The great physicist Richard Feynman adds to three other giants of physics, Maxwell, Clausius, and Carnot, who have explained the "greenhouse effect" is solely a consequence of gravity, atmospheric mass, pressure, density, and heat capacities, and is not due to "trapped radiation" from IR-active or 'greenhouse' gas concentrations.
Only one 33C greenhouse theory can be correct, either the 33C Arrhenius radiative greenhouse theory (the basis of CAGW alarm and climate models) or the 33C Maxwell/Clausius/Carnot/Feynman gravito-thermal greenhouse effect, since if both were true, the surface temperature would be an additional 33C warmer than the present. As we have previously shown, the Arrhenius greenhouse theory confuses the cause (gravito-thermal) with the effect (radiation from greenhouse gases).
In addition, the US Standard Atmosphere, the International Standard Atmosphere, the HS 'greenhouse equation,' Chilingar, et al derive the observed atmospheric temperature profile without use of a single greenhouse gas radiative transfer equation or calculation, and using the same basic atmospheric physics discussed by Feynman in his lecture below. Feynman does not make a single mention of radiation, radiative transfer, greenhouse gases, CO2, nor does he derive any radiative transfer equations to derive the atmospheric temperature profile, and instead utilizes the barometric and statistical mechanics formulas necessary to describe the gravito-thermal greenhouse effect of Maxwell et al (who Feynman quotes extensively below). Feynman demonstrates that an atmosphere comprised solely of the non-greenhouse gases N2 & O2 (99.94% of our atmosphere, but 100% in Feynman's demonstrations) would establish the temperature gradient/"greenhouse effect" observed in the troposphere.
Feynman demonstrates that the conservative force of gravity does indeed do continuous thermodynamic Work upon the atmosphere (a common false argument by those who do not accept the gravito-thermal GHE theory is that gravity allegedly can't do Work upon the atmosphere), and describes gravitational potential energy (PE) accumulated as air parcels rise/expand/cool, which is then exchanged for kinetic energy (KE) as the air parcel descends/compresses/warms, creating the temperature gradient & greenhouse effect.
Another online version here with larger print
Showing posts sorted by relevance for query feynman gravito-thermal. Sort by date Show all posts
Showing posts sorted by relevance for query feynman gravito-thermal. Sort by date Show all posts
Tuesday, July 28, 2015
Tuesday, October 20, 2015
Jupiter emits 67% more radiation than it receives from the Sun -only explanation is the gravito-thermal greenhouse effect, not greenhouse gases
An article published at The Conversation asks Is the Red Spot shrinking superstorm evidence of climate change on Jupiter?, and indeed finds that this and other observed changes are evidence of climate change (of unknown cause) on Jupiter.
The article incidentally notes that,
In the case of Jupiter, a gas planet composed almost entirely of the non-IR-active, non-greenhouse gases hydrogen and helium, there is no solid planetary surface nor greenhouse gases to allegedly "trap" solar radiation, yet Jupiter has an "internal heat source" that causes a thermal enhancement ("gravito-thermal greenhouse effect") resulting in emission of 67% more radiation than it receives from the Sun. The only possible explanation of this is gravity, not radiative forcing from the Sun nor greenhouse gases, and hence the mass/pressure/gravity gravito-thermal greenhouse effect of Maxwell, Clausius, Carnot, Boltzmann, Helmholtz, Feynman, US Std Atmosphere, the HS greenhouse equation is corroborated on 9 planets.
Likewise, the ice planet Uranus has recently been observed to have storms at the top of the atmosphere radiating at blackbody temperatures hotter than required to melt steel. In addition,
On Venus, we know from the NASA Fact Sheet:
We can easily calculate the gravito-thermal greenhouse effect surface temperature of Venus using the ideal gas law
T = PV/nR = 92000/(65000/43.45*0.083144621) = 739K
which is within 2K (or 2C) of NASA observations of 737K as noted above, leaving essentially no room for any sort of Arrhenius radiative greenhouse effect on Venus. Note below also, the blackbody temperature of Venus is 184.2K, therefore mass/gravity/pressure alone has thermally enhanced the surface temperature of Venus by a factor of
737K/184.2K = 4 times
Thus, the Arrhenius radiative greenhouse effect is falsified on the basis of observations and first physical principles, and the only possible alternative greenhouse theory of Maxwell et al confirmed.
The article incidentally notes that,
"We do know that Jupiter emits 67% more radiation than it receives from the Sun. This is due to an internal heat source, which is thought to drive much of Jupiter\'s weather, including, presumably, the Great Red Spot. The heat likely is generated by the gradual contraction of matter under Jupiter's enormous gravity."Warmists claim gravity cannot be the cause of any so-called "greenhouse effect" (or the "gravito-thermal greenhouse effect") on Earth, Jupiter, nor any other planet, yet overwhelming observational evidence for every planet in our solar system (with adequate observational data - 8 planets at this point) clearly demonstrates that surface and atmospheric temperatures are a sole function of gravity/mass/pressure and independent of greenhouse gas concentrations.
In the case of Jupiter, a gas planet composed almost entirely of the non-IR-active, non-greenhouse gases hydrogen and helium, there is no solid planetary surface nor greenhouse gases to allegedly "trap" solar radiation, yet Jupiter has an "internal heat source" that causes a thermal enhancement ("gravito-thermal greenhouse effect") resulting in emission of 67% more radiation than it receives from the Sun. The only possible explanation of this is gravity, not radiative forcing from the Sun nor greenhouse gases, and hence the mass/pressure/gravity gravito-thermal greenhouse effect of Maxwell, Clausius, Carnot, Boltzmann, Helmholtz, Feynman, US Std Atmosphere, the HS greenhouse equation is corroborated on 9 planets.
Likewise, the ice planet Uranus has recently been observed to have storms at the top of the atmosphere radiating at blackbody temperatures hotter than required to melt steel. In addition,
"the base of the troposphere on the planet Uranus is 320K, considerably hotter than on Earth [288K], despite being nearly 30 times further from the Sun. The base of the troposphere on Uranus is 320K at 100 bars pressure, despite the planet only receiving 3.71 W/m2 energy from the Sun. By the Stefan-Boltzmann Law, a 320K blackbody radiates 584.6 W/m2. This is 157.5 times the energy received from the Sun, due to the atmospheric temperature gradient produced within a planetary gravity field. The temperature at the base of the troposphere is determined by the ideal gas law PV=nRT, where pressure from gravity and atmospheric mass raise the temperature at the base of the troposphere from the equilibrium temperature with the Sun of Uranus of 89.94K to 320K, regardless of the atmospheric mixture of greenhouse gases."Once again, the only possible explanation of both of these phenomena on Uranus is the Maxwell et al gravito-thermal greenhouse effect, thus bringing the number of planets for which very strong evidence exists to a total of ten.
On Venus, we know from the NASA Fact Sheet:
Venus Atmosphere
Surface pressure: 92 bars = 92000 mbar
Surface density: ~65. kg/m3 = 65000 g/m3
Scale height: 15.9 km
Total mass of atmosphere: ~4.8 x 1020 kg
Average temperature: 737 K (464 C)
Diurnal temperature range: ~0
Wind speeds: 0.3 to 1.0 m/s (surface)
Mean molecular weight: 43.45
Atmospheric composition (near surface, by volume):
Major: 96.5% Carbon Dioxide (CO2), 3.5% Nitrogen (N2)
Minor (ppm): Sulfur Dioxide (SO2) - 150; Argon (Ar) - 70; Water (H2O) - 20;
Carbon Monoxide (CO) - 17; Helium (He) - 12; Neon (Ne) - 7
We can easily calculate the gravito-thermal greenhouse effect surface temperature of Venus using the ideal gas law
T = PV/nR = 92000/(65000/43.45*0.083144621) = 739K
which is within 2K (or 2C) of NASA observations of 737K as noted above, leaving essentially no room for any sort of Arrhenius radiative greenhouse effect on Venus. Note below also, the blackbody temperature of Venus is 184.2K, therefore mass/gravity/pressure alone has thermally enhanced the surface temperature of Venus by a factor of
737K/184.2K = 4 times
Thus, the Arrhenius radiative greenhouse effect is falsified on the basis of observations and first physical principles, and the only possible alternative greenhouse theory of Maxwell et al confirmed.
Bulk parameters Venus vs. Earth
Venus Earth Ratio (Venus/Earth) Mass (1024 kg) 4.8676 5.9726 0.815 Volume (1010 km3) 92.843 108.321 0.857 Equatorial radius (km) 6051.8 6378.1 0.949 Polar radius (km) 6051.8 6356.8 0.952 Volumetric mean radius (km) 6051.8 6371.0 0.950 Ellipticity (Flattening) 0.000 0.00335 0.0 Mean density (kg/m3) 5243 5514 0.951 Surface gravity (eq.) (m/s2) 8.87 9.80 0.905 Surface acceleration (eq.) (m/s2) 8.87 9.78 0.907 Escape velocity (km/s) 10.36 11.19 0.926 GM (x 106 km3/s2) 0.3249 0.3986 0.815 Bond albedo 0.90 0.306 2.94 Visual geometric albedo 0.67 0.367 1.83 Visual magnitude V(1,0) -4.40 -3.86 - Solar irradiance (W/m2) 2613.9 1367.6 1.911 Black-body temperature (K) 184.2 254.3 0.724 Topographic range (km) 15 20 0.750 Moment of inertia (I/MR2) 0.33 0.3308 0.998 J2 (x 10-6) 4.458 1082.63 0.004 Number of natural satellites 0 1 Planetary ring system No No
 |
| Thermal enhancement or gravito-thermal greenhouse curve for 8 planets |
Is shrinking superstorm evidence of climate change on Jupiter?
Andrew Coates is Professor of Physics, Head of Planetary Science at the Mullard Space Science Laboratory, UCL.
(CNN) It makes our most turbulent terrestrial storms look like mere pipsqueaks. But remarkable new Hubble footage shows that Jupiter\'s Great Red Spot -- an anticyclonic storm system twice the size of Earth -- is shrinking and turning orange. Is this evidence of Jovian climate change? And could the planet\'s violent storm finally be giving way to more clement conditions, at least by Jupiter\'s dramatic standards?
Jupiter, the largest planet in our solar system, is a gas giant dominated by hydrogen with some helium and smaller amounts of other gases, a mixture that resembles the composition of the early solar nebula and results in some staggeringly beautiful weather. The planet\'s cloud systems, which counter-rotate in zones and belts, with eastward and westward winds reaching 100 meters per second, are among the solar system\'s most spectacular sights and come in a blaze of different colors -- red due to ammonia, white due to ammonium hydrosulphide, and brown and blue due to additions to water ice.
A raging storm
But one of the most recognizable and persistent features of Jupiter\'s atmosphere is the Great Red Spot (GRS). Swirling around the planet\'s southern hemisphere, it covers a huge 10 degrees of latitude. (2-3 times the size of Earth)
This vast anticyclonic (high pressure) storm system has been observed raging for perhaps 350 years -- the first likely observations were reported in 1664-1655 by Robert Hooke and Gian-Dominique Cassini. It is cooler than its surroundings, rotates anticlockwise with a four to six day period, and is located between zonal winds moving at 100 meters per second.
The Great Red Spot\'s stability over such a long period of time is remarkable. A fluid instability would disappear in a few days to weeks, as in the case of the scars caused when several fragments of the comet Shoemaker-Levy 9 struck Jupiter in 1994 -- so an energy source must be powering it. Models have been suggested, but none fully explain the Great Red Spot: is it really a hurricane, a shear instability, an eddy or a solitary wave?
Inside the pressure cooker
We do know that Jupiter emits 67% more radiation than it receives from the Sun. This is due to an internal heat source, which is thought to drive much of Jupiter\'s weather, including, presumably, the Great Red Spot. The heat likely is generated by the gradual contraction of matter under Jupiter\'s enormous gravity. In the planet\'s deeper layers, for example, hydrogen enters a liquid metallic state and the pressure is 3m atmospheres.
We also know that after years of relative stability, the Great Red Spot is now changing. Since 2012, Hubble observations as part of the Outer Planets Atmospheres Legacy (OPAL) program have shown that the spot has been shrinking -- and that the rate of shrinkage has increased in recent years. The latest measurement, published by Amy Simon and colleagues, show a further reduction of 240km, although this rate of shrinkage is less than in preceding years and there are not enough observations yet to know if this is a periodic feature as seen with Neptune\'s great dark spot.
It is not just a matter of size, however. The Hubble results also show that the spot\'s shape is continuing its evolution from oval to circular, and that a new wispy filament, spiralling inwards and driven by winds of at least 150 meters per second, has developed within the Great Red Spot. The core region has also been shrinking, consistent with the overall trend, and is also becoming less distinct. It is also now deep orange in color.
Jovian climate change
There are other changes in the Jovian atmosphere, too. The Hubble observations show a new wave structure about 16 degrees north of Jupiter\'s equator, in a region of cyclones and anticyclones. It is similar to the only previous observation of such a structure by Voyager 2 in 1979 and may herald the birth of a new cyclone there.
It\'s clear that Jupiter\'s atmosphere is changing, and the Great Red Spot is evolving. The question is: why? Is the Great Red Spot fizzling out, or oscillating over time?
The jury is still out, but continued observations by the annual OPAL campaign, combined with in-situ measurements of the atmospheric dynamics and interior structure, may yet reveal intriguing new clues. The JUNO polar orbiter will also reach Jupiter in July next year and doubtless offer answers of its own.
Jupiter\'s mysterious Great Red Spot may be shrinking, then, but the world will be talking about Jupiter\'s weather for a good while yet.
Saturday, August 22, 2015
New paper confirms the gravito-thermal greenhouse effect on 6 planets including Earth, falsifies CAGW
An important new paper published in Advances in Space Research determines that the Earth surface temperature (as well as the surface temperatures of 5 other rocky planets in our solar system) can be very accurately determined (R2 = 0.9999! & tiny standard error σ=0.0078) solely on the basis of two variables:
1) atmospheric pressure at the surface, and
2) solar irradiance at the top of the atmosphere,
and without any consideration of any greenhouse gas concentrations or 'radiative forcing' from greenhouse gases whatsoever.
Thus, the paper adds to the works of at least 40 others (partial list below) who have falsified the Arrhenius radiative theory of catastrophic global warming from increased levels of CO2, and also thereby demonstrated that the Maxwell/Clausius/Carnot/Boltzmann/Feynman atmospheric mass/gravity/pressure greenhouse theory is instead the correct explanation of the 33C greenhouse effect on Earth, and which is independent of "radiative forcing" from greenhouse gases.
Using observed data from the planets Earth, Venus, the Moon, Mars, Titan, and Triton, the authors,
The authors have used a new empirical non-linear regression method of determining the gravito-thermal greenhouse effect on 6 planets, and "might be describing a macro-level thermodynamic property of planetary atmospheres heretofore unbeknown to science," but are apparently unaware of and do not cite any of the over 36 scientific works/papers (partial list below) which have described the theoretical basis of the same 33C Maxwell/Clausius/Carnot gravito-thermal effect of atmospheric pressure, some of which also utilize the Poisson relation as illustrated in Fig 7. from the paper above.
The HS greenhouse equation
The Maxwell/Clausius et al gravito-thermal 'greenhouse effect'
Richard Feynman
Boltzmann
Chilingar et al
1976 US Standard Atmosphere
International Standard Atmosphere & here
Hans Jelbring
Connolly & Connolly
Nikolov & Zeller
Mario Berberan-Santos et al
Claes Johnson and here
Velasco et al
Huffman
Giovanni Vladilo et al
1) atmospheric pressure at the surface, and
2) solar irradiance at the top of the atmosphere,
and without any consideration of any greenhouse gas concentrations or 'radiative forcing' from greenhouse gases whatsoever.
Thus, the paper adds to the works of at least 40 others (partial list below) who have falsified the Arrhenius radiative theory of catastrophic global warming from increased levels of CO2, and also thereby demonstrated that the Maxwell/Clausius/Carnot/Boltzmann/Feynman atmospheric mass/gravity/pressure greenhouse theory is instead the correct explanation of the 33C greenhouse effect on Earth, and which is independent of "radiative forcing" from greenhouse gases.
Using observed data from the planets Earth, Venus, the Moon, Mars, Titan, and Triton, the authors,
"apply the Dimensional Analysis (DA) methodology to a well-constrained data set of six celestial bodies representing highly diverse physical environments in the solar system, i.e. Venus, Earth, the Moon, Mars, Titan (a moon of Saturn), and Triton (a moon of Neptune). Twelve prospective relationships (models) suggested by DA are investigated via non-linear regression analyses involving dimensionless products comprised of solar irradiance, greenhouse-gas partial pressure/density and total atmospheric pressure/density as forcing variables, and two temperature ratios as dependent (state) variables. One non-linear regression model is found to statistically outperform the rest by a wide margin. Our analysis revealed that GMATs [Global Mean Atmospheric Temperatures] of rocky planets can accurately be predicted over a broad range of atmospheric conditions [0% to over 96% greenhouse gases] and radiative regimes only using two forcing variables: top-of-the-atmosphere solar irradiance and total surface atmospheric pressure [a function of atmospheric mass & gravity]. The new model displays characteristics of an emergent macro-level thermodynamic relationship heretofore unbeknown to science that deserves further investigation and possibly a theoretical interpretation."
 |
| Fig. 4.
Dependence of the relative atmospheric thermal enhancement (Ts/Tna) on mean surface air pressure according to Eq. (10a) derived from data representing a broad range of planetary environments in the Solar System. Saturn’s moon Titan has been excluded from the regression analysis leading to Eq. (10a). Error bars of some bodies are not clearly visible due to their small size relative to the scale of the axes. See Table 2 for the actual error estimates.
|
"The above comparisons indicate that Eq. (10b) rather accurately reproduces the observed variation of mean surface temperatures across a wide range of planetary environments characterized in terms of solar irradiance (from 1.5 W m-2 to 2,602 W m-2), total atmospheric pressure (from near vacuum to 9,300 kPa), and greenhouse-gas concentrations (from 0.0% to over 96% per volume). While true that Eq. (10a) is only based on data from 6 planetary bodies, one should keep in mind that these represent all objects in the Solar System meeting our criteria (discussed in Section 2.3) for the quality of available data. The fact that only one of the investigated twelve non-linear regressions yielded a tight relationship suggests that Model 12 might be describing a macro-level thermodynamic property of planetary atmospheres heretofore unbeknown to science . A function of such predictive skill spanning the breadth of the Solar System may not be just a result of chance. Indeed, complex natural systems consisting of myriad interacting agents have been known to exhibit emergent behaviors at higher levels of hierarchical organization that are amenable to accurate modeling using top-down statistical approaches (e.g. Stolk et al. 2003). Equation (10) also displays several other characteristics that lend further support to the above conjecture."
 |
| Comparison of the two best-performing regression models according to statistical scores presented inTable 5. Vertical axes use linear scale to better illustrate the difference in skills between the models. Added: The top model incorporates greenhouse gas partial pressures and has a standard error over 20 times worse than the bottom model which does not consider greenhouse gas concentrations or radiative forcing whatsoever. |
 |
| Fig. 5.
Absolute differences between predicted average global surface temperatures (Eq. 10b) and observed GMATs (Table 2) for studied celestial bodies. Titan represents an independent data point, since it was excluded from the non-linear regression analysis leading to Eq. (10a).
Added: The surface temperatures of 5 planets are determined within hundredths of degrees C using the Eqn 10a as a sole function of surface pressure and solar insolation.
|
 |
| Fig. 7.
a) Dry adiabatic response of the air/surface temperature ratio to pressure changes in the free atmosphere according to Poisson’s formula (Eq. 12). The reference pressure is arbitrarily assumed to be po=100 kPa;b) The SB radiation law expressed as a response of a blackbody temperature ratio to variation in photon pressure (see text for details). Note the similarity in shape between these two curves and the one portrayed in Fig. 4 depicting Eq. (10a).
|
Only one possible explanation of the 33C 'greenhouse' effect temperature gradient on Earth can be possible, otherwise the greenhouse effect would be twice as large (i.e. 66C):
1) The 33C Arrhenius radiative greenhouse theory from greenhouse gases (which confuses the cause with the effect and fails to explain the planetary temperatures of Venus, Earth, Mars, Titan, Jupiter, Saturn, Uranus, Neptune, etc.)
OR
2) The 33C Maxwell/Clausius/Carnot gravito-thermal effect, proven by this new paper and the works/papers of at least 36 others (and very accurately predicts the surface and atmospheric temperatures of all rocky planets with an atmosphere in our solar system):
The HS greenhouse equation
The Maxwell/Clausius et al gravito-thermal 'greenhouse effect'
Richard Feynman
Boltzmann
Chilingar et al
1976 US Standard Atmosphere
International Standard Atmosphere & here
Hans Jelbring
Connolly & Connolly
Nikolov & Zeller
Mario Berberan-Santos et al
Claes Johnson and here
Velasco et al
Huffman
Giovanni Vladilo et al
Verity Jones
William C. Gilbert & here
The Barometric Formulae
Richard C. Tolman
Lorenz & McKay
Peter Morecombe
Ozawa et al
Murry Salby
Goran Ahlgren
Joe Postma
Charles Anderson
Wing and Cronin
Kimoto
Kalmanovitch/quantum physics
William C. Gilbert & here
The Barometric Formulae
Richard C. Tolman
Lorenz & McKay
Peter Morecombe
Ozawa et al
Murry Salby
Goran Ahlgren
Joe Postma
Charles Anderson
Wing and Cronin
Kimoto
Kalmanovitch/quantum physics
Highlights
- •
- Dimensional Analysis is used to model the average temperature of planetary bodies.
- •
- The new model is derived via regression analysis of measured data from 6 bodies.
- •
- Planetary bodies used by the model are Venus, Earth, Moon, Mars, Titan and Triton.
- •
- Two forcing variables are found to accurately predict mean planetary temperatures.
- •
- The predictor variables include solar irradiance and surface atmospheric pressure.
Abstract
The Global Mean Annual near-surface Temperature (GMAT) of a planetary body is an expression of the available kinetic energy in the climate system and a critical parameter determining planet’s habitability. Previous studies have relied on theory-based mechanistic models to estimate GMATs of distant bodies such as extrasolar planets. This ‘bottom-up’ approach oftentimes relies on case-specific parameterizations of key physical processes (such as vertical convection and cloud formation) requiring detailed measurements in order to successfully simulate surface thermal conditions across diverse atmospheric and radiative environments. Here, we present a different ‘top-down’ statistical approach towards the development of a universal GMAT model that does not require planet-specific empirical adjustments. Our method is based on Dimensional Analysis (DA) of observed data from the Solar System. DA provides an objective technique for constructing relevant state and forcing variables while ensuring dimensional homogeneity of the final model. Although widely utilized in some areas of physical science to derive models from empirical data, DA is a rarely employed analytic tool in astronomy and planetary science. We apply the DA methodology to a well-constrained data set of six celestial bodies representing highly diverse physical environments in the solar system, i.e. Venus, Earth, the Moon, Mars, Titan (a moon of Saturn), and Triton (a moon of Neptune). Twelve prospective relationships (models) suggested by DA are investigated via non-linear regression analyses involving dimensionless products comprised of solar irradiance, greenhouse-gas partial pressure/density and total atmospheric pressure/density as forcing variables, and two temperature ratios as dependent (state) variables. One non-linear regression model is found to statistically outperform the rest by a wide margin. Our analysis revealed that GMATs of rocky planets can accurately be predicted over a broad range of atmospheric conditions and radiative regimes only using two forcing variables: top-of-the-atmosphere solar irradiance and total surface atmospheric pressure. The new model displays characteristics of an emergent macro-level thermodynamic relationship heretofore unbeknown to science that deserves further investigation and possibly a theoretical interpretation.
Tuesday, September 22, 2015
Lapse Rates for Dummies or Smarties, With & Without Greenhouse Gases
Some commenters have claimed that a theoretical pure Nitrogen (N2) Earth atmosphere without any IR-active 'greenhouse gases' could not have a lapse rate nor a Maxwell et al gravito-thermal greenhouse effect.
However, many prior posts have shown this to be false for a number of reasons, including two posts quoting the Feynman lectures on statistical mechanics of a Boltzmann Distribution pure N2 atmosphere, and the HS post, "Why Greenhouse Gases Don't Affect the Greenhouse Equation or Lapse Rate," which also calculates a pure N2 Boltzmann Distribution for Earth.
We will now use a couple of illustrations for smarties or dummies to understand why the so-called 'greenhouse gas' water vapor cools, not warms, the Earth surface by up to ~25C via changes in heat capacity (Cp) alone (not even including additional cooling from latent heat transfer or clouds). We will also show why a pure N2 atmosphere without any greenhouse gases would have a surface temperature ~25C warmer than the present, due to a much steeper lapse rate.
Recall that the dry adiabatic lapse rate formula is a very simple, linear relationship whereby the change in temperature (dT) with change in height from the surface (dh) is solely dependent upon the gravitational acceleration constant (g) divided by the heat capacity of the atmosphere at constant pressure (Cp):
dT/dh = -g/Cp
And note that change in temperature dT is inversely related to change in heat capacity (Cp). Since water vapor has a much higher heat capacity Cp than air or pure N2, addition of water vapor greatly decreases the lapse rate (dT/dh) by almost one-half (from ~9.8K/km to ~5K/km), thereby cooling, not warming, the surface by up to 25C.
In our hypothetical 1st atmosphere consisting only of N2 plus addition of < 1% water vapor, we assume the addition of water vapor creates a wet adiabatic lapse rate of 5K/km, the same as the wet adiabatic lapse rate on Earth. By calculating the center of mass as the HS Greenhouse Eqn does, and calculating the fixed 255K equilibrium temperature between the Earth and Sun, we can then calculate the entire tropospheric temperature profile from the surface to tropopause, and replicate the 1976 US Standard Atmosphere model:
Thus, we find the net effect of the addition of < 1% 'greenhouse gas' water vapor was to cool, not warm the surface of an N2 atmosphere by up to ~25C.
Thus, the Arrhenius radiative greenhouse theory (which confuses the cause with the effect) is once again demonstrated to be unphysical and falsified, and the Maxwell et al gravito-thermal greenhouse effect once again vindicated. One and only one of these two competing greenhouse theories can be correct, otherwise the observed effect would be double (66C) that observed (33C). The Maxwell et al theory is the only option which does not violate any laws of thermodynamics.
However, many prior posts have shown this to be false for a number of reasons, including two posts quoting the Feynman lectures on statistical mechanics of a Boltzmann Distribution pure N2 atmosphere, and the HS post, "Why Greenhouse Gases Don't Affect the Greenhouse Equation or Lapse Rate," which also calculates a pure N2 Boltzmann Distribution for Earth.
We will now use a couple of illustrations for smarties or dummies to understand why the so-called 'greenhouse gas' water vapor cools, not warms, the Earth surface by up to ~25C via changes in heat capacity (Cp) alone (not even including additional cooling from latent heat transfer or clouds). We will also show why a pure N2 atmosphere without any greenhouse gases would have a surface temperature ~25C warmer than the present, due to a much steeper lapse rate.
Recall that the dry adiabatic lapse rate formula is a very simple, linear relationship whereby the change in temperature (dT) with change in height from the surface (dh) is solely dependent upon the gravitational acceleration constant (g) divided by the heat capacity of the atmosphere at constant pressure (Cp):
dT/dh = -g/Cp
And note that change in temperature dT is inversely related to change in heat capacity (Cp). Since water vapor has a much higher heat capacity Cp than air or pure N2, addition of water vapor greatly decreases the lapse rate (dT/dh) by almost one-half (from ~9.8K/km to ~5K/km), thereby cooling, not warming, the surface by up to 25C.
In our hypothetical 1st atmosphere consisting only of N2 plus addition of < 1% water vapor, we assume the addition of water vapor creates a wet adiabatic lapse rate of 5K/km, the same as the wet adiabatic lapse rate on Earth. By calculating the center of mass as the HS Greenhouse Eqn does, and calculating the fixed 255K equilibrium temperature between the Earth and Sun, we can then calculate the entire tropospheric temperature profile from the surface to tropopause, and replicate the 1976 US Standard Atmosphere model:
 |
| Thought experiment 1 of a N2 atmosphere with < 1% GHG water vapor. Note for easy illustrative purposes only, the actual numbers are rounded slighly, e.g. the actual height of the center of mass is ~5.1km rather than 5.0 km, and the actual dry adiabatic lapse rate is ~9.8K/km, not 10K/km.
Note in the above "greenhouse atmosphere," there is a ~33C "greenhouse effect" from the 255K center of mass to the ~288K surface, as well as an even larger "anti-greenhouse effect" of negative 35K from the 255K center of mass to the ~220K top of troposphere. Thus, gravity has not added any energy to the atmospheric system; gravity has simply redistributed the available energy from the only source the Sun, more towards the surface and less towards the top of the troposphere. That is the gravito-thermal greenhouse effect of Poisson, Maxwell, Clausius, Carnot, Boltzmann, Feynman, US Std Atmosphere, HS greenhouse eqn et al, and has no dependence whatsoever upon IR emission/absorption from greenhouse gases.
Now lets consider a hypothetical Earth atmosphere without any greenhouse gases, consisting solely of pure N2. We again use the dry lapse rate equation above, since obviously N2 is affected by gravity (g) and has a heat capacity (Cp). In this pure N2 Boltzmann distribution, the lapse rate can thus be calculated as ~10K/km, essentially the same as our present atmosphere dry lapse rate (9.8K/km).
For illustrative purposes only, the atmospheric mass of a pure N2 atmosphere is close to that of our present atmosphere, and thus the center of mass is also located near ~5km in the troposphere. However, since the lapse rate is much steeper in a pure N2 atmosphere, the "greenhouse effect" is about 50K from the 255K center of mass to 305K surface, and the "anti-greenhouse effect" is also ~50K from the 255K center of mass to the ~205K top of the troposphere, producing a ~100K temperature gradient from the surface to top of the troposphere:
|
Thus, we find the net effect of the addition of < 1% 'greenhouse gas' water vapor was to cool, not warm the surface of an N2 atmosphere by up to ~25C.
Thus, the Arrhenius radiative greenhouse theory (which confuses the cause with the effect) is once again demonstrated to be unphysical and falsified, and the Maxwell et al gravito-thermal greenhouse effect once again vindicated. One and only one of these two competing greenhouse theories can be correct, otherwise the observed effect would be double (66C) that observed (33C). The Maxwell et al theory is the only option which does not violate any laws of thermodynamics.
Tuesday, September 1, 2015
Why the effective radiating level (ERL) is always located at the center of mass of the atmosphere & not controlled by greenhouse gas concentrations
The Arrhenius radiative greenhouse effect proponents, having abandoned "back-radiation" from greenhouse gases as the explanation of the greenhouse effect, now claim global warming is instead due to an increase of the "effective radiating height" or "effective radiating level" [ERL] of greenhouse gases in the atmosphere. So the theory goes, an increase of CO2 levels will cause longwave (~15 micron) infrared emissions from CO2 to occur from colder heights in the atmosphere, and since colder blackbodies emit less radiation, more radiation will allegedly be "trapped" by the colder CO2 "blackbody" in the fabled tropospheric "hot spot" & unable to escape to space.
In contrast, the competing 33C gravito-thermal greenhouse effect of Maxwell, Clausius, Carnot, Boltzmann, Feynman, Poisson, Helmholtz, et al, shows that the "effective radiating level" or ERL is fixed at the center of mass (COM) of the atmosphere.
As we can see in Fig 1a, the observed ERL or "emission level for OLR (Outgoing Longwave Radiation)" global average is right around 500 millibars or 0.49 atmospheres ~ 0.5 atmospheres, exactly at the center of mass of the entire atmosphere as predicted in the HS greenhouse equation below.
The HS greenhouse equation "triangulates" the geopotential height of the 255K ERL at the center of mass using:
1. The center of mass (COM) of the atmosphere where P=0.5 atmospheres (after density correction), i.e. exactly one-half of the surface pressure
2. The adiabatic lapse rate = -(gravitational acceleration constant g)/(heat capacity at constant pressure Cp)
3. The equilibrium temperature of Earth with the Sun = 255K
all of which are essentially constants in the atmosphere, and without any knowledge of the surface temperature, greenhouse gas concentrations, or Arrhenius "radiative forcing" from greenhouse gases.
Why use the center of mass of the atmosphere in calculation of the gravito-thermal greenhouse effect? Because the force of gravity by Newton's Second Law is F = ma = mg, and for a system of particles like our atmosphere, one must determine the center of mass in applying Newton's 2nd Law F = mg to the force of gravity.
Thus, since the height of the ERL is fixed at the COM, and the COM is essentially a constant, the height of the ERL will not change, regardless of greenhouse gas concentrations.
In addition, in the longwave infrared band of Earth’s thermal radiation, the only band in which CO2 absorbs and emits is centered at ~15 microns. The kinetic temperature of the surrounding atmosphere and the CO2 molecules has nothing to do with the fact that CO2 emits at a fixed ~15 microns in the longwave IR due to its fixed molecular structure bending transitions. The entire atmosphere surface to space is warmer than the CO2 “equivalent partial blackbody” fixed band-emitting temperature of 193K at ~15 microns.
Also, absorption followed by emission of a photon by CO2 only takes microseconds, and all the bouncing around at the speed of light between greenhouse gases in the atmosphere only delays the average photon a few milliseconds on its way from the surface to space. Thus, the only "slowing of cooling" or "heat trapping" by CO2 absorption/emission is a few milliseconds and easily reversed and erased over a 12 hour night.
In contrast, the competing 33C gravito-thermal greenhouse effect of Maxwell, Clausius, Carnot, Boltzmann, Feynman, Poisson, Helmholtz, et al, shows that the "effective radiating level" or ERL is fixed at the center of mass (COM) of the atmosphere.
As we can see in Fig 1a, the observed ERL or "emission level for OLR (Outgoing Longwave Radiation)" global average is right around 500 millibars or 0.49 atmospheres ~ 0.5 atmospheres, exactly at the center of mass of the entire atmosphere as predicted in the HS greenhouse equation below.
The HS greenhouse equation "triangulates" the geopotential height of the 255K ERL at the center of mass using:
1. The center of mass (COM) of the atmosphere where P=0.5 atmospheres (after density correction), i.e. exactly one-half of the surface pressure
2. The adiabatic lapse rate = -(gravitational acceleration constant g)/(heat capacity at constant pressure Cp)
3. The equilibrium temperature of Earth with the Sun = 255K
all of which are essentially constants in the atmosphere, and without any knowledge of the surface temperature, greenhouse gas concentrations, or Arrhenius "radiative forcing" from greenhouse gases.
Why use the center of mass of the atmosphere in calculation of the gravito-thermal greenhouse effect? Because the force of gravity by Newton's Second Law is F = ma = mg, and for a system of particles like our atmosphere, one must determine the center of mass in applying Newton's 2nd Law F = mg to the force of gravity.
Thus, since the height of the ERL is fixed at the COM, and the COM is essentially a constant, the height of the ERL will not change, regardless of greenhouse gas concentrations.
In addition, in the longwave infrared band of Earth’s thermal radiation, the only band in which CO2 absorbs and emits is centered at ~15 microns. The kinetic temperature of the surrounding atmosphere and the CO2 molecules has nothing to do with the fact that CO2 emits at a fixed ~15 microns in the longwave IR due to its fixed molecular structure bending transitions. The entire atmosphere surface to space is warmer than the CO2 “equivalent partial blackbody” fixed band-emitting temperature of 193K at ~15 microns.
Also, absorption followed by emission of a photon by CO2 only takes microseconds, and all the bouncing around at the speed of light between greenhouse gases in the atmosphere only delays the average photon a few milliseconds on its way from the surface to space. Thus, the only "slowing of cooling" or "heat trapping" by CO2 absorption/emission is a few milliseconds and easily reversed and erased over a 12 hour night.
Addition of more CO2 increases the few milliseconds delay by adding a few more milliseconds, but once again is easily reversed and erased over a 12 hour night.
More importantly, increased CO2 increases radiative surface area, which increases radiative loss to space. That’s why increased CO2 cools the stratosphere through thermosphere, and troposphere as well as I’ve shown.
And even more importantly, the probability of CO2 transferring heat by collisions with N2/O2 in the troposphere is about 2 orders of magnitude higher than emitting a photon, which increases convective cooling.
An earlier post also provides nine additional reasons why the effective radiating level (ERL) is always located at the center of mass of the atmosphere & not controlled by greenhouse gas concentrations.
More importantly, increased CO2 increases radiative surface area, which increases radiative loss to space. That’s why increased CO2 cools the stratosphere through thermosphere, and troposphere as well as I’ve shown.
And even more importantly, the probability of CO2 transferring heat by collisions with N2/O2 in the troposphere is about 2 orders of magnitude higher than emitting a photon, which increases convective cooling.
An earlier post also provides nine additional reasons why the effective radiating level (ERL) is always located at the center of mass of the atmosphere & not controlled by greenhouse gas concentrations.
Thus, the false notion that global warming is instead due to an increase of the "effective radiating height" or "effective radiating level" [ERL] of greenhouse gases in the atmosphere is effectively disproven.
The HS greenhouse equation and quick & dirty explanation below, followed by the derivation from first principles:
We will use the ideal gas law, 1st law of thermodynamics, Newton's second law of motion (F = ma), and well-known barometric formulae in this derivation to very accurately determine Earth's surface temperature, the height in the atmosphere at which the effective equilibrium temperature of Earth with the Sun is located, and show that this height is located as expected at the center of mass of the atmosphere on Earth and Titan.
The HS greenhouse equation and quick & dirty explanation below, followed by the derivation from first principles:
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| http://hockeyschtick.blogspot.com/2014/11/quick-and-dirty-explanation-of.html |
We will use the ideal gas law, 1st law of thermodynamics, Newton's second law of motion (F = ma), and well-known barometric formulae in this derivation to very accurately determine Earth's surface temperature, the height in the atmosphere at which the effective equilibrium temperature of Earth with the Sun is located, and show that this height is located as expected at the center of mass of the atmosphere on Earth and Titan.
We will show that the mass/pressure greenhouse effect theory can also be used to accurately determine the temperatures at any height in the troposphere from the surface to the tropopause, and compute the mass/gravity/pressure greenhouse effect to be 33.15C, the same as determined from radiative climate models and the conventional radiative greenhouse effect theory.
1. Conservation of energy and the ideal gas law
We will start once again with the ideal gas law
PV = nRT (1)
an equation of state that relates the pressure P, volume V, temperature T, number of moles n of gas and the gas law constant R = 8.3144621 J/(mol K).
The properties of gases fall into two categories:
1. Extensive variables are proportional to the size of the system: volume, mass, energy
2. Intensive variables do not depend on the size of the system: pressure, temperature, density
To conserve energy (and to ensure that no radiative imbalances from greenhouse gases are affecting this derivation) of the mass/gravity/pressure greenhouse effect, we assume
Energy incoming from the Sun (Ein) = Energy out (Eout) from Earth to space
Observations indeed show Ein = Eout = 240 W/m2 (2)
which by the Stefan-Boltzmann law equates to a blackbody radiating at 255 K or -18C, which we will call the effective or equilibrium temperature (Te) between the Sun and Earth. As seen by satellites, the Earth radiates at the equilibrium temperature 255K from an average height referred to as the "effective radiating level" or ERL or "effective radiating height."
2. Determine the "gravity forcing" upon the atmosphere
Returning to the ideal gas law above, pressure is expressed using a variety of measurement units including atmospheres, bars, and Pascals, and for this derivation we will use units in atmospheres, which is defined as the pressure at mean sea level at the latitude of Paris, France in terms of Newtons per square meter [N/m2]
Newtons per square meter corresponds to the force per unit area [or "gravity forcing" upon the atmospheric mass per unit area of the Earth surface].
Now let's determine the mass of the atmosphere above one square meter at the Earth surface:
By Newton's 2nd law of motion equation, force (F) is
F = ma (3) where m = mass and a = acceleration
As we noted above, the atmospheric pressure is a force or forcing per unit area. The force in this case is the weight (note weight is not the same as mass and is in physical definitions of mass, length, time-2) or mass of the atmosphere times the gravitational acceleration, therefore
F = mg (4) where g is the gravitational constant 9.8 m/s2, i.e. the acceleration due to gravity in meters per second squared.
If we assume that g is a constant for the entire column of the atmosphere above the 1 meter2 area (A) we obtain
m = PA/g = (1.0325 x 10^5 N/m2 )(1 m2 )/(9.8 m/s2 ) = 1.05 x 10^4 kg
thus, the weight of the atmosphere over 1 square meter of the surface is 10,500 kilograms, quite a remarkable gravitational forcing upon the atmosphere.
If m is the mass of the atmosphere and g is the gravitational acceleration, the gravitational force is thus
F = mg (4)
The density (p) is the mass (m) per unit Volume (V), thus,
p = m/V
SI units of pressure refer to N/m2 as the Pascal (Pa). There are 1.0325 x 10^5 Pa per atmosphere (unit).
Starting again with equation (3) above
F = ma (3)
F = mg (4)
F = (PA/g)g = PA (5)
P = F/A = mg/A = phAg/A = phg (6)
where
h=height along either a gas or liquid column under pressure or gravity field
g = gravitational constant
p = density = mass/volume
3. Determine the atmospheric pressures from gravitational forcing, and the height of the effective equilibrium temperature (ERL)
Now we will determine the atmospheric pressures in a gravitational field using (6) above
First let's determine the pressure at the ERL since the temperature must equal the equilibrium temperature of 255K at the ERL.
The pressure is a function of height
P(h) = ρgh (7)
and the change in pressure dP is related to the change in height dh by
dP = -ρg dh (8)
The minus sign arises from the fact that pressure decreases with height, subject to an adjustment for density which changes with height. We will determine this adjustment from the ideal gas law. The density is
ρ = nM/V (9)
where n is the number of moles, M is the molar mass, and V is the volume. We can obtain n/V from the ideal gas law:
n/V = P/RT (10)
thus
ρ = MP/RT (11)
We can now substitute the density into the pressure vs. height formula:
dP = -(MPg/RT)dh (12)
∫dP/P = -(Mg/RT) ∫dh (13) (the first integral is from 1 to P, second from 0 to h)
ln(P) = -(Mgh/RT) (14)
P = e^-((Mgh/(RT)) (15)
We will now determine the height (h) at the ERL where the temperature = the effective equilibrium temperature = 255K, and without use of radiative forcing from greenhouse gases.
Plugging in numbers of M = 29 grams/mole (0.029 kg/mole) as average molar mass for atmosphere, g = 9.8 m/s^2, Pressure = 0.50 atmospheres at the approximate center of mass of the atmosphere, R=8.31, and T=Te=255K effective equilibrium temperature we obtain:
So the height of the ERL set by gravity forcing is located at 5100 meters and is where T=Te=255K and pressure = 0.5 atmospheres, right at the center of mass of the atmosphere as we predicted from our gravity forcing hypothesis.
4. Determine the temperatures at any location in the troposphere, and the magnitude of the mass/pressure greenhouse effect
Now that we have solved for the location of the ERL at 5100 meters, we can use the adiabatic lapse rate equation to determine all troposphere temperatures from the surface up to the ERL at 255K and then up to the top of the troposphere. The derivation of the lapse rate equation from the ideal gas law and 1st law of thermodynamics is described in this post, thus will not be repeated here, except to mention that the derivation of the lapse rate
dT/dh = -g/Cp where Cp = heat capacity of the atmosphere at constant pressure
is also completely independent of any radiative forcing from greenhouse gases, greenhouse gas concentrations, emission/absorption spectra from greenhouse gases, etc., and is solely a function of gravity and heat capacity of the atmosphere.
Plugging the average 6.5C/km lapse rate and 5100 meter or 5.1 km height of the ERL we determine above into our derived lapse rate equation (#6 from prior post) gives
T = -18C - (6.5C/km × (h - 5.1km))
Using this equation we can perfectly reproduce the temperature at any height in the troposphere as shown in Fig 1. At the surface, h = 0, thus temperature at the surface Ts is calculated as
Ts = -18 - (6.5 × (0 - 5.1))
Ts = -18 + 33.15C (gravity forced greenhouse effect)
Ts = 15.15°C or 288.3°K at the surface
which is exactly the same as determined by satellite observations and is 33.15C above the equilibrium temperature -18C or 255K with the Sun as expected.
Thus, we have determined the entire 33.15C greenhouse effect, the surface temperature, and the temperature of the troposphere at any height, and the height at which the equilibrium temperature with the Sun occurs at the ERL entirely on the basis of the Newton's 2nd law of motion, the 1st law of thermodynamics, and the ideal gas law, without use of radiative forcing from greenhouse gases, nor the concentrations of greenhouse gases, nor the emission/absorption spectra of greenhouse gases at any point in this derivation, demonstrating that the entire 33C greenhouse effect is dependent upon atmospheric mass/pressure/gravity, rather than radiative forcing from greenhouse gases. Also note, it is absolutely impossible for the conventional radiative theory of the greenhouse effect to also be correct, since if that was the case, the Earth's greenhouse effect would be at least double (66C+ rather than 33C).
In essence, the radiative theory of the greenhouse effect confuses cause and effect. As we have shown, temperature is a function of pressure, and absorption/emission of IR from greenhouse gases is a function of temperature. The radiative theory tries to turn that around to claim IR emission from greenhouse gases controls the temperature, the heights of the ERL and tropopause, and thus the lapse rate, pressure, gravity, and heat capacity of the atmosphere, which is absurd and clearly disproven by basic thermodynamics and observations. The radiative greenhouse theory also makes the absurd assumption a cold body can make a hot body hotter,disproven by Pictet's experiment 214 years ago, the 1st and 2nd laws of thermodynamics, the principle of maximum entropy production, Planck's law, the Pauli exclusion principle, and quantum mechanics. There is one and only one greenhouse effect theory compatible with all of these basic physical laws and millions of observations. Can you guess which one it is?
We will start once again with the ideal gas law
PV = nRT (1)
an equation of state that relates the pressure P, volume V, temperature T, number of moles n of gas and the gas law constant R = 8.3144621 J/(mol K).
The properties of gases fall into two categories:
1. Extensive variables are proportional to the size of the system: volume, mass, energy
2. Intensive variables do not depend on the size of the system: pressure, temperature, density
To conserve energy (and to ensure that no radiative imbalances from greenhouse gases are affecting this derivation) of the mass/gravity/pressure greenhouse effect, we assume
Energy incoming from the Sun (Ein) = Energy out (Eout) from Earth to space
Observations indeed show Ein = Eout = 240 W/m2 (2)
which by the Stefan-Boltzmann law equates to a blackbody radiating at 255 K or -18C, which we will call the effective or equilibrium temperature (Te) between the Sun and Earth. As seen by satellites, the Earth radiates at the equilibrium temperature 255K from an average height referred to as the "effective radiating level" or ERL or "effective radiating height."
2. Determine the "gravity forcing" upon the atmosphere
Returning to the ideal gas law above, pressure is expressed using a variety of measurement units including atmospheres, bars, and Pascals, and for this derivation we will use units in atmospheres, which is defined as the pressure at mean sea level at the latitude of Paris, France in terms of Newtons per square meter [N/m2]
Newtons per square meter corresponds to the force per unit area [or "gravity forcing" upon the atmospheric mass per unit area of the Earth surface].
Now let's determine the mass of the atmosphere above one square meter at the Earth surface:
By Newton's 2nd law of motion equation, force (F) is
F = ma (3) where m = mass and a = acceleration
As we noted above, the atmospheric pressure is a force or forcing per unit area. The force in this case is the weight (note weight is not the same as mass and is in physical definitions of mass, length, time-2) or mass of the atmosphere times the gravitational acceleration, therefore
F = mg (4) where g is the gravitational constant 9.8 m/s2, i.e. the acceleration due to gravity in meters per second squared.
If we assume that g is a constant for the entire column of the atmosphere above the 1 meter2 area (A) we obtain
m = PA/g = (1.0325 x 10^5 N/m2 )(1 m2 )/(9.8 m/s2 ) = 1.05 x 10^4 kg
thus, the weight of the atmosphere over 1 square meter of the surface is 10,500 kilograms, quite a remarkable gravitational forcing upon the atmosphere.
If m is the mass of the atmosphere and g is the gravitational acceleration, the gravitational force is thus
F = mg (4)
The density (p) is the mass (m) per unit Volume (V), thus,
p = m/V
SI units of pressure refer to N/m2 as the Pascal (Pa). There are 1.0325 x 10^5 Pa per atmosphere (unit).
Starting again with equation (3) above
F = ma (3)
F = mg (4)
F = (PA/g)g = PA (5)
P = F/A = mg/A = phAg/A = phg (6)
where
h=height along either a gas or liquid column under pressure or gravity field
g = gravitational constant
p = density = mass/volume
3. Determine the atmospheric pressures from gravitational forcing, and the height of the effective equilibrium temperature (ERL)
Now we will determine the atmospheric pressures in a gravitational field using (6) above
First let's determine the pressure at the ERL since the temperature must equal the equilibrium temperature of 255K at the ERL.
The pressure is a function of height
P(h) = ρgh (7)
and the change in pressure dP is related to the change in height dh by
dP = -ρg dh (8)
The minus sign arises from the fact that pressure decreases with height, subject to an adjustment for density which changes with height. We will determine this adjustment from the ideal gas law. The density is
ρ = nM/V (9)
where n is the number of moles, M is the molar mass, and V is the volume. We can obtain n/V from the ideal gas law:
n/V = P/RT (10)
thus
ρ = MP/RT (11)
We can now substitute the density into the pressure vs. height formula:
dP = -(MPg/RT)dh (12)
∫dP/P = -(Mg/RT) ∫dh (13) (the first integral is from 1 to P, second from 0 to h)
ln(P) = -(Mgh/RT) (14)
P = e^-((Mgh/(RT)) (15)
We will now determine the height (h) at the ERL where the temperature = the effective equilibrium temperature = 255K, and without use of radiative forcing from greenhouse gases.
Plugging in numbers of M = 29 grams/mole (0.029 kg/mole) as average molar mass for atmosphere, g = 9.8 m/s^2, Pressure = 0.50 atmospheres at the approximate center of mass of the atmosphere, R=8.31, and T=Te=255K effective equilibrium temperature we obtain:
 |
| 0.50 atmosphere P at the ERL= e^-((.029*9.8*5100)/(8.31*255)) |
So the height of the ERL set by gravity forcing is located at 5100 meters and is where T=Te=255K and pressure = 0.5 atmospheres, right at the center of mass of the atmosphere as we predicted from our gravity forcing hypothesis.
4. Determine the temperatures at any location in the troposphere, and the magnitude of the mass/pressure greenhouse effect
Now that we have solved for the location of the ERL at 5100 meters, we can use the adiabatic lapse rate equation to determine all troposphere temperatures from the surface up to the ERL at 255K and then up to the top of the troposphere. The derivation of the lapse rate equation from the ideal gas law and 1st law of thermodynamics is described in this post, thus will not be repeated here, except to mention that the derivation of the lapse rate
dT/dh = -g/Cp where Cp = heat capacity of the atmosphere at constant pressure
is also completely independent of any radiative forcing from greenhouse gases, greenhouse gas concentrations, emission/absorption spectra from greenhouse gases, etc., and is solely a function of gravity and heat capacity of the atmosphere.
Plugging the average 6.5C/km lapse rate and 5100 meter or 5.1 km height of the ERL we determine above into our derived lapse rate equation (#6 from prior post) gives
T = -18C - (6.5C/km × (h - 5.1km))
Using this equation we can perfectly reproduce the temperature at any height in the troposphere as shown in Fig 1. At the surface, h = 0, thus temperature at the surface Ts is calculated as
Ts = -18 - (6.5 × (0 - 5.1))
Ts = -18 + 33.15C (gravity forced greenhouse effect)
Ts = 15.15°C or 288.3°K at the surface
which is exactly the same as determined by satellite observations and is 33.15C above the equilibrium temperature -18C or 255K with the Sun as expected.
Thus, we have determined the entire 33.15C greenhouse effect, the surface temperature, and the temperature of the troposphere at any height, and the height at which the equilibrium temperature with the Sun occurs at the ERL entirely on the basis of the Newton's 2nd law of motion, the 1st law of thermodynamics, and the ideal gas law, without use of radiative forcing from greenhouse gases, nor the concentrations of greenhouse gases, nor the emission/absorption spectra of greenhouse gases at any point in this derivation, demonstrating that the entire 33C greenhouse effect is dependent upon atmospheric mass/pressure/gravity, rather than radiative forcing from greenhouse gases. Also note, it is absolutely impossible for the conventional radiative theory of the greenhouse effect to also be correct, since if that was the case, the Earth's greenhouse effect would be at least double (66C+ rather than 33C).
In essence, the radiative theory of the greenhouse effect confuses cause and effect. As we have shown, temperature is a function of pressure, and absorption/emission of IR from greenhouse gases is a function of temperature. The radiative theory tries to turn that around to claim IR emission from greenhouse gases controls the temperature, the heights of the ERL and tropopause, and thus the lapse rate, pressure, gravity, and heat capacity of the atmosphere, which is absurd and clearly disproven by basic thermodynamics and observations. The radiative greenhouse theory also makes the absurd assumption a cold body can make a hot body hotter,disproven by Pictet's experiment 214 years ago, the 1st and 2nd laws of thermodynamics, the principle of maximum entropy production, Planck's law, the Pauli exclusion principle, and quantum mechanics. There is one and only one greenhouse effect theory compatible with all of these basic physical laws and millions of observations. Can you guess which one it is?
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