How Gravity continuously does Work on the atmosphere to control pressure & temperature

Some commenters claim gravity is not continuously performing thermodynamic Work upon the atmosphere to generate the thermal gradient from the continuous compression/expansion of gas parcels or packets continuously moving up and down within the lower atmosphere. This is the source of the 33C gravito-thermal greenhouse effect, so we will now demonstrate why this misconception is incorrect by using the 1st Law of Thermodynamics (law of conservation of energy), ideal gas law, and barometric formulae. 

Beginning with the 1st Law of Thermodynamics: 

where

  is change in internal energy 

  and  are quantities of heat supplied to the system by its surroundings and of work done by the system on its surroundings, respectively. 

When a system expands [e.g. the inflation of the atmosphere by solar radiative forcing] in a fictive quasistatic process, the work done by the system on the environment is the product, +P dV,  of pressure, P, and volume change, dV, whereas the work done on the system is  -P dV.  Using either sign convention for work, the change in internal energy of the system is:

The two sides of the 1st law equation must balance with change in internal energy for the atmosphere ~0. Note the Work done on the right side of the equation is the work done by gravitational forcing on the atmosphere = F = ma = mg for the atmosphere by the continuous compression of cold, descending air packets and the gravitational potential energy PE that convecting warm air packets accumulate as they rise, expand, and cool. In the 1st law above, the Work done on the right side is from the expansion/compression of air packets continuously rising and falling in the atmosphere ad infinitum. 
This continuous compression by gravity of cold gas packets descending adiabatically from the upper atmosphere down to the surface is what is continuously doing Work (W = pda = Pressure*change in specific volume (a)) upon the atmosphere. By the ideal gas law, this continuous work or compression of gas packets increases their pressure as they descend toward the surface, thus creating the temperature gradient within the troposphere.
Also note, greenhouse gases are passive IR absorbers/emitters and not a source of any heat energy on the left side of the equation.

Applying the 1st Law to gases or the atmosphere provides these various forms for a gas of mass m:

Note "changes in temperature result from either expansion or contraction" and "adiabatic processes play a large role in deep convective processes"

The Poisson Relation as the entire source of the atmospheric temperature gradient (gravito-thermal greenhouse effect), not radiative forcing from greenhouse gases, was perhaps first described by the great physicist Maxwell. These same barometric relations are the basis of all the barometric formulae and the greenhouse equation. 

Thus, gravity is continuously doing the work upon air packets/parcels ascending (which are accumulating gravitational potential energy) and air packets/parcels descending (which in the process are using up their gravitational potential energy in exchange for the work done by gravity on continuous compression of air packets/parcels). 

This demonstrates how gravity creates the thermal gradient above and below the equilibrium temperature with the Sun, while conserving energy:

Equilibrium temperature with the Sun = 255K

Ts = temperature at Earth's surface = 288K

Tt = temperature at the tropopause = 220K at around 15,000 km height

"Average temperature" of the quasi-linear [lapse rate] temperature gradient of the troposphere:

(288K + 220K)/2 = 254K ~ 255K = Equilibrium temperature with the Sun

288K - 255K = 33C gravito-thermal greenhouse effect

Thus fulfilling the 1st law requirement of conservation of energy. (Before someone comments, I know you can't properly average temperatures, and that temperature is not a direct proxy for heat energy because calorimetry requires the mass, specific heats, heats of fusion and vaporization, and all phase changes be accounted, but use of temperature as a proxy of heat is done for illustrative purposes and simplification of the explanation)

Note the units of pressure used in the greenhouse equation are in unit atmospheres, and by definition 1 atmosphere of pressure at the surface = 1.01325×10⁵ Newtons/meter squared, which is the continuous gravitational forcing F = mg upon the atmosphere by gravity which is producing the gravito-thermal greenhouse effect. Newton's 2nd law of motion F = ma = mg appears in the greenhouse equation as annotated below to calculate this gravitational forcing upon the atmospheric mass:

Also note, we previously calculated the adiabatic lapse rate and temperature distribution in a theoretical Earth atmosphere of 100% Nitrogen, a non-greenhouse gas, and found the adiabatic lapse rate and troposphere temperature distribution almost the same as our Earth, surface temperature warmer on the theoretical 100% Nitrogen atmosphere Earth, thus proving greenhouse gases act as cooling agents rather than warming. 

Derivation of the entire 33°C greenhouse effect without radiative forcing from greenhouse gases

We will derive the entire 33°C greenhouse effect using the 1st law of thermodynamics and 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, thus demonstrating that the entire 33C greenhouse effect is dependent upon atmospheric mass/pressure/gravity, rather than radiative forcing from greenhouse gases. Secondly, we will show why multiple observations perfectly confirm the mass/gravity/pressure theory of the greenhouse effect, and disprove the radiative forcing theory of the greenhouse effect.

Note, this physical derivation is absolutely not suggesting the ~33C greenhouse effect doesn't exist. On the contrary, the physical derivation and observations demonstrate the 33C greenhouse effect does exist, but is explained by a different mechanism not dependent on radiative forcing from greenhouse gases. Also note, it is impossible for both explanations of the greenhouse effect to be true, since the global temperature would have to increase by an additional 33C (at least) above the present. You cannot have it both ways. We will show how the mass/gravity/pressure theory causes the temperature gradient and that the emission spectra of greenhouse gases seen from space are a consequence rather than the cause of that temperature gradient. 

This derivation uses very well-known physical principles and barometric formulae possibly first described by the great physicist Maxwell in 1872, who demonstrated that the atmospheric temperature gradient and greenhouse effect are due to pressure from Earth's gravitational field, not radiative forcing. Maxwell makes no mention of any influence of radiation as the cause of the temperature gradient of the atmosphere, but rather relates temperature at a given height to pressure. He discusses the convective (dominated) equilibrium of the atmosphere in his book Theory of Heat, pp. 330-331:

"...In the convective equilibrium of temperature, the absolute temperature is proportional to the pressure raised to the power (γ-1)/γ, or 0,29..."

Twenty four years later, Arrhenius devised his radiative forcing theory of the greenhouse effect, which unfortunately makes a huge false assumption that convection doesn't dominate over radiative-convective equilibrium in the lower atmosphere, and thus Arrhenius completely ignored the dominant negative-feedback of convection over radiative forcing in his temperature derivations. Johns Hopkins physicist RW Wood completely demolished Arrhennius' theory in 1909, as did other published papers in 1963, 1966, 1973, (and others below), but it still refuses to die given its convenience to climate alarm.

We now know from Robinson & Catling's paper in Nature 2014 (and others) that radiative-convective equilibrium on all planets with thick atmospheres in our solar system (including Earth of course) is dominated by convection/pressure/lapse rate in the troposphere up to where the tropopause begins at pressure = 0.1bar. When P < 0.1 bar, the atmosphere is too thin to sustain convection and radiation from greenhouse gases takes over to cause cooling of the stratosphere and above. 

Since Maxwell's book was published in 1872, many others have confirmed that the greenhouse effect is due to atmospheric mass/pressure/gravity, rather than radiative forcing from greenhouse gases, including Hans Jelbring, Connolly & Connolly, Nikolov & Zeller, Mario Berberan-Santos et al, Claes Johnson and here, Velasco et al, Giovanni Vladilo et al, Heinz Thieme, Jacques Henry, Stephen Wilde, Alberto Miatello, Gerhard Gerlich and Ralf D. Tscheuschner, Verity Jones, William C. Gilbert & here, Richard C. Tolman, Lorenz & McKay, Peter Morecombe, Robinson and Catling, and many others, so this concept is not new and preceded the Arrhenius theory. 

Step 1: Derivation of the dry adiabatic lapse rate from the 1st Law of Thermodynamics and ideal gas law:

First, the basic assumption can be adopted that the atmosphere, in hydrostatic terms, is a self-gravitating system in constant hydrostatic equilibrium due to the balance of the two opposing forces of gravity and the atmospheric pressure gradient, according to the equation:

 dP/dz = - ρ × g (1)

where ρ is the density (mass per volume) and g the acceleration due to gravity. This equation, from a mathematical point of view, can be derived by considering the hydrostatic equilibrium function as a system of partial derivatives depending on P and ρ and considering all three spatial dimensions:

 ∂P/∂x = ρ × X, ∂P/∂y = ρ × Y, ∂P/∂z = ρ × Z (2)

As, within a fluid mass in equilibrium, pressure and density does not vary along the horizontal axes (X and Y), the related partial derivatives equal zero. But, in the remaining vertical dimension, the partial derivative is non-zero, with density and pressure varying inversely as a function of fluid height (density and pressure decrease with increasing height relative to the bottom) and, considering gravitational force as a constant connected to the measure of density, thus equation (2) can be derived.

For a precise calculation involving the valid parameters, the 1st Law of Thermodynamics can be used:

 Δ U = Q – W (3)

where U is the total internal energy of the system, Q its heat energy, and W the mechanical work the system is undergoing. Applying this relationship to Earth's atmosphere, yields:

 U = C(p)T + gh (4)

where U is the total energy of atmospheric system in hydrostatic equilibrium and equal to the sum of the thermal energy (kinetic plus dissipative and vibro-rotational), the specific heat C(p) multiplied by the temperature T plus the gravitational potential energy, with gravitational force g at height h of the gas. In this case, because the force of gravity has a negative sign as the system is undergoing work, the potential energy ( -g × h) can be equated to the mechanical work (-W) that the system undergoes in the 1st Law of Thermodynamics.

Based on this equation, the atmosphere's "average" temperature change can be found for any point with the system in equilibrium; for now and for simplicity, weather phenomena and disturbances at specific locations are not considered because, with the system in overall hydrostatic and macroscopic equilibrium, any local internal, microclimatic perturbation by definition triggers a rebalancing reaction. In fact, to calculate the energy change of the system in equilibrium (here U is constant) as a function of temperature and height change, differentiation yields: 

dU = 0 = C(p)dT + gdh,

which becomes: 

dT/dh = -g/C(p), or dT = (-g/C(p))dh.  [Dry adiabatic lapse rate equation]

This is a splendid equation, describing precisely the temperatures’ distribution of a gas (as the air of Earth’s atmosphere) in hydrostatic equilibrium between the 2 forces of the lapse-rate (preventing the collapse of the atmosphere at the Earth’s surface) and gravity (preventing the escape of the atmosphere in the void of space). 

In other words, temperature variation (dT) is a function of altitude variation (dh), whose solution at any point of height (h°) and for any temperature (T°), can be found by integrating as follows:

∫dT = -g/C(p) × ∫dh (5)

and whose solution is:

 T - T° = -g/C(p) × (h - h°)   (6)

where:

T – T° = ∆ T (or dT) = Interval of temperatures
g = Gravitational acceleration constant = 9.8 m/s^2
h – h° = ∆ h (or dh) = Space interval (vertical) in the atmosphere
Cp = heat capacity at constant pressure

Step 2: Determine the height at the center of mass of the atmosphere

We are determining the temperature gradient within the mass of the atmosphere using a linear function of atmospheric mass (the lapse rate), therefore the equilibrium temperature is located at the center of mass. The "effective radiating level" or ERL of planetary atmospheres is located at the approximate center of mass of the atmosphere where the temperature is equal to the equilibrium temperature with the Sun. The equilibrium temperature of Earth with the Sun is commonly assumed to be 255K or -18C as calculated here. As a rough approximation, this height is where the pressure is ~50% of the surface pressure. It is also located at the approximate half-point of the troposphere temperature profile set by the linear adiabatic lapse rate, since to conserve energy in the troposphere, the increase in temperature from the ERL to the surface is offset by the temperature decrease from the ERL to the tropopause.

Fig 1. From Robinson & Catling, Nature, 2014 with added notations in red showing at the center of mass of Earth's atmosphere at ~0.5 bar the temperature is ~255K, which is equal to the equilibrium temperature with the Sun. Robinson & Catling also demonstrated that the height of the tropopause is at 0.1 bar for all the planets in our solar system with thick atmospheres, as also shown by this figure, and that convection dominates over radiative-convective equilibrium in the troposphere to produce the troposphere lapse rates of each of these planets as shown above. R&C also show the lapse rates of each of these planets are remarkably similar despite very large differences in greenhouse gas composition and equilibrium temperatures with the Sun, once again proving pressure, not radiative forcing from greenhouse gases, determines tropospheric temperatures. 

Step 3: Determine the surface temperature

For Earth, surface pressure is 1 bar, so the ERL is located where the pressure ~0.5 bar, which is near the middle of the ~10 km high troposphere at ~5km. The average lapse rate on Earth is 6.5C/km, intermediate between the 10C/km dry adiabatic lapse rate and the 5C/km wet adiabatic lapse rate, since the atmosphere on average is intermediate between dry and saturated with water vapor. 

Plugging the average 6.5C/km lapse rate and 5km height of the ERL into our equation (6) above gives

T = -18 - (6.5 × (h - 5)) 

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)) 

Ts = -18 + 32.5  

Ts = 14.5°C or 288°K

which is the same as determined by satellite observations and is ~33C above the equilibrium temperature with the Sun.

Thus, we have determined the entire 33C greenhouse effect, the surface temperature, and the temperature of the troposphere at any height, entirely on the basis of the 1st law of thermodynamics and 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.

The greenhouse gas water vapor does have a very large negative-feedback cooling effect on the surface and atmospheric temperature by reducing the lapse rate by half from the 10C/km dry rate to the 5C/km wet rate. Increased water vapor increases the heat capacity of the atmosphere Cp, which is inversely related to temperature by the lapse rate equation above:

dT/dh = -g/Cp

Plugging these lapse rates into our formula for Ts above:

Ts = -18 - (10 × (0 - 5)) = 32C using dry adiabatic lapse rate

Ts = -18 - (5 × (0 - 5)) = 7C using wet adiabatic lapse rate [fully saturated]

showing a cooling effect of up to 25C just from changes in the lapse rate from water vapor. Water vapor also cools the planet via evaporation and clouds, and which is confirmed by observations. Water vapor is thus proven by observations and theory to be a strong negative-feedback cooling agent, not a positive-feedback warming agent as assumed by the overheated climate models to amplify warming projections by a factor of 3-5 times. 

What about CO2? At only 0.04% of the atmosphere, CO2 contributes negligibly to atmospheric mass and only slightly increases the heat capacity Cp of the atmosphere, which as we have shown above, is inversely related to temperature. CO2 would thus act as a cooling agent by slightly increasing troposphere heat capacity. Increased CO2 also increases the radiative surface area of the atmosphere to enhance outgoing radiation to space, analogous to putting a larger heat sink on your microprocessor which increases radiative surface area and convection to cause cooling. 

It is well-known that CO2 and ozone are the primary cooling agents of the stratosphere up to the thermosphere, but even the warmist proponents are unable to agree on a coherent explanation why CO2 would assume the opposite role of a warming agent in the troposphere. As the mass/gravity/pressure greenhouse theory shows, and just like water vapor, CO2 also acts to cool the troposphere, and the rest of the atmosphere by increasing radiative surface loss and outgoing radiation to space. 

Millions of weather balloon observations confirm that there is no greenhouse gas-induced "hot spot" in the mid-upper troposphere, which is the alleged "fingerprint of AGW." The 2nd law of thermodynamics principle of maximum entropy production also explains why such a "hot spot" will not form. However, observations do show a cooling of the stratosphere over the satellite era, which would be consistent with increased CO2 increasing outgoing radiation to space. Observations also show an increase of outgoing longwave radiation to space over the past 62 years, which is entirely consistent with increased outgoing radiation from greenhouse gases and a decrease of "heat trapping", the opposite of AGW theory. 

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 and thus pressure 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?

Update: The atmospheric center of mass assumption in step 2 above also appears to be applicable to Titan, the closest Earth analog with a thick atmosphere in our solar system. For Titan, the surface temperature is 94K, equilibrium temperature with the Sun is 82K, and surface pressure is 1.47 bar. 

Thus, the center of mass of the atmosphere is located at ~1.47/2 = ~0.74 bar, which observations show is where Titan's atmospheric temperature is ~82K, the same as the equilibrium temperature with the Sun. I have added the notations in red to Robinson and Catling's graph below:

Update 2: Some still claim the ERL is set by radiative forcing, but this is false because:

1) A purely radiative model of the atmosphere without convection sets the ERL too high, at ~7km instead of ~5 km where observations show it is located. At 7km altitude, observations show the temperature to be 242K instead of the equilibrium temperature of 255K.

Solely radiative "greybody" model of the atmosphere without convection shown in blue. I have added in red the actual temperatures from the US Standard Atmosphere calculator. Note how the purely radiative model is up to 20K hotter, e.g. at the top of the troposphere, than the observations show. This is because convection dominates and "short-circuits" radiative forcing in the troposphere to cause cooling.

2. Observations show no correlation between tropopause height and troposphere temperature 1980-2004:

Open symbols show no relationship between tropopause height and troposphere temperatures

That's because, as Robinson and Catling have shown, the height of the troposphere and the adiabatic lapse rate that extends from the 0.1 bar tropopause all the way to the surface is controlled by pressure, not temperature nor radiative forcing from greenhouse gases:

"At higher pressures [P > 0.1 bar], atmospheres become opaque to thermal radiation, causing temperatures to increase with depth and convection to ensue. A common dependence of infrared opacity on pressure, arising from the shared physics of molecular absorption, sets the 0.1 bar tropopause"

3. We have already shown that temperature is a function of pressure, and radiance and emission spectra from greenhouse gases are in turn a function of temperature, not the other way around.  

Why Man-Made Global Warming Theory Confuses the Cause With the Effect

This next post in a series demonstrating physical & mathematical proofs why Maxwell's atmospheric mass/gravity/pressure (33C) greenhouse effect is the only correct explanation of the greenhouse effect will now show why the entire physical basis of the competing anthropogenic global warming theory (now out of necessity called "man-made climate change" since it hasn't warmed for 18-26 years), somehow conveniently ignored the well-established basic and atmospheric physics, physical chemistry, and barometric relations that had been well-established for more than the past two centuries, and effectively hide this in their overheated & untouchable black-box computer models. 

The models then serve the purpose of providing a veritable & impenetrable safety deposit box of ancient Fortran computer code, completely secured from inspection by anyone who doesn't have the key, or understand poorly-documented Fortran.  

The CAGW computer modelers also completely ignored the hundreds of physicists, atmospheric and rocket scientists, physical chemists, and other scientists who just a decade earlier (during the 1970's ice age scare) provided the immense, overwhelming physical, chemical, and observational proof of the gold standard 1976 US Standard Atmosphere calculations and the first computer model of the atmosphere (and the only model which has been verified with (millions) of observations), offering overwhelming evidence that greenhouse gases have no significant "radiative forcing" or "radiative imbalance" effects upon the Earth's atmosphere whatsoever, from the surface to edge of space. 

The Standard Atmosphere model does no radiative calculations from greenhouse gases or other gases, since these hundreds of scientists had previously established any such effects to be negligible. The calculations and std. atmosphere model do not ever utilize the absolutely essential Stefan-Boltzmann equation, nor any absorption/emission spectra from any IR-active gases at all to determine temperatures from "radiative imbalance," or "heat trapping," or "radiative forcing from greenhouse gases."

Bad things can happen when climate modelers conveniently ignore over 200 years of well-established physics, including confusing a cause with an effect, but that is unfortunately what has happened. We will now show additional reasons why man-made or natural CO2 cannot be the Earth's climate control knob, demonstrating how the IR emission spectra from greenhouse gases are simply an effect of and not the cause of the mass densities/gravity/pressure/viscosities of all gases present in each layer of the atmosphere all the way from the surface to the edge of space, which in-turn are entirely responsible for the resulting temperatures (via the Ideal Gas Law and other physical laws) at every altitude, not IR backradiation from passive IR absorbers/emitting gases (so-called "greenhouse gases" for the first time a decade later). 

The cause must always precede the effect, and the cause never follows the effect. As the greatest physicist in history on the topics of radiation and heat, J Clerk Maxwell, wrote in 1872, the atmospheric temperatures and gradients are a function of and caused by atmospheric pressure/density/specific heat capacity of the particular gases in the atmosphere, not the other way around as falsely assumed by CAGW proponents and the falsified & overheated climate models. 

Atmospheric pressure/density/specific heat capacity of the particular gases in the atmosphere produce temperature gradients without violating the 1st and 2nd laws of thermodynamics, increasing the surface temperature by ~33C above the equilibrium temperature with the Sun, and decreasing the top of the troposphere by even more 35C below of the equilibrium temperature with the Sun (an anti-greenhouse effect). By way of illustration (ignoring that temperature cannot be properly "averaged"):

Temperature at top of the troposphere at ~11,000 meters average ~220K (35C colder than the equilibrium temperature with the Sun of 255K

Temperature at the surface average ~288K (33C warmer than the equilibrium temperature with the Sun of 255K

(220 + 288)/2 = 254K ~ 255K

Thus energy is conserved as required by the 1st law of thermodynamics: 

dU = Q + W = 0 change in internal energy

where

dU = change in internal energy which must be zero or infinitesimally small in order to conserve energy
Q = any heating source of the system (i.e. the Sun only)
W = work done 

Thus

Q = -W (note the minus sign in front of the Work done, which must be exactly equal and opposite)

which in the case of the atmosphere, the Q is radiative forcing from the Sun, and Work done is the adiabatic compression and expansion of gases in the troposphere, which must be equal and opposite for energy to be conserved:

The climate modelers claim, however, that passive IR absorbers/radiators greenhouse gases somehow add 33C of heat energy to the planet to the 255K already provided by the Sun, causing the 255+33K = 288K surface temperature. However, they never mention (for very good reasons) that the US Standard Atmosphere above and observations show the troposphere also has an even greater 35C negative greenhouse effect from 255K falling to 220K at the top of the troposphere. 

How can any greenhouse gas allegedly "know" that it is supposed to heat only the troposphere by 33C below ~5100 meters altitude while simultaneously cooling the remainder of the troposphere by 35C from ~5100 - 11,000 meters altitude? They cannot, nor can computer models, without violating the 1st and 2nd laws of thermodynamics, and common sense. 

According to the radiative greenhouse proponents, the emission/absorption spectra shown below somehow prove greenhouse gases are the cause of and not the effect of the tropospheric lapse rate temperature gradient

But the annotations below show that the big notch in the emission spectra due to H2O and CO2 is simply the exact same temperatures all along the linear adiabatic lapse rate corresponding Planck blackbody curves. As we have shown many times, the lapse rate is controlled only by gravity and atmospheric heat capacity and not affected in the least by greenhouse gas concentrations. This proves that the greenhouse gases in the atmosphere are simply radiating at the temperatures set by the lapse rate equation, as expected:

dT/dh = -g/Cp

thus the temperature is a function of and an effect of gravity/molecular mass, not the other way around from greenhouse gas "radiative forcing" or "backradiation." Irradiance or "backradiation" from greenhouse gases is in turn a function of the 4th power of temperature (by the Stefan Boltzmann equation), not the cause of the temperatures to begin with.

The cause absolutely cannot follow the effect. Mass/gravity/pressure cause the Maxwell greenhouse effect and lapse rates, which causes the resulting temperature, which in-turn causes the greenhouse gases at each atmospheric temperature thus established to passively radiate IR at the above blackbody curves and absorption/emission spectra, not the other way around. You cannot have it both ways. One and only one 33C greenhouse effect theory can be correct, not both since otherwise the surface would be at least 33C warmer. 

In the next post of this series we will introduce newly improved and greatly simplified versions of the greenhouse equation proving all atmospheric temperatures can be derived without any knowledge of the surface temperature in advance, only the equilibrium temperature of Earth and the Sun plus the barometric formulae:

New renewable energy device generates power from the emission of infrared from Earth's surface

A new renewable energy source generates power from the net emission of infrared radiation from the surface of Earth to space, "a vast and untapped energy source." This "strange and new" device is "something akin to a photovoltaic solar panel, but instead of capturing incoming visible light, the device would generate electric power by releasing infrared light" to the atmosphere, and ultimately to space. 

How is this possible? Based upon the 2nd law of thermodynamics, heat only flows from hot to cold, i.e. from the hot +15C Earth surface to the average -15C cold atmosphere and then to very cold -455F [= -270C = 2K] outer space. This device generates electricity by releasing infrared radiation to the cold atmosphere, which causes cooling of the device and generates flow of current. In similar fashion, a solar cooker pointed at a clear night or day sky acts as a refrigerator to make ice when the ambient temperature is 10 degrees above freezing, by increasing cooling at the focal point. 

The ancient Romans also used this principle to make ice [and some speculate ice cream] at ambient temperatures well above freezing by digging a hole and putting a pan of water at the bottom. The hole allows increased loss of heat from the warm water since it is only pointed at the -15C sky, thus causing the water to freeze at ambient temperatures higher than freezing. 

What significance does this have for the conventional explanation of the 33K greenhouse effect on Earth? The conventional explanation claims infrared radiation from greenhouse gases or "radiative forcing" is forcing Earth's surface temperature to warm from the equilibrium temperature with the Sun of 255K up to the measured surface temperature of 288K [15C]. Per the Stefan-Boltzmann Law, this increase in temperature requires a net increase of heat flux from the atmosphere to the Earth surface of 150W/m2 [390-240]. This is absolutely impossible, because net heat flux must always be from hot to cold and entropy always increases per the 2nd Law of Thermodynamics. The fact that these devices work by cooling to the atmosphere proves the net effect of the atmosphere is cooling, not warming. Heat flow from cold to hot requires a decrease of entropy, which is impossible without work input [like in a refrigerator], and greenhouse gases cannot add any work input whatsoever.

Does this mean I'm a greenhouse effect denier? No, absolutely not. On the contrary, the 33K greenhouse effect absolutely does exist, but it is due entirely to the adiabatic compression of all gases [Earth's atmosphere is >99% non-greenhouse gases] within a gravity field, and is completely independent of man-made CO2. An atmosphere without greenhouse gases would be even warmer than one with greenhouse gases, because greenhouse gases increase radiative surface area and increase the emissivity of infrared radiation to space. 

A new renewable energy source? Device captures energy from Earth's infrared emissions to outer space

Date: March 3, 2014

Source: Harvard School of Engineering and Applied Sciences

Summary:
When the sun sets on a remote desert outpost and solar panels shut down, what energy source will provide power through the night? A battery, perhaps, or an old diesel generator? Perhaps something strange and new. Scientists now envision a device that would harvest energy from Earth's infrared emissions into outer space. Heated by the sun, our planet is warm compared to the frigid vacuum beyond. Thanks to recent technological advances, the researchers say, that heat imbalance could soon be transformed into direct-current (DC) power, taking advantage of a vast and untapped energy source.

"We’re talking about the use of physics at the nanoscale for a completely new application," says Federico Capasso.

When the sun sets on a remote desert outpost and solar panels shut down, what energy source will provide power through the night? A battery, perhaps, or an old diesel generator? Perhaps something strange and new.

Physicists at the Harvard School of Engineering and Applied Sciences (SEAS) envision a device that would harvest energy from Earth's infrared emissions into outer space.

Heated by the sun, our planet is warm compared to the frigid vacuum beyond. Thanks to recent technological advances, the researchers say, that heat imbalance could soon be transformed into direct-current (DC) power, taking advantage of a vast and untapped energy source.

Their analysis of the thermodynamics, practical concerns, and technological requirements will be published this week in the Proceedings of the National Academy of Sciences.

"It's not at all obvious, at first, how you would generate DC power by emitting infrared light in free space toward the cold," says principal investigator Federico Capasso, the Robert L. Wallace Professor of Applied Physics and Vinton Hayes Senior Research Fellow in Electrical Engineering at Harvard SEAS. "To generate power by emitting, not by absorbing light, that's weird. It makes sense physically once you think about it, but it's highly counterintuitive. We're talking about the use of physics at the nanoscale for a completely new application."

Challenging convention

Capasso is a world-renowned expert in semiconductor physics, photonics, and solid-state electronics. He co-invented the infrared quantum-cascade laser in 1994, pioneered the field of bandgap engineering, and demonstrated an elusive quantum electrodynamical phenomenon called the repulsive Casimir force -- work for which he has received the SPIE Gold Medal, the European Physical Society Prize for Quantum Electronics and Optics, and the Jan Czochralski Award for lifetime achievement. His research team seems to specialize in rigorously questioning other physicists' assumptions about optics and electronics.

"The mid-IR has been, by and large, a neglected part of the spectrum," says Capasso. "Even for spectroscopy, until the quantum cascade laser came about, the mid-IR was considered a very difficult area to work with. People simply had blinders on."

Now, Capasso and his research team are proposing something akin to a photovoltaic solar panel, but instead of capturing incoming visible light, the device would generate electric power by releasing infrared light.

"Sunlight has energy, so photovoltaics make sense; you're just collecting the energy. But it's not really that simple, and capturing energy from emitting infrared light is even less intuitive," says lead author Steven J. Byrnes (AB '07), a postdoctoral fellow at SEAS. "It's not obvious how much power you could generate this way, or whether it's worthwhile to pursue, until you sit down and do the calculation."

As it turns out, the power is modest but real.

As Byrnes points out, "The device could be coupled with a solar cell, for example, to get extra power at night, without extra installation cost."

Two proposed devices -- one macro, one nano

To show the range of possibilities, Capasso's group suggests two different kinds of emissive energy harvesters: one that is analogous to a solar thermal power generator, and one that is analogous to a photovoltaic cell. Both would run in reverse.

The first type of device would consist of a "hot" plate at the temperature of the Earth and air, with a "cold" plate on top of it. The cold plate, facing upward, would be made of a highly emissive material that cools by very efficiently radiating heat to the sky. Based on measurements of infrared emissions in Lamont, Oklahoma (as a case study), the researchers calculate that the heat difference between the plates could generate a few watts per square meter, day and night. Keeping the "cold" plate cooler than the ambient temperature would be difficult, but this device illustrates the general principle: differences in temperature generate work.

"This approach is fairly intuitive because we are combining the familiar principles of heat engines and radiative cooling," says Byrnes.

The second proposed device relies on temperature differences between nanoscale electronic components -- diodes and antennas -- rather than a temperature that you could feel with your hand.

"If you have two components at the same temperature, obviously you can't extract any work, but if you have two different temperatures you can," says Capasso. "But it's tricky; at the level of the electron behaviors, the explanation is much less intuitive."

"The key is in these beautiful circuit diagrams," he adds (see image). "We found they had been considered before for another application -- in 1968 by J.B. Gunn, the inventor of the Gunn diode used in police radars -- and been completely buried in the literature and forgotten. But to try to explain them qualitatively took a lot of effort."

Simply put, components in an electrical circuit can spontaneously push current in either direction; this is called electrical noise. Gunn's diagrams show that if a valve-like electrical component called a diode is at a higher temperature than a resistor, it will push current in a single direction, producing a positive voltage. Capasso's group suggests that the role of the resistor could be played by a microscopic antenna that very efficiently emits the Earth's infrared radiation toward the sky, cooling the electrons in only that part of the circuit.

The result, says Byrnes, is that "you get an electric current directly from the radiation process, without the intermediate step of cooling a macroscopic object."

According to the paper, a single flat device could be coated in many of these tiny circuits, pointed at the sky, and used to generate power.

Technological challenges -- and promise

The optoelectronic approach, while novel, could be feasible in light of recent technological developments -- advances in plasmonics, small-scale electronics, new materials like graphene, and nanofabrication. The Harvard team says a strength of their research is that it clarifies the remaining challenges.

"People have been working on infrared diodes for at least 50 years without much progress, but recent advances such as nanofabrication are essential to making them better, more scalable, and more reproducible," says Byrnes.

However, even with the best modern infrared diodes, there is a problem. "The more power that's flowing through a single circuit, the easier it is to get the components to do what you want. If you're harvesting energy from infrared emissions, the voltage will be relatively low," explains Byrnes. "That means it's very difficult to create an infrared diode that will work well."

Engineers and physicists, including Byrnes, are already considering new types of diodes that can handle lower voltages, such as tunnel diodes and ballistic diodes. Another approach would be to increase the impedance of the circuit components, thereby raising the voltage to a more practical level. The solution might require a little of both, Byrnes predicts.

Speed presents another challenge. "Only a select class of diodes can switch on and off 30 trillion times a second, which is what we need for infrared signals," says Byrnes. "We need to deal with the speed requirements at the same time we deal with the voltage and impedance requirements."

"Now that we understand the constraints and specifications," Byrnes adds, "we are in a good position to work on engineering a solution."

Romain Blanchard, who completed his Ph.D. at Harvard SEAS, was also a coauthor of the paper in PNAS. This research was supported in part by King Abdullah University of Science and Technology (CRG-1-2012-FRA-005-HAR).

Story Source:

The above story is based on materials provided by Harvard School of Engineering and Applied Sciences. The original article was written by Caroline Perry. Note: Materials may be edited for content and length.

Journal Reference: Steven J. Byrnes, Romain Blanchard, and Federico Capasso. Harvesting renewable energy from Earth's mid-infrared emissions. PNAS, 2014

Harvesting renewable energy from Earth’s mid-infrared emissions

1. Steven J. Byrnes, 
2. Romain Blanchard, and 
3. Federico Capasso1

Author Affiliations

1. Contributed by Federico Capasso, February 3, 2014 (sent for review November 1, 2013)

Significance

Renewable energy can be generated whenever heat flows from a hotter to a colder body. One such flow is from the warm surface of Earth to cold outer space, via infrared thermal radiation. An emissive energy harvester (EEH) is a device that can generate energy from emitting thermal radiation into the clear sky. We calculate how much power is thermodynamically available, using a location in Oklahoma as a case study. We discuss two possible ways to make such a device: A thermal EEH (analogous to solar thermal power generation) and an optoelectronic EEH (analogous to photovoltaic power generation). For the latter, we propose using a rectifying antenna, and we discuss its operating principles, efficiency limits, system design considerations, and possible technological implementations.

Abstract

It is possible to harvest energy from Earth's thermal infrared emission into outer space. We calculate the thermodynamic limit for the amount of power available, and as a case study, we plot how this limit varies daily and seasonally in a location in Oklahoma. We discuss two possible ways to make such an emissive energy harvester (EEH): A thermal EEH (analogous to solar thermal power generation) and an optoelectronic EEH (analogous to photovoltaic power generation). For the latter, we propose using an infrared-frequency rectifying antenna, and we discuss its operating principles, efficiency limits, system design considerations, and possible technological implementations.