The thermal heating effect of back radiation from greenhouse gases is calculated using Stefan-Boltzmann laws
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Scientific literature confirms that thermal radiation calculations and effective radiating temperatures related to planetary greenhouse effects and radiative balances rely on the Stefan-Boltzmann law.
The presence of atmosphere can appreciably warm a planet’s surface above the temperature of an airless environment. Known as a natural Greenhouse Effect (GE), this near-surface Atmospheric Thermal Enhancement (ATE) as named herein is presently entirely attributed to the absorption of up-welling long-wave radiation by greenhouse gases. Often quoted as 33 K for Earth, GE is estimated as a difference between planet’s observed mean surface temperature and an effective radiating temperature calculated from the globally averaged absorbed solar flux using the Stefan-Boltzmann (SB) radiation law. This approach equates a planet’s average temperature in the absence of greenhouse gases or atmosphere to an effective emission temperature assuming ATE ≡ GE. The SB law is also routinely employed to estimating the mean temperatures of airless bodies. We demonstrate that this formula as applied to spherical objects is mathematically incorrect owing to Hölder’s inequality between integrals and leads to biased results such as a significant underestimation of Earth’s ATE. We derive a new expression for the mean physical temperature of airless bodies based on an analytic integration of the SB law over a sphere that accounts for effects of regolith heat storage and cosmic background radiation on nighttime temperatures. Upon verifying our model against Moon surface temperature data provided by the NASA Diviner Lunar Radiometer Experiment, we propose it as a new analytic standard for evaluating the thermal environment of airless bodies. Physical evidence is presented that Earth’s ATE should be assessed against the temperature of an equivalent airless body such as the Moon rather than a hypothetical atmosphere devoid of greenhouse gases. Employing the new temperature formula we show that Earth’s total ATE is ~90 K, not 33 K, and that ATE = GE + TE, where GE is the thermal effect of greenhouse gases, while TE > 15 K is a thermodynamic enhancement independent of the atmospheric infrared back radiation. It is concluded that the contribution of greenhouse gases to Earth’s ATE defined as GE = ATE – TE might be greater than 33 K, but will remain uncertain until the strength of the hereto identified TE is fully quantified by future research.
The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases and clouds, and is
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, transfer of energy by phase changes, and evaporative cooling. Engineers also consider the transfer of mass of differ
T
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are the absolute temperatures (in kelvins or degrees Rankine) for the two objects.
The blackbody limit established by the Stefan-Boltzmann equation can be exceeded when the objects exchanging thermal radiation or the distances separating them are comparable in scale or smaller than the dominant thermal wavelength. The study of these cases is called near-field radiative heat transfer.
Radiation from the sun, or solar radiation, can be harvested for heat and power. Unlike conductive and convective forms of heat transfer, thermal radiation – arriving within a narrow-angle i.e. coming from a source much smaller than its distance – can be concentrated in a small spot by using reflecting mirrors, which is exploited in concentrating solar power generation or a burning glass. For example, the sunlight reflected from mirrors heats the PS10 solar power tower and during the day it can heat water to 285 °C (545 °F).
The reachable temperature at the target is limited by the temperature of the hot source of radiation. (T4-law lets the reverse flow of radiation back to the source rise.) The (on its surface) somewhat 4000 K hot sun allows to reach coarsely 3000 K (or 3000 °C, which is about 3273 K) at a small probe in the focus spot of a big concave, concentrating mirror of the Mont-Louis Solar Furnace in France.
The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases and clouds, and is re-radiated in all directions, resulting in a reduction in the amount of thermal radiation reaching space relative to what would reach space in the absence of absorbing materials. This reduction in outgoing radiation leads to a rise in the temperature of the surface and troposphere until the rate of outgoing radiation again equals the rate at which heat arrives from the Sun.
it receives—it is "heated" from below only, but radiates heat in two directions. With another application of the Stefan - Boltzmann law , then, we know that:
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