 0.644 is 258.8 W.

Our last option to get the emissivity is to invent it by means of introducing a flawed value of the emissions from the Earth:

*e* = (249 W) / [A (*σ*) (*T _{Earth}*^4 –

This way, we make the hypothesis matches with the Earth’s energy budget model.

However, this is not a valid procedure in science because the scientific methodology starts with observations and after it proceeds to produce hypotheses, which must be proven by means of experimentation, or more observations.

If we consider the correlation coefficient 0.82 as the total emissivity of the Earth, the absorbed energy by the Earth would be 601.92 J. The latter magnitude represents 44% of the solar constant (1368 W/m^2 x 0.44 = 601.92 W/m^2). NASA assigns a theoretical absorption of solar energy by the Earth of 48%.

Here, the power emitted by an ideal Earth should be 401 W. However, the measurements of the Earth’s emissivity reveal a correlation factor of 0.82.

Consequently, the observations of the real world reveal that the value of 0.62 assigned *a priori *to the emissivity of the Earth is not real and rise serious doubts about the total amount of solar power absorbed and the amount of power emitted by our planet.

*Microstates and the Outer Space*

To properly talk about microstates, we need that any amount of matter is present in a given medium. We cannot talk about microstates if we have not, at least, one Hydron (H^{+}) in a given medium.

A microstate refers to any initial of final configuration of the energy in a given system.

The Second Law of Thermodynamics, although initially was derived from the observation of thermal processes, has been proven to be acting on every level of energy exchange between two or more systems.

Initially, the Second Law was described in terms of the directionality in the flow of the energy in transit (a process function), which depends on the states of the systems involved in the exchange of such energy in transit. The Second Law clearly specified that the work only can be done by a higher energy density system on a lower energy density system and not the opposite.

However, with the advent of Quantum Physics, the scientists wondered whether this Law was valid at the quantum level or not. The answer to this question was given heuristically through the calculations of Maxwell, Boltzmann and Gibbs. The heuristic character of the calculations vanished when those hypotheses were later confirmed by experimentation.

In consequence, the definition of the Second Law was amplified to include its influence on the quantum level and not only on those process functions where heat and work were implied.

This shift was important because it defined the real concept of entropy and detached it from contextual derivations. For example, now we know that the fundamental concept of entropy has nothing to do with disorder, movement, complexity or heat “content”, but with the configurations that the energy adopts in a given system and the directionality of the energy exchange.

Entropy is now defined as the natural trend of the energy to flow towards the system or systems with a higher number of available microstates.

Let us say that two systems permit six configurations of the energy. One of them, let us say the system A, has four “occupied” configurations and only two available configurations. The other system, or system B, has only one “occupied” configuration and five available configurations. According to the Second Law of Thermodynamics, the energy will flow spontaneously from the system A to the system B and never the opposite.

Perhaps, you are wondering if the energy could flow from B to A during the process. The answer is **no** because two systems implied in an energy exchange process cannot adopt the same configuration at once, although any system could adopt any configuration.

To calculate the number of microstates that a system can adopt, we resort to the following formula:

*N _{ms}* =

Where *N _{ms }*is the number of available microstates (Maxwell-Boltzmann Number),

*N _{ms}* =

Then, 30 is the number of available microstates for this system.

Let us consider a system B with the same number of particles (six) and the same number of levels of energy, i.e. six, but where each particle is occupying a level of energy, i.e. one particle at level 0E, one particle at level 1E, one particle at level 2E, etc. The solution is as follows:

*N _{ms}* = 6! / (1! * 1! * 1! *1! * 1! * 1!) = 720 / 1 = 720

This system offers more available microstates, that is, more configurations to be adopted by the energy in a radiation process. Therefore, the radiation will flow from system A, with 30 available microstates, towards system B, with 720 available microstates.

What about the outer space, where there is only one particle per cubic meter? Is it possible that it has more available microstates than the massive Earth?

All the particles in the deep space are in their basic configuration, that is, there are no particles occupying any level of energy, but only high speed protons, therefore:

*N _{ms}* = 6! / (0!) = 720 / 1 = 720

Consequently, the radiation **trajectory** will be always from the Earth towards the deep space, the most efficient sink of radiation of any kind. Notice that it has nothing to do with temperature, disorder, complexity, etc.

Kevan Hashemi asked Cohenite if a particle at 300 K will or will not emit photons. Any particle at 300 K is at its fundamental energy state, i.e. its available microstates will be higher than those of any particle with a temperature above 300 K. Such particle won’t radiate, but it will absorb energy.

**By Nasif S. Nahle, ****Scientific Research Director at Biology Cabinet Mexico, **

**Nasif’s website ****http://www.biocab.org**

More from Nasif at this blog http://jennifermarohasy.com/blog/author/nasif-s-nahle/

*Acknowledgements *

This topic has been magisterially touched by Alan Siddons in Chapters 2 and 3 of the book “Slaying the Sky Dragon-Death of the Greenhouse Theory”.

Alan Siddons explains how the models on the Earth’s energy budget cannot depict the real exchange of energy through radiation between the Sun and the Earth and the Earth and the deep space [1].

This essay deals with the exchange of energy between the Earth and the deep space, already explained by Alan Siddons in his articles, and with the quantum concept of microstates, which agrees with the explanation given by Alan Siddons on his articles in the book Slaying the Sky Dragon-Death of the Greenhouse Theory.

*Further Reading*

- http://slayingtheskydragon.com
- http://map.gsfc.nasa.gov/
- John D. Cutnell and Kenneth W. Johnson.
*Physics, 3rd Edition*. John Wiley and Sons, Inc. 1995. New York. Page 434. - http://www.gisdevelopment.net/technology/rs/ma03196.htm

Key diagrams on the Earth’s energy budget depicts an exchange of energy between the surface and the atmosphere and their subsystems considering each system as if they were blackbodies with emissivities and absorptivities of 100% ^{1, 2}.

This kind of analyses shows a strange “multiplication” of the heat transferred from the surface to the atmosphere and from the atmosphere to the surface which is unexplainable from a scientific viewpoint. The authors of those diagrams adduce that such increase of energy in the atmosphere obeys to a “recycling” of the heat coming from the surface by the atmosphere ^{1,} ^{2}, as if the atmosphere-surface were a furnace or a thermos and the heat was a substance.

Such “recycling” of heat by the atmosphere does not occur in the real world for the reasons that I will expose later in this note.

Few authors have avoided plotting such unreal recycling of heat and only show the percentages related to the flow of energy among systems and subsystems of the Earth ^{3, 4}.

We do know that serious science makes a clear distinction between heat and internal energy. However, we will not touch this abnormal definition of heat from those erroneous diagrams^{1, 2} on the annual Earth’s energy budget.

In addition to the wrong concept of *heat* that the authors let glimpse in their articles ^{1, 2}, the recycling of heat by the atmosphere does not and cannot occur in the real world. There are many physical factors, already proven experimentally and observationally^{5}, that nullify the ideas of the recycling of heat by the atmosphere.

The principal physical factor that inhibits the recycling of heat in the atmosphere is the degradation of the energy each time it is absorbed and emitted by any system^{10}. This degradation of energy is well described by the second law of thermodynamics^{6}, whose fundamental formulation is as follows:

*The energy is always dispersed or diffused from an energy field with lesser available microstates towards an energy field with higher available microstates*^{5}.

In other words, the energy is always dispersed or diffused from the system with a higher energy density towards the system with a lower energy density^{5, 10}.

The purpose of this essay is to demonstrate that some evaluations ^{1, 2} on the Earth’s annual energy budget are not considering the laws of basic physics and thermodynamics, that the “recycling” of heat in the atmosphere is unphysical and that the carbon dioxide works like a coolant of the surface, rather than like a warmer.

*Analysis*

The Earth and all its subsystems are gray-bodies^{3}; consequently, any calculations made on the basis of blackbodies greatly differ from the real world, but only provide us an idea about what could be happening in such or that physical situation^{5}. This means that they cannot absorb all the energy that they receive from a source and that, equally, they cannot emit the whole amount of such absorbed energy in the form of energy capable to do work on other systems, but rather that the main part of that energy is no longer accessible for making work and it is lost irremediably into the natural heat sinks.

All the spontaneous processes occurring in nature are irreversible processes ^{7, 8}. **Absolutely-reversible processes do not exist in the natural world **^{9}, while absolutely-irreversible processes do exist in the natural world.

*Shift to Red of Dispersed Quantum/Waves and Emitted by the Atmosphere Quantum/Waves*

There are three bands of absorption of IR radiation by the carbon dioxide, i.e. 2.6 µm, 4.3 µm and 14.77 µm.

In this assessment, we will analyze the absorption of the energy of quantum/waves with wavelengths of 4.3 µm and 14.77 µm

The energy of an IR quantum/wave with a wavelength of 4.3 µm, emitted from the Earth’s surface is **4.62 x 10^-20 J**. From this energy, a molecule of CO_{2} absorbs **9.24 x 10^-23 J**.

**4.61 x 10^-20 J** are dispersed to other systems, except to the molecules that dispersed it. This amount of energy corresponds to a wavelength of **4.31 µm**. The wavelength has been lengthened (redshift) by 0.01 µm.

A quantum/wave with wavelength = **14.77 µm **–the band at which the carbon dioxide exhibits its maximum absorption potential- has an energy density of **1.345 x 10^-20 J**. If it hits a molecule of CO_{2}, the carbon dioxide molecule absorbs only **2.7 x 10^-23 J, **while the energy carried by the dispersed quantum/wave is 1.3423 x 10^-20 J.

The carbon dioxide molecule emits a quantum/wave with energy = **5.4 x 10^-26 J**, which corresponds to a wavelength *λ* of **3.75 m**. The quantum/wave emitted by the carbon dioxide **is not an IR quantum wave, but a Radio quantum/wave**; therefore, its energy cannot be absorbed as heat neither by the surface neither by molecules of carbon dioxide.

Notice that **1.32145 x 10^-20 J** is dispersed towards another energy field with more available microstates that resides in other systems; for example, the outer space, water vapor molecules, or dust. The wavelength of the dispersed quantum/waves has been elongated up to **14.8 µm **(redshift); this elongation puts the IR quantum/wave out of the range of absorptivity of carbon dioxide by the ** specificity and sensitivity of absorption and emission potentials**; consequently,

The following calculation over the resulting quantum/wave with wavelength of 14.8 µm** absorbed by the carbon dioxide does not happen in nature**; however, I decided to include it for readers take notice of the impossibility that heat can be “recycled” in the atmosphere.

Assuming that the absorption of that quantum/wave is still possible and another molecule of carbon dioxide could absorb it, we would have that:

For a wavelength **14.8 µm**, the energy absorbed by the molecule of CO_{2} would be **1.3215 x 10^-20 J**.

The energy of a quantum/wave emitted by that molecule of carbon dioxide would be **2.643x 10^-23 J**, which would correspond to a wavelength of **0.7515 cm**. This magnitude would match with the band of microwaves in the EM spectrum (microwaves’ wavelength = **0.01 to 20 cm**). It still contains usable energy, but this energy can no longer be absorbed by molecules of carbon dioxide and it is lost into any of the energy sinks.

At this point, let us remember that the longer the wavelength is, the lower the energy density of that quantum/wave is.

The energy required to excite an electron for it shifts from a lower quantum microstate to the next higher quantum microstate is **5.4468 x 10^-19 J**.^{ Ref. 5}

Therefore, the percentage of energy absorbed by a molecule of carbon dioxide with a wavelength of **14.77 µm **represents **0.2%** of the total energy required to excite an electron of the atoms of a molecule of carbon dioxide.

In that case, for an electron in the carbon dioxide molecule becomes excited and changes its energy configuration, a contribution of energy, supplied by 20554 IR quantum/waves, is required. Consequently, the carbon dioxide in the Earth’s atmosphere is in an energy field with higher number of available microstates.

This is the reason by which the flow of power is always transferred on a very specific directionality, i.e. from higher to lower and never the opposite.

How many molecules of carbon dioxide would be needed to get **249 Joules** of energy in the total volume of carbon dioxide in the atmosphere?

~4.6 x 10^20 molecules of carbon dioxide are needed to get a volume of air absorbing 249 Joules of energy within the wavelength 14.77 µm.

There are ~2.61 x 10^9 molecules of carbon dioxide in one cubic meter of air; therefore, we need 1.76 x 10^11 m^3 of air for the molecules of carbon dioxide can absorb, simultaneously, 249 J.

The total volume of the Earth’s air is 4.2 × 10^18 m^3. There are ~1.1 x 10^28 molecules of carbon dioxide in the whole volume of air on Earth; consequently, almost the whole volume of molecules of carbon dioxide in the Earth’s atmosphere would absorb 249 J.

Therefore, there are 6.23 x 10^26 probabilities that the total amount of carbon dioxide in the Earth’s atmosphere absorbs the whole load of energy of 249 J; however, each molecule of carbon dioxide would absorb only **2.3 x 10^-26 J**.

The molecules of carbon dioxide which had absorbed **2.3 x 10^-26 J** of energy would emit quantum/waves with wavelength = **4.3 km**, which correspond to the spectrum of vertical gravity waves (buoyancy). Therefore, those waves are lost in the gravity field.

As a result, the carbon dioxide is a coolant, rather than a warmer, of the Earth.

*In conclusion*

Key diagrams that purport to show the annual energy budget of Earth show a recycling in the atmosphere of the heat emitted by the surface. But they are wrong.

The lengthening of the wavelength of quantum/waves emitted by the absorber systems and the decrease of their frequency inhibit any possibility of re-absorption of the absorbed energy -in the form of infrared radiation- by the same absorber once it has been emitted out from the absorber system.

Additionally, this assessment confirms that the second law of thermodynamics is applicable to molecular and quantum levels.

The carbon dioxide does not act like a warmer of the Earth’s surface, but rather like a coolant of the Earth’s surface.

*References*

1. Kiehl, J. T. and Trenberth, K. E. (1997). *Earth’s Annual Global Mean Energy Budget*. Bulletin of the American Meteorological Association. No. **78**. Pp. 197-208.

2. http://www.globalwarmingart.com/wiki/Image:Greenhouse_Effect.png

3. Peixoto, José P., Oort, Abraham H. 1992. *Physics of Climate*. Springer-Verlag New York Inc. New York. Page 366.

4. http://eosweb.larc.nasa.gov/EDDOCS/images/Erb/components2.gif

5. Castellan, Gilbert W. *Physical Chemistry-3 ^{rd} Edition*. Addison-Wesley-Longman Publishing Company, Inc. 1998.

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

7. http://www.brighthub.com/engineering/mechanical/articles/4616.aspx

8. http://pubs.acs.org/doi/abs/10.1021/ed010p45

9. http://www.ecourses.ou.edu/cgi-bin/eBook.cgi?doc=&topic=th&chap_sec=05.3&page=theory

10. http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node49.html

***********************

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The theory dealing with the effect of gravity on quantum/waves radiation was proposed by Albert Einstein in 1905 ^{[1, 2]}. This theory was followed by the release of Einstein’s concepts and calculations on induced negative absorption^{ [2]}.

So the effect of pressure on EM quantum waves as the induced negative absorption have been verified empirically ^{[6]} and have been applied to high tech laboratory devices (lasers, cyclotrons, plasma chambers, etc.), as for domestic technologies (microwave ovens), most of them patented by engineers.

Mass is associated with matter, although energy also possesses effective inertial mass. Is it possible to think about mass without associating it with matter? Yes, it is possible. To do this, we have to stop associating mass with matter, i.e. *all matter possesses mass; however, mass is not only related to matter*.

Electromagnetic energy has effective inertial mass. The same is true for internal energy that is determined by the absorbed electromagnetic energy. Unquestionably, we can apply the same concept to kinetic energy and potential energy.

Remember that, although the units to express mass are the same units that we use for weight, mass is not weight or vice-versa.

We do know the definition of matter is incomplete and inadequate; nevertheless, our poor definition of matter yet is useful on defining weight.

Weight is the attraction *force* exerted on a body by effect of gravity. For example, a rock on the Earth’s surface is attracted by means of the gravitational force exerted by the Earth on the rock and it depends on the Earth’s mass and the mass of the rock. Such force is what we know as weight. If we take the same rock and place it on the surface of the Moon, *the mass of the rock does not change*, but its weight decreases because the gravitational force on the Moon exerted on the matter placed on its surface is lower than that on Earth.

On the other hand, mass is the amount of concentrated energy in a given region of space^{ [3]}. This definition of mass relates energy with matter because matter actually is condensed energy, and mass and energy are properties of matter. ^{[3]}

Therefore, energy has effective inertial mass and its equivalent in gravitational mass^{ [6]}. IR quantum/waves have gravitational mass which is equivalent to their effective inertial mass.

The effective inertial mass of a single quantum/wave is analogous to (*hf*)/*c*^2; hence, we apply this formula to calculate the gravitational mass of quantum/waves, which is written in the following form:

(*gH*)/*c*^2

Where *g* is the gravity acceleration 9.8 cm/s^2, *H* is height (for the Earth’s troposphere, the average is 7.7 x 10^5 cm), and *c*^2 is the speed of light raised to the second power.

*Analysis*

The formula to calculate the fraction of frequency change is as follows:

*Δf/f = *(*gH*)/*c*^2 ^{[6]}

Where *Δf* is the change of the quantum/wave frequency due to gravity, *f* is the instantaneous frequency of the quantum/wave, *g* is the gravitational acceleration = 9.8 m/s^2, *H* is altitude and *c*^2 is the speed of light raised to the second power.

Up to an altitude of 770000 *cm*, the average altitude of the Earth’s troposphere, the fraction of frequency of the IR quantum/waves radiated from the ground and outgoing to the space, with a frequency of 4.3 × 10^{14} *Hz*, is:

*Δf/f = *(*gH*)/*c*^2

Introducing magnitudes:

*Δf/*4.3 × 10^{14}* Hz = *(980* cm/s*^2* * *770000 *cm*)/ (2.99792458 x 10^10 cm/s)^2 = 8.396 x 10^(-13)

And the displacement of the frequency *Δf *is:

*Δf* = 4.3 × 10^{14}* Hz * *(8.396 x 10^(-13)) = 361.03 *Hz*

Notice that the change of frequency is very low; however, it has a significant effect on energy density and wavelength.

For the circumstances of visible light, *Δf* is:

*Δf *= 7.9 x 10^14* Hz* [(9.8 x 10^2 (cm/s^2)*(770000 cm))/(2.99792458 x 10^10 (cm/s))^2] =

= 7.9 x 10^14 Hz [(7.546 x 10^8 (cm^2/s^2)/(8.987551 x 10^20 (cm^2/s^2))] = 663.3 Hz

Consequently, the power of an IR quantum/wave emitted from the ground towards the atmosphere is lower at a height of 7.7 km than at the boundary layer surface-atmosphere. In other words, the energy density of the quantum/wave is lower at higher altitudes than at the surface level in the finite moment that the quantum/wave is emitted ^{[5]}^{ }(U = a *T^4). Therefore, the air immediately above the surface is warmed further than the air at higher heights.

The same observable fact occurs to quantum/waves that are emitted by the air. Considering the frequency of IR quantum/waves emitted towards the space by the air layer immediately above the surface, we obtain a change of frequency of 4.61 *Hz*.

The resistance to the onward movement of quantum/waves exerted by the Earth’s gravity causes a reduction of the frequency if the radiation is emitted toward minor altitudes. For example, the change of frequency of a quantum/wave emitted by the surface towards the upper limit of 10 meters, above the ground, is 0.86 *Hz*.

Nevertheless, the frequency of quantum/waves decrease as it goes farther away from the emitter; for example, at 7.7 *km* of altitude, the change of quantum/wave frequency is 663.3 *Hz*, and the final frequency *f _{f}* is:

*f _{f }*= 7.9 x 10^14

From here, we conclude that the IR quantum/wave’s redshift due to the gravitational force of Earth is quite evident.

By calculating the average tropospheric radius, for an IR quantum/wave frequency of 7.9 x 10^14 *Hz*, we obtained Graph 1.

Notice that the change of frequency is linear while the resulting frequency is a continuous non-linear curve (a polynomial function). As the IR Quantum/Waves travel towards the space, their Frequency decreases; consequently, the energy density in IR Quantum/Waves also decreases.

Graph 2 depicts the energy density of IR Quantum/Waves as they travel from the surface towards the outer space, although the plot only represents 7.7 km of altitude from the total altitude of Earth’s troposphere.

I have added linear trend lines to both curves to provide evidence of the non-linear trend in both properties of IR quantum/waves. The energy density of the quantum/waves magnitudes is proportional to the final frequency; specifically, to a higher frequency, a higher energy density; to a lower frequency, a lower energy density. This requires the application of thermodynamics of non-linear systems, specifically, quantum thermodynamics, i.e. the procedures I have been applying on these calculations.

Therefore, the formula to calculate the final frequency *f*’ is:

*f’*/*cm* = *f* (1-(*gH*/*rc*^2))

Where *f’* is the resulting frequency, *f* is is the initial frequency, and *r* is the Earth’s troposphere’s radius. For example, for an initial frequency of 7.9 x 10^14 *Hz*, the red shift is at the resulting frequency of 7.89 x 10^14 *Hz*/*cm*:

And, by isolating the variable *f’* we obtain:

*f’* = (*cm*) * 7.89 x 10^14 *Hz*/*cm** *= 7.89 x 10^14 *Hz*

Given that wavelength is inversely proportional to frequency -i.e. the higher the frequencies, the lower the wavelengths and vice versa, for systems emitting IR quantum/waves of a frequency equal to 2.998 x 10^13 *Hz* and a wavelength λ = 1.0 x 10^4 nm, we obtain a wavelength displacement *Δλ* (redshift) of:

*Δλ* = 8.396 x 10^(-13) x 0.001 *cm* = 8.396 x 10^(-9) *nm*.

And the resulting wavelength *λ* is 0.000999 *cm*.

Therefore, the energy density of a quantum/wave decreases as its wavelength is lengthened. The longer the wavelength is, the lower the energy density is.

The inverse proportionality between* **Δλ* and* **Δf* is evidenced by Graph 3.

As* Δf* decreases, *Δλ* increases. As* Δf* increases and* Δλ* decreases, the energy density of the IR quantum/wave increases.

*Conclusion*

The correlation between the frequency of IR quantum/waves radiated from the surface being affected by the Earth’s gravity and the energy density of those IR quantum/waves demonstrates that gravity exerts an important effect on the warming of the troposphere.

The results indicate that the energy density of the IR quantum/waves near the surface increases as the frequency of the quantum/waves increases. Due to the effect of the gravity on the frequency of quantum/waves, the wavelength is also inversely affected with respect to the frequency fraction generating a shift towards the red spectrum, which means a decrease of the energy density of the quantum/waves.

This is the most plausible explanation to the adiabatic effect observed in the Earth’s atmosphere and evidence against any influence of the carbon dioxide on the Earth’s temperature.

The low total emissivity of the carbon dioxide (0.002), the induced negative absorption that determines the directionality of emissions from the carbon dioxide towards the outer space, the radiation pressure that always is higher in emissions from the surface than in emissions from the atmosphere, and the effect of gravity on the frequency and wavelength of the IR quantum/wave radiation, are clear evidence that the “greenhouse effect” caused by “greenhouse gases” is not real, and that the warming of the Earth obeys to the load and characteristics of the energy that the Earth receives from the Sun.

*Questions*

After evaluating the effect of gravity on photons, three basic questions arise:

- Is the gravity field a sink to heat?
- Does gravity field donate energy to photons?
- Do photons donate energy to the gravity field?

In cosmology and astrophysics, the three questions have a single positive answer. This is because, in modern cosmological theories, all the arguments concerning to the energy are handled as fields; for example, Higgs’ fields, Electromagnetic field and gravity field. This way, a cosmologist does not have any problem on attributing to the gravitons the capacity of absorbing and emitting energy that no longer can be used as work. Universe’s energy-in-transit ends by being absorbed by the gravity field.

Nasif S. Nahle is Director of the Scientific Research Division at Biology Cabinet Mexico.

*References *

- http://nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-bio.html
- Zee, A.
*Einstein’s Universe; Gravity at Work and Play*. 1989. Oxford University Press. New York, NY. - http://www.newscientist.com/article/dn16095-its-confirmed-matter-is-merely-vacuum-fluctuations.html
- http://arxiv.org/ftp/gr-qc/papers/0504/0504116.pdf
- http://www.chemguide.co.uk/analysis/uvvisible/radiation.html
- Serway, Raymond A., Moses, Clement J., Moyer, Curt A.
*Modern Physics-3*. Brooks Cole. 2005.^{rd}Edition

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]]>OSRAM is one of the leading manufacturers of light bulbs in the world. They claim their OSRAM Tungsten light bulb is an “ecological” lamp* ^{3}* because of a reduction in losses due to thermal radiation.

In particular, they claim that due to a sophisticated coating on the bulb the thermal (infrared) radiation is reflected and the heat emitted from the filament is reflected back to the filament. As a result, the filament is heated further. This means that less electrical energy has to be supplied to the filament.

This is the equivalent argument used by proponents of the man-made global warming hypothesis, that is that a cooler system (the atmosphere) can reflect radiation back and heat up a warmer system (the Earth’s surface).

These claims violate the Second Law of Thermodynamics.

Scientific analysis, not of the misleading marketing blurb from OSRAM, but of the physical Tungsten light bulb, however, show that there is no violation of the Second Law of Thermodynamics. Nature behaves as she always does, even in the case of these artificial devices.

*Introduction*

The second law can be expressed in several ways, but all of them coincide with a common meaning, i.e. an ineludible universal directionality of every process taking place in the Universe.

The way in which the Second Law is expressed depends on what we are considering at a given moment; for example, we could be considering the work done by one system on another system, or the universal entropic directionality, or the process of energy transfer from one system towards another system.

Any of these cases could be the most suitable explanation; however, with respect to the unalterable directionality which leads every process and phenomenon, this definition is the one granted by quantum mechanics* ^{1, 2}*. The context provided by quantum mechanics for the Second Law of Thermodynamics deepens further the gap between pseudoscience and real science.

The Second Law of Thermodynamics is enunciated as follows:

“*The energy is always dispersed or diffused towards the system or systems with more available microstates*.”^{1}

This law applies to every thermodynamic system and to any place in the known universe. Additionally, it considers every association and every contextual function derived from the main statement. For example, we apply this concept to gas diffusion, chemical reactions, biotic processes, work, pressure, etcetera, etcetera.

Bearing this statement in mind, let us examine the Tungsten light bulb that, allegedly, beats this universal law.

*Antecedents*

OSRAM says that its innovative Tungsten light bulb will provide the benefit of

*A reduction in losses due to thermal radiation (IRC):*

*Special bulb geometry and a sophisticated coating on the bulb ensure that the thermal (infrared) radiation is reflected and the heat emitted from the filament is reflected back to the filament. As a result the filament is heated further. This means that less electrical energy has to be supplied to the filament. This technology is used for all low-voltage ECO lamps (12 V) because of the optimum geometric conditions ^{3}*

And that the consumer will also take advantage from

*A reduction in the thermal losses via the filler gas (xenon):*

*As the size (mass and diameter) of the gas atoms increases, the thermal conductivity of the filler gas decreases. By using the appropriate lamp filler gas, the heat loss of the tungsten filament via the gas can be reduced. This means that less electrical energy is needed to heat the filament. In addition, the use of a filler gas with atoms as heavy as possible slows down the vaporization of the tungsten atoms from the filament. This prolongs the life of the lamps. Xenon is an extremely rare gas (making up only 0.0000087% of the atmosphere, or 0.087 ppm). Of all the inert gases, xenon best meets these requirements. Despite the high cost we therefore use xenon as the filler gas in al (sic) the OSRAM ECO lamps*.^{3}

*Scientific Analysis*

The first assertion gives us the main characteristics of the lamp:

It has a Tungsten (W, from Latin *Wolframium* pertaining to “wolf foam”) filament, which is energized by fast unidirectional electrons and is the source of energy for the lamp, and a “special” geometry of the bulb. Additionally, the inner surface of the bulb is layered with a “sophisticated coating”* ^{3}*.

The second description says that the fluorescent gas inside the bulb is Xenon (*Xe*).^{ 3}

What is the “special” geometry of the bulb? From the picture of the product, the bulb’s “special” geometry is that of a paraboloidal integrating mirror; nothing “special” about this particular characteristic which has been exploited for many years in integrating mirror reflectometers, which are highly advantageous over spherical mirrors when the energy source is low.^{4, 5}

Paraboloidal integrating mirrors concentrate the radiation onto a given focal point that is accurately determined by the angle of curvature of the bulb^{5}, which, for this case, works in a similar way to a TV parabolic antenna as it concentrates the reflected quantum/waves (visible, IR, UV, radio) onto a receptor (focal point) that is built in front of the paraboloidal antenna’s surface. Magnifying glasses also work in this way, but work by refracting radiation.

In OSRAM Tungsten light bulbs, the focal point upon which the radiation is concentrated is the Tungsten filament. We, therefore, have the first explanation on the overheating of the Tungsten filament:

It is not warmed up by a colder system inside the bulb, but by IR quantum/waves reflected towards the Tungsten filament by the **“special coating”** covering the inner surface of the **paraboloidal integrating mirror bulb**.

Now, does the Tungsten filament have the ability to absorb the reflected IR quantum/waves and reach a higher temperature? The answer is: Yes, Tungsten (W), in pure form, is the metal that has the highest melting point, and it is 3422 °C^{6}. In addition, of all pure metals, Tungsten has the lowest coefficient of thermal expansion* ^{7}*, which is 4.3 x 10

We have seen that the reflected radiation **is concentrated** on the Tungsten filament **by the** “**sophisticated geometry**” of the bulb; the energy reflected by the “**special** **coating”** and sent towards the Tungsten filament (the focal point) is, therefore, higher than the energy of the filament. Consequently, the energy in the OSRAM Tungsten light bulb is dispersed from a Tungsten surface in a higher energy state (the point where the radiation is concentrated) to the remaining structure of the filament where the molecules are in an energetically lower state.

The filament will not absorb reflected radiation beyond its limited and limiting available microstates, while the walls will not reflect radiation outgoing from the filament above their reflectance coefficient. Furthermore, the Tungsten filament will not emit radiation beyond its total emissivity power at maximum temperature. Remember that the Tungsten filament is not a blackbody and it does not behave like a blackbody.

So, there is not any violation to the Second Law of Thermodynamics.

Additionally, the second characteristic of the Tungsten light bulb refers to its content, which OSRAM says is Xenon (*Xe*). What OSRAM does not specify is that the noble gas Xenon inside the light bulb can be excited by the energy released by the Tungsten filament and transformed into ephemeral *Xe dimers*, i.e. Xe_{2}.

The noble gas Xenon was first used in strobe lights for high speed photography, but was soon playing an important role in the manufacture of other devices, such as halogen lamps, nuclear reactors, lasers, etcetera.

After receiving a load of energy from the Tungsten filament, the over-energized Xenon fills its outer shell of electrons by taking an electron from a neighboring atom and forms a dimer, which is called an *excimer*.

After ~3 ns, the excimer returns to its energetic ground state and the absorbed energy is released towards other atoms and the Tungsten filament^{8}. Nevertheless, each ~3 ns, the environment surrounding the Tungsten filament gets warmer than the Tungsten filament^{8}. Consequently, we have again the same case of the reflected and concentrated radiation, i.e. the energy is transferred from a system with a higher energy density towards other systems with a lower energy density.

What we are seeing here is the same process that occurs in auroras, that is, a current of plasma. The plasma created by Xe excimers reaches an energy density that could be 1000 times higher than that of the source of photons^{9}, that is, than the energy density of the Tungsten filament.

To avoid the light bulb overheating and exploding, OSRAM has integrated a resistor, to control the energy transferred to the Tungsten filament, and small magnetic ballasts, integrated in one or both extremes of the light bulb, to absorb the bulk of the excess of heat produced during the functioning of the lamp.

That is how the OSRAM “ECO-lamp” works. We do not see here any violation to the Second Law of Thermodynamics.

*Conclusions*

First of all, we notice an incorrect statement in the opening argument from the OSRAM technical description of its Tungsten light bulb.

The first effect of warming of the Tungsten filament is produced by concentrating IR quantum/waves onto the surface of the Tungsten filament, which is caused by a paraboloidal integrating mirror bulb within which the Tungsten filament is placed.

After the focal spot on the Tungsten filament’s surface is heated up, the energy transfer occurs to the remaining molecules of the Tungsten filament, which are energetically “colder” than the focal spot.

Once the Tungsten filament warms up, it starts emitting more radiation toward the volume of “normal” Xe inside the bulb, the “normal” Xe becomes excited and is transformed into an excimer, formed by two atoms of Xe (Xe_{2}), which reaches an energy density state that is higher than that of the Tungsten filament and establishes a plasma current that transfers energy towards the Tungsten filament, i.e. from a warmer system (Xe_{2}) towards the colder system (the Tungsten filament).

There is NOT any violation to the Second Law of Thermodynamics going on inside OSRAM Tungsten ECO-lamps.

In trying to convince potential clients of the ecological benefits of its product, OSRAM presents a misleading explanation that could be wrongly interpreted as a “violation to the Second Law of Thermodynamics”. In fact, as I have demonstrated, this is not what happens in either OSRAM lamps, or in the climate system, nor anywhere in the observable universe.

*References*

- Lambert, Frank L
*. Entropy Is Simple, Qualitatively*.*J. Chem. Educ.*, 2002,*79*(10), p 1241. - http://entropysite.oxy.edu
- http://www.osram.com/osram_com/Professionals/General_Lighting/Halogen_lamps/Technologies/HALOGEN_ECO_technology/index.html
- Fried, Michael N. and Unguru, Sabetai.
*Apollonius of Perga’s Conica*. 2001. Koninklijke. Netherlands. - Modest, Michael F.
*Radiative Heat Transfer-Second Edition*. 2003. Elsevier Science, USA and Academic Press, UK. - http://www.chemicool.com/elements/tungsten.html
- http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thexp.html
- Salvermoser, M. and Murnick, D. E.
*High-efficiency, High-Power, Stable 172 nm Xenon Excimer Light Source*. Appl. Phys. Lett. 83, Page 1932 (2003). - Suplee, Curt.
*The Plasma Universe*. 2009. Division of Plasma Physics of the American Physical Society. Cambridge University Press. NY.

**By Nasif S. Nahle **

University Professor, Scientist and Director of Scientific Research Division at Biology Cabinet, Mexico

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