# Greenhouse effect

70 to 75% of the short-wave radiation (red) emitted by the sun reaches the earth's surface through the atmosphere, which heats up and emits long-wave infrared radiation (blue), the radiation of which into space is hindered by greenhouse gases. Three radiation curves of infrared radiation from bodies between −63 ° C and +37 ° C (violet, blue, black) are shown. The graphics below show which greenhouse gases absorb which parts of the spectrum.

The greenhouse effect is the effect of greenhouse gases in an atmosphere on the temperature of the planet's surface, such as that of the earth. It causes a temperature increase there. The effect arises from the fact that the atmosphere is largely transparent for the short-wave radiation arriving from the sun , but not very transparent for the long-wave infrared radiation emitted by the warm earth's surface and the warmed air .

The analogy between the atmospheric greenhouse effect and a greenhouse has in common that light penetrates the system almost unhindered, while the resulting heat can leave the system less easily. The more the heat flow to the outside is insulated, the higher the temperature rises inside until a balance is reached between converted light energy and heat loss. The mechanisms are different: In the greenhouse, the warm air rising from the floor cannot escape through the glass walls. As a result, the air temperature rises until the heated glass walls release the corresponding heat output to the environment. In the atmosphere, on the other hand, the effect is based on thermal radiation and backscattering from greenhouse gases.

## Research history

### discovery

The greenhouse effect was discovered in 1824 by the French mathematician and physicist Joseph Fourier , combined with the assumption that the earth's atmosphere has insulating properties that prevent part of the incoming thermal radiation from being reflected into space. Building on this, the British naturalist John Tyndall was able to identify some of the gases responsible for the greenhouse effect such as water vapor and carbon dioxide by means of precise measurements in 1862 . In a publication published in 1896, the Swedish physicist and chemist Svante Arrhenius (1859–1927) succeeded in describing the atmospheric greenhouse effect more precisely for the first time , taking into account the ice-albedo feedback . The first proof of the increase in the atmospheric carbon dioxide concentration and thus the anthropogenic greenhouse effect was made in 1958 by Charles D. Keeling . A large number of measuring stations for carbon dioxide were set up on Keeling's initiative; the most famous is on the Mauna Loa in Hawaii . In addition to a global network of stations, there are several earth observation satellites in operation or in the planning stage, whose task, among other things, is to collect data on greenhouse gas concentrations, radiation levels, cloud formation or aerosol distribution .

### Historical course

Since the beginning of the industrial age , additional greenhouse gas shares have been released in the atmosphere from combustion processes and agriculture: carbon dioxide , methane , nitrous oxide and the indirectly caused formation of tropospheric ozone . This increase is called the anthropogenic greenhouse effect and is the reason for the global warming that has occurred since the beginning of the industrial age and has continued to increase in the 21st century . Several components of the greenhouse effect have now been verified by measurements, such as the increase in radiative forcing due to anthropogenic greenhouse gas emissions, as well as the assumption published in 1908 that the tropopause shifts upwards with increasing CO 2 concentration. The current level of carbon dioxide is the highest in at least 800,000 years. According to paleoclimatological analyzes , no significantly higher CO 2 values occurred during the last 14 million years (since the climatic optimum of the Middle Miocene ) .

### Possible developments

The most important greenhouse gases responsible for the greenhouse effect on earth today are water vapor (share 62%), followed by carbon dioxide (share 22%). Global warming also increases z. B. through the water vapor feedback or the decrease in CO 2 storage in the warmer ocean, the concentration of these greenhouse gases further. It is discussed again and again whether these positive feedbacks in the climate system can in principle set in motion a galloping greenhouse effect , which in the past must also have taken place on the planet Venus, for example . Even without a completely destabilizing feedback, one or more tipping points in the Earth's climate system can easily be exceeded as a result of the warming , from which the climate levels off to a new state of equilibrium with rising sea ​​levels and a significant decrease in biodiversity . Such a development would seriously change the image of the earth, above all due to the associated shift in climate and vegetation zones and the extensive melting of the West Antarctic and Greenland ice sheets .

## Physical mode of action

Sankey diagram of the energy balance of the earth's atmosphere: the essential energy flows

Fundamental to the physical understanding of the temperature of the earth is its radiation balance . Energy in the form of electromagnetic radiation radiates from the sun towards the earth. From this, the earth receives an output of 1367 watts per square meter on the cross-sectional area of ​​the day side - about that of a hotplate. The matter that the radiation hits reflects back around 30% of it directly in the case of Earth. The rest of the absorbed part heats the matter until it in turn emits the same amount of heat output. Globally, the earth radiates about the same amount of electromagnetic energy back into space as it receives on average from the sun.

### Mean equilibrium temperature

The mean equilibrium temperature that is established on earth can first be calculated with the simplified assumption that there is no atmosphere: In this case, it would be −18 ° C in the global, daily and seasonal mean. Only at this mean temperature is there an equilibrium in which, on average, just as much thermal radiation is given off to the −270 ° C cold universe as the radiation energy from the sun is absorbed.

If there is an atmosphere, the same effective temperature of −18 ° C must also prevail on its outside so that the radiation equilibrium can exist. From space, thermal images of the earth would also confirm this mean temperature of −18 ° C. However, a significantly higher mean temperature of +14 ° C is measured below the atmosphere on the earth's surface. The difference of 32 ° C is attributed to the greenhouse effect.

#### Comparison with other planets

Comparisons with other planets or calculations of idealized planetary models illustrate the effects of the greenhouse effect.

An example without any atmosphere can be found at the moon . It receives the same radiation power per area as the earth and has an average surface temperature of −55 ° C. It is lower than the expected −18 ° C on earth, as the moon can radiate heat for half a month on the shadow side, while the temperature on the sunny side saturates.

There is a huge difference in our neighboring planet Venus : Instead of the calculated -46 ° C of the radiation equilibrium, an average of 464 ° C was actually measured under the dense and almost pure CO 2 atmosphere on the planet's surface. The cause is very clear here: the greenhouse effect.

The most common wavelength of the photons of the sun light are around 500 nm. This corresponds to green light, wherein the sum of all the visible rays of the sun is perceived as white light. From this radiation maximum one can infer the surface temperature of the sun: about 5600 ° C or 5900 K. The same applies to thermal radiation , which is radiated from heated objects in the form of electromagnetic waves at terrestrial temperatures and whose most frequent wavelength is around 10,000 nm ( infrared radiation ). Wien's law of displacement describes the crucial connection : the lower the temperature of a radiator, the greater the wavelength of the radiation it emits. Below the maximum, the spectrum tends towards long waves, so that half of the sunlight also consists of infrared radiation.

### Mechanism of the greenhouse effect

In the spectral range of visible sunlight, the earth's air envelope (like glass panes in a greenhouse) only absorbs little radiation - one speaks of high transparency . The radiation can therefore penetrate the greenhouse almost unhindered. Only the infrared part can heat parts of the atmosphere directly. The matter inside the greenhouse, i.e. essentially the earth's surface, absorbs a large part of the photons and warms up as a result. The heat is radiated from there directly or indirectly through the heated air upwards again electromagnetically.

Since most of the energy radiated back from the earth consists only of infrared radiation, the greenhouse effect becomes noticeable: the atmosphere is less permeable to infrared radiation due to the greenhouse gases . The same applies to the analogue of the glass roof, which stops both thermal radiation and rising warm air. Greenhouse gases play a decisive role in the atmosphere . Due to the asymmetry of the charge distribution, they have the property of absorbing energy from the thermal radiation very efficiently from the electromagnetic field. The energy is used to stimulate internal vibrations, in which negative and positive charges oscillate against each other or rotate around each other. The individual molecules mediate a two-way exchange of energy between the thermal radiation and the surrounding gases. Net energy is transported from the earth's surface to the greenhouse gas and finally to space. The thermal fluctuations, which also radiate energy against the temperature gradient towards the earth, reduce the effective cooling capacity of the surface, which results in a higher equilibrium temperature.

## Greenhouse gases

Short-wave radiation from the sun hits the atmosphere and the earth's surface. Long-wave radiation is emitted from the earth's surface and almost completely absorbed in the atmosphere. In thermal equilibrium, half of the absorbed energy in the atmosphere is radiated towards earth and half towards space. The numbers indicate the power of the radiation in watts / square meter for the period 2000-2004. The earth is currently not in thermal equilibrium. It heats up due to the increased concentration of greenhouse gases as a result of human activity. The irradiation of 341.3 W / m² contrasts with a radiation of 340.4 W / m². The representation is a Sankey diagram .
Permeability of the atmosphere to electromagnetic radiation of different wavelengths. The yellow area is called the Atmospheric Window; there the atmosphere is permeable to electromagnetic waves of the infrared range.

In the earth's atmosphere, greenhouse gases such as water vapor , carbon dioxide , methane and ozone have had a greenhouse effect that has had a decisive influence on the history of the climate in the past and on today's climate . The greenhouse gases are permissible for the short-wave portion of solar radiation , whereas long-wave heat radiation is absorbed and emitted in different wavelengths depending on the greenhouse gas.

The molecules of a greenhouse gas are physically characterized by a certain asymmetry. The center of gravity of all positive charges has to be somewhat distant from that of the negative charges, which corresponds to a dipole moment . As a result, an external alternating electric field can periodically deflect parts of the molecule in opposite directions and thus stimulate them to oscillate. The amplitude of this oscillation becomes particularly strong when the resonance frequency agrees well with the excitation frequency, which is the case with greenhouse gases and thermal radiation. The molecular vibration absorbs energy and radiates it again in different directions, partly back towards earth. Symmetrical molecules like O 2 and N 2 do not have such a dipole moment and are therefore almost completely transparent to thermal radiation.

The largest part of the greenhouse effect is caused by water vapor in the atmosphere with a share of approx. 36–70% (without taking into account the effects of clouds) . Carbon dioxide in the earth's atmosphere contributes around 9–26% to the greenhouse effect, methane around 4–9% and tropospheric ozone around 3–7%. The climate impact of ozone differs greatly between stratospheric ozone and tropospheric ozone. Stratospheric ozone absorbs the short-wave UV component in the incident sunlight and thus has a cooling effect (based on the earth's surface). Tropospheric ozone is created from the products of anthropogenic combustion processes and, like other greenhouse gases, has a warming effect due to its IR absorption.

An exact percentage of the effect of the individual greenhouse gases on the greenhouse effect cannot be given, as the influence of the individual gases varies depending on the degree of latitude and mixing (the higher percentage values ​​indicate the approximate proportion of the gas itself, the lower values ​​result from the mixtures of the Gases).

With the great mass of the earth, heat storage plays a significant role, which can be seen from the fact that the warmest time on earth in summer only occurs after the highest point of the sun (the " solstice "). The highest point of the sun is on June 21st in the northern hemisphere and on December 21st in the southern hemisphere. Because of this large storage effect, the energy balances in the atmosphere are always calculated using the mean value over the entire earth's surface.

## Energy balance

The heat processes on the earth's surface and in the atmosphere are driven by the sun. The strength of solar radiation in the earth's orbit is known as the solar constant and has a value of around 1367 W / m². Depending on the distance from the earth and solar activity, this fluctuates between 1325 W / m² and 1420 W / m²; In the graphic on the right, a solar constant of 1365.2 W / m² was used.

So-called energy balances are calculated with an average value of the irradiation on the earth's surface: The earth receives solar radiation on the area of ​​the earth's cross-section and has a surface of . These two areas have a ratio of 1: 4; H. averaged over the entire globe, radiation of 341.3 W / m² reaches the surface. Clouds, air and soil (especially ice and snow, see albedo ) reflect around 30% of the radiated solar energy back into space - that is around 102 W / m². The remaining 70% is absorbed (78 W / m² from the atmosphere, 161 W / m² from the ground) - that is a total of 239 W / m². If the earth were only exposed to radiation of 239 W / m², the earth's surface would assume an average temperature of about −18 ° C if the heat were evenly distributed over the earth. ${\ displaystyle \ pi R ^ {2}}$${\ displaystyle 4 \ pi R ^ {2}}$

Because according to the Stefan-Boltzmann law :

${\ displaystyle P = A \ sigma T ^ {4}}$,

with  power,  area, Stefan-Boltzmann constant . The earth has an albedo of 0.3, i.e. H. 30% of the incident radiation is reflected. So the effective radiation is and the equation for the radiation equilibrium of the earth without atmosphere becomes: ${\ displaystyle P =}$${\ displaystyle A =}$${\ displaystyle \ sigma =}$${\ displaystyle P _ {\ mathrm {W}}}$${\ displaystyle (1-0 {,} 3) \ cdot P}$

${\ displaystyle (1-0 {,} 3) \ cdot P = A \ sigma T ^ {4}}$.

Moved after results ${\ displaystyle T}$

${\ displaystyle T = {\ sqrt [{4}] {\ frac {0 {,} 7 \ ​​cdot P} {\ sigma A}}}}$

and with the parameters of the planet earth:

${\ displaystyle {\ sqrt [{4}] {\ frac {0 {,} 7 \ ​​cdot 342 \, \ mathrm {W}} {\ sigma \ cdot \ mathrm {m} ^ {2}}}} = 254 {,} 9 \, \ mathrm {K} = -18 ^ {\ circ} \ mathrm {C}}$.

But there is further radiation from the heated greenhouse gases with 333 W / m², the so-called atmospheric counter-radiation . The earth's surface absorbs a total of 161 W / m² + 333 W / m² = 494 W / m² - and these are emitted in several ways at the actual mean earth surface temperature of +14 ° C. Part of it is given off by radiation, which is again described by Planck's law of radiation .

Water vapor distribution in the earth's atmosphere. Specification of the height of the water column in the event of condensation in centimeters

Due to the radiation into space from the atmosphere with 169 W / m², the radiation from the clouds with 30 W / m², the 40 W / m² from the earth's surface and the albedo proportion of 102 W / m², this is roughly equal to the mean irradiation of 342 W / m², d. That is, radiation is roughly the same as radiation. This can also be seen in the fact that the temperature of the earth changes only slowly - from which it necessarily follows that the earth releases the absorbed solar energy again - but because of the low earth temperature, the energy is mainly emitted as long-wave infrared radiation ( Wien's law of displacement ).

The heat flow from the earth's mantle is practically irrelevant. It is about 0.06 W / m².

The heat flow ( power ) from fuels used by humans is even lower and is 0.026 watts per square meter. It is calculated from the world energy consumption (in 2004) of 432 exajoules and the size of the earth's surface of around 510 million km².

In summary: The reflection from the atmosphere to the earth leads to additional warming of the earth's surface. This explains the average measured global temperature of 14 ° C instead of the theoretically calculated equilibrium temperature without atmosphere of −18 ° C.

the atmosphere
Remainder of the
greenhouse
effect
as until now 100%
without H 2 O, CO 2 , O 3 050%
without H 2 O 064%
without clouds 086%
without CO 2 088%
without O 3 097%
without all greenhouse gases 000%
Source: Ramanathan and Coakley (1978) p. a.

The height distribution from where the thermal radiation reaches the earth's surface is also important. Only the share of radiation from low altitudes is directly significant for the greenhouse effect, because only this radiation reaches the ground without being absorbed again by the greenhouse gases (see next paragraph). The “low” is very wavelength-dependent, because the length after which the radiation is absorbed again ( absorption length ) depends on the wavelength and the concentration. If the absorption length is greater than the thickness of the atmosphere, the atmosphere is almost transparent at these wavelengths. Since the strength of a radiation depends on the temperature of the source, the radiation strength increases when the absorption length becomes shorter: because of the decrease in temperature with altitude, the mean temperature increases over the shorter absorption length. This means that the atmospheric counter-radiation in a wavelength range can become even stronger with increasing amounts of greenhouse gases, even if the atmosphere in this wavelength range is already as good as opaque.

The temperature profile up to an altitude of approx. 11 km is practically only adiabatic, the energy lost through the emission of greenhouse gases is replaced by convection and radiation absorption. The absorbed radiation comes from various sources:

• Solar radiation (very low proportion)
• Radiation from the earth's surface

The proportion of long-wave thermal radiation emitted by greenhouse gases such as

and other gases is called the dry greenhouse effect . The inclusion of water vapor leads to the moist greenhouse effect . About 62% of the greenhouse effect is caused by water vapor and about 22% by carbon dioxide.

The complete combustion of ( anthropogenic ) hydrocarbons with the empirical formula C x H y results in x molecules of CO 2 and y / 2 molecules of H 2 O, both of which contribute to the global greenhouse effect.

The temperature profile of the atmosphere as a function of the pressure altitude (earth's surface = 1.013 bar) - the tropopause is best approximated with an isentropic exponent of 0.19.

The temperature profile as a function of the pressure height is interesting (the highest pressure on the earth's surface is 1.013 bar). The pressure decreases upwards because the gas mass is lower. The same pressure changes correspond to the same number of gas particles. In the troposphere, the temperature curve is best described by an adiabatic with the exponent 0.19. Above the troposphere, the gas mass is low and there is no longer an adiabatic course. The peak of the real atmosphere at low pressures is caused by the UV absorption of oxygen (ozone formation and decomposition). The existence of the troposphere can also be explained by the curvature of the curve in the troposphere: If the curve were a straight line, the energy absorbed by the greenhouse gases would on average be equal to the energy emitted - but because of the curvature and its type, the energy emitted is greater than the absorbed energy, so the air is cooled and sinks down. This sets in motion a vertical circulation which, according to the gas laws with constant heat content (the radiation loss is small compared to the heat content), leads to an adiabatic course.

The importance of the global greenhouse effect can therefore also be seen in the extremely different surface temperatures of the planets Venus , Earth and Mars . These temperature differences depend not only on the distance to the sun, but above all on the different atmospheres (due to various causes).

## Anthropogenic greenhouse effect

How the greenhouse effect works. Explanatory video from Terra X

The anthropogenic greenhouse effect is the intensification of the natural greenhouse effect through human activities. This mainly results from the release of various greenhouse gases such as carbon dioxide (CO 2 ), methane (CH 4 ), nitrous oxide (N 2 O) and tropospheric ozone (O 3 ). Its consequence is global warming , i. H. an increase in the global average temperature since the beginning of industrialization, or particularly strongly in the last 30 years, by around 1 degree Celsius. In the meantime, this effect is not only understood theoretically. B. be measured with satellites that record the energy radiation on the earth and the energy radiated from the earth. Satellite data show that the heat radiation from the earth into space decreases with the increasing concentration of greenhouse gases, as is expected with an increased greenhouse gas concentration. The decline takes place in the wavelength range of greenhouse gases such as carbon dioxide, methane and ozone, the proportion of which in the atmosphere increases due to anthropogenic emissions.

CO 2 concentration in the atmosphere: The last 100 million years and a prognosis for the next 300 years are shown.
Temperature reconstructions and instrumentally measured temperatures for the past 2000 years.

### speed

In contrast to the natural climate changes that take place on geological time scales, anthropogenic climate change occurs in an extremely short time. According to more recent studies, the currently observed release of carbon dioxide occurs faster than in all known warming phases of the last 66 million years. The same is true for the rate of temperature change currently observed. The global warming from the last ice age to the present warm period was a warming of about one degree per 1000 years. The increase in greenhouse gas concentrations over the past 100 years has led to an increase in the global average temperature of around 0.85 degrees. In a “business as usual” scenario ( representative concentration path RCP 8.5), the most likely future temperature increase of approx. 5 ° C by 2100 would even occur at a rate of 5 ° C / 100 years.

### mechanism

The relationship between CO 2 concentration and instant radiative forcing is logarithmic for CO 2 concentrations up to about 3000 ppm.

As early as 1856, Eunice Foote investigated the greenhouse effect of various gases. As a woman, Foote was not allowed to present her results to the " American Association for the Advancement of Science ", but she managed to publish her research in the scientific journal " The American Journal of Science and Arts ". Foote concluded from her data: "If, as some assume, at some point in the history of the earth a greater proportion of it [of carbon dioxide] was added to the air than it is today, then this inevitably should have resulted in an increased temperature."

## Criticism and misunderstandings

The results of climate research on the anthropogenic greenhouse effect and global warming can hardly be checked by individuals and laypeople and therefore appear abstract. At the same time, the effect in the atmosphere is based on abstract physical processes, which are not known from everyday experience, despite the clear analogue to the glass house. The supposedly common sense can be deceiving here and leads some people to skepticism or even to deny globally recognized research results (see also climate denial ).

The criticism is usually based on misunderstandings and misjudgments. For example, the very low concentration of CO 2 in the atmosphere is mistaken for a weak effect. The total amount of CO 2 molecules present in the atmosphere is the only decisive factor for backscattering, while neutral gases are penetrated by radiation almost unhindered, like a vacuum. Without the other gases, the pure CO 2 in the atmosphere would correspond to a 3-meter-thick layer under normal pressure, one meter of which has been added since industrialization. Although the CO 2 is also thermally influenced by shocks when it is mixed with the neutral gases, only a limited number of shocks can take place per unit of time, so that the resulting cooling capacity of the ambient air does not increase arbitrarily with increasing dilution.

Some skeptics of the greenhouse effect argue that greenhouse gases that radiate heat towards the earth's surface (169 W / m²) would conduct energy from a cooler body (around −40 ° C) to a warmer body (earth's surface around +14 ° C), which supposedly contradicts the second law of thermodynamics . In fact, even with a higher greenhouse temperature, more energy flows from the warmed surface of the earth to the cooler greenhouse gas. The thermal exchange of radiation by means of infrared photons, however, basically takes place in both directions. This can be seen from the physical interpretation of the temperature , which describes in a system which energy its degrees of freedom absorb on average. In the case of molecules, these are the vibration excitations and speed components. However, even at a balanced temperature, this energy is not evenly distributed microscopically, but is constantly superimposed to form random fluctuations according to the Boltzmann statistics . If you apply the term temperature to individual molecules, you will find a very specific number of molecules that are warmer than the earth's surface even in the cold greenhouse gas. These pass their heat energy on to the colder atoms on the earth's surface with a certain probability, so that an energy flow of 169 W / m² is created. The opposite case is much more common, however, so that according to the II. Law of thermodynamics, net more energy is transported from the warm earth's surface to the colder greenhouse gases. Compared to the full temperature gradient to the −270 ° C cold universe, the effective cooling capacity is significantly reduced by the greenhouse gas, so that an increased temperature in the greenhouse earth is established in equilibrium.

## Greenhouse effect in the glass house

→ Main article: Glass house effect

Tropical plants can thrive in the greenhouse in temperate latitudes.

For more than 100 years it has been known that the warming of a greenhouse is for the most part not a result of the fact that, as with the atmospheric greenhouse effect, the thermal radiation penetrates more poorly than the solar radiation. The following happens behind glass: The substances in the room absorb solar radiation and heat up, and consequently also the indoor air, above the level of the ambient temperature. The glass prevents cooling by preventing convection . To demarcate both effects, the effect in the greenhouse is sometimes called greenhouse effect referred to. In the English-speaking world and in international specialist literature, the term greenhouse effect is used throughout , but almost always in relation to the atmospheric greenhouse effect.

In addition to using the effect in under-glass cultures and greenhouses , the passive use of the sun also saves heating energy in architecture . With large glass fronts and winter gardens facing south , the building mass is warmed by the sun's rays. In the case of well-insulated low-energy and passive houses , in particular, the glass surfaces need to be shaded at lunchtime so that the buildings do not overheat. This effect also occurs in a car parked in the sun.

## literature

Commons : greenhouse effect  - collection of images, videos and audio files
Wiktionary: greenhouse effect  - explanations of meanings, word origins, synonyms, translations

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33. ^ Eunice Foote: Circumstances affecting the heat of the Sun's rays. In: American Journal of Science and Arts, 2ndSeries, v. XXII / no. LXVI, November 1856, p. 382-383. November 1, 1856, accessed January 17, 2020 .
34. So little CO2 has such a big effect , by Mathias Tertilt, October 26, 2018, at www.quarks.de.
35. CO 2 layer thickness = air pressure / acceleration due to gravity * CO2 mass fraction / CO2 mass density = 1bar / 9.8 m / s² * 0.06% / 1.98kg / m³ = 3.09 m. Before industrialization: 0.04% CO2.
36. See e.g. B. Mojib Latif , Are we getting the climate out of sync? Background and forecasts. Fischer-Taschenbuch-Verlag, Frankfurt 2007, ISBN 978-3-596-17276-4 ., See chapter The public discussion .
37. ^ G. Thomas Farmer, John Cook: Climate Change Science. A modern synthesis. Volume 1 - The Physical Climate. Dordrecht 2013, p. 21.
38. For further explanation see also Can a duvet violate the second law of thermodynamics? by Stefan Rahmstorf , 20 Sep 2016, at scilogs.spektrum.de.
39. For the basics of physics see z. B. one of the standard textbooks for studying physics: D. Meschede, Gerthsen Physik , 23rd revised edition, 2006, ISBN 3-540-25421-8 , Springer-Verlag, especially chapters 11.2 Radiation laws and 5.5.5 The 2nd main clause of Thermodynamics .