Climate change mitigation

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The concept of the black body is an idealization, as perfect black bodies do not exist in nature. Black-body radiation has a characteristic, continuous frequency spectrum that depends only on the body's temperature, [9] called the Planck spectrum or Planck's law.

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In developing countries, institutions may be insufficiently developed for the collection of emissions fees from a wide variety of sources. According to Mark Z. Another indirect method of encouraging uses of renewable energy, and pursue sustainability and environmental protection, is that of prompting investment in this area through legal means, something that is already being done at national level as well as in the field of international investment.

With the creation of a market for trading carbon dioxide emissions within the Kyoto Protocol, it is likely that London financial markets will be the centre for this potentially highly lucrative business; the New York and Chicago stock markets may have a lower trade volume than expected as long as the US maintains its rejection of the Kyoto. However, emissions trading may delay the phase-out of fossil fuels.

In the north-east United States, a successful cap and trade program has shown potential for this solution. Twenty three multinational corporations have come together in the G8 Climate Change Roundtable , a business group formed at the January World Economic Forum.

On 9 June the Group published a statement [] stating that there was a need to act on climate change and claiming that market-based solutions can help. It called on governments to establish "clear, transparent, and consistent price signals" through "creation of a long-term policy framework" that would include all major producers of greenhouse gases.

The scheme was due to be developed by April but has not yet been completed. Implementation puts into effect climate change mitigation strategies and targets. These can be targets set by international bodies or voluntary action by individuals or institutions.

This is the most important, expensive and least appealing aspect of environmental governance. Implementation requires funding sources but is often beset by disputes over who should provide funds and under what conditions. This is an environmental funding mechanism in the World Bank which is designed to deal with global environmental issues. The GEF funds projects that are agreed to achieve global environmental benefits that are endorsed by governments and screened by one of the GEF's implementing agencies.

There are numerous issues which result in a current perceived lack of implementation. The relationships between many climatic processes can cause large levels of uncertainty as they are not fully understood and can be a barrier to implementation. When information on climate change is held between the large numbers of actors involved it can be highly dispersed, context specific or difficult to access causing fragmentation to be a barrier.

Institutional void is the lack of commonly accepted rules and norms for policy processes to take place, calling into question the legitimacy and efficacy of policy processes. The Short time horizon of policies and politicians often means that climate change policies are not implemented in favour of socially favoured societal issues. Statements are often posed to keep the illusion of political action to prevent or postpone decisions being made. Missing motives and willingness to start adapting is a large barrier as it prevents any implementation.

Despite a perceived lack of occurrence, evidence of implementation is emerging internationally. Some examples of this are the initiation of NAPA's and of joint implementation. Efforts to reduce greenhouse gas emissions by the United States include energy policies which encourage efficiency through programs like Energy Star , Commercial Building Integration , and the Industrial Technologies Program.

In , Transportation Secretary Mary Peters , with White House approval, urged governors and dozens of members of the House of Representatives to block California's first-in-the-nation limits on greenhouse gases from cars and trucks, according to e-mails obtained by Congress.

The Bush administration pressured American scientists to suppress discussion of global warming, according to the testimony of the Union of Concerned Scientists to the Oversight and Government Reform Committee of the US House of Representatives. In the absence of substantial federal action, state governments have adopted emissions-control laws such as the Regional Greenhouse Gas Initiative in the Northeast and the Global Warming Solutions Act of in California.

In order to reconcile economic development with mitigating carbon emissions, developing countries need particular support, both financial and technical. An important point of contention, however, is how overseas development assistance not directly related to climate change mitigation is affected by funds provided to climate change mitigation.

The main point being that there is a conflict between the OECD states budget deficit cuts, the need to help developing countries adapt to develop sustainably and the need to ensure that funding does not come from cutting aid to other important Millennium Development Goals.

However, none of these initiatives suggest a quantitative cap on the emissions from developing countries. This is considered as a particularly difficult policy proposal as the economic growth of developing countries are proportionally reflected in the growth of greenhouse emissions. In an attempt to provide more opportunities for developing countries to adapt clean technologies, UNEP and WTO urged the international community to reduce trade barriers and to conclude the Doha trade round "which includes opening trade in environmental goods and services".

While many of the proposed methods of mitigating global warming require governmental funding, legislation and regulatory action, individuals and businesses can also play a part in the mitigation effort. Environmental groups encourage individual action against global warming , often aimed at the consumer.

Common recommendations include lowering home heating and cooling usage, burning less gasoline, supporting renewable energy sources , buying local products to reduce transportation, turning off unused devices, and various others. A geophysicist at Utrecht University has urged similar institutions to hold the vanguard in voluntary mitigation, suggesting the use of communications technologies such as videoconferencing to reduce their dependence on long-haul flights.

In , climate scientist Kevin Anderson raised concern about the growing effect of rapidly increasing global air transport on the climate in a paper, [] and a presentation, [] suggesting that reversing this trend is necessary to reduce emissions.

Part of the difficulty is that when aviation emissions are made at high altitude, the climate impacts are much greater than otherwise.

Others have been raising the related concerns of the increasing hypermobility of individuals, whether traveling for business or pleasure, involving frequent and often long distance air travel, as well as air shipment of goods.

On 21 June a group of leading airlines , airports , and aerospace manufacturers pledged to work together to reduce the negative environmental impact of aviation , including limiting the impact of air travel on climate change by improving fuel efficiency and reducing carbon dioxide emissions of new aircraft by fifty percent per seat kilometre by from levels.

The group aims to develop a common reporting system for carbon dioxide emissions per aircraft by the end of , and pressed for the early inclusion of aviation in the European Union 's carbon emission trading scheme. Climate change is also a concern for large institutional investors who have a long term time horizon and potentially large exposure to the negative impacts of global warming because of the large geographic footprint of their multi-national holdings.

SRI Socially responsible investing Funds allow investors to invest in funds that meet high ESG environmental, social, governance standards as such funds invest in companies that are aligned with these goals. In some countries, those affected by climate change may be able to sue major producers. Attempts at litigation have been initiated by entire peoples such as Palau [] and the Inuit, [] as well as non-governmental organizations such as the Sierra Club. For a legal action for negligence or similar to succeed, "Plaintiffs This has sometimes been translated to a requirement of a relative risk of at least two.

Besides countries suing one another, there are also cases where people in a country have taken legal steps against their own government. In the Netherlands and Belgium, organisations such as Urgenda [] [] [] and the vzw Klimaatzaak in Belgium [] [] have also sued their governments as they believe their governments aren't meeting the emission reductions they agreed to.

Urgenda have already won their case against the Dutch government. According to a study commissioned by Friends of the Earth , ExxonMobil , and its predecessors caused 4. The group suggested that such studies could form the basis for eventual legal action. In , Exxon received a subpoena.

According to the Washington Post and confirmed by the company, the attorney general of New York, Eric Schneiderman , opened an investigation into the possibility that the company had misled the public and investors about the risks of climate change.

Low carbon investment and ethical banking has been suggested as a tactic to allow consumers to drive a low-carbon transition []. Voluntarily funded, low-carbon investment funds have been suggested as a way to provide revenue for adaptation costs in the post-fossil fuel era []. It is suggested that voluntary donations can be invested, rather than spent, and long-term returns used to pay for adaptation costs.

Environmental organizations organize different actions like Peoples Climate Marches , Divestment from fossil fuels see pages. From Wikipedia, the free encyclopedia. Stabilizing CO 2 emissions at their present level would not stabilize its concentration in the atmosphere. Stabilizing the atmospheric concentration of CO 2 at a constant level would require emissions to be effectively eliminated. Efficient energy use and Energy conservation. Renewable energy , Renewable energy commercialization , and Renewable energy debate.

Some of the world's largest solar power stations: This section needs expansion. You can help by adding to it. Carbon sink and Negative carbon dioxide emission. Deforestation , Reforestation , and Biosequestration. Carbon capture and storage. Carbon dioxide removal , Greenhouse gas remediation , and Carbon sequestration.

Stratospheric aerosol injection climate engineering. Sustainable architecture and Green building. Climate change and agriculture. Economics of climate change mitigation. Politics of global warming. Emission trading or carbon tax under consideration. List of countries by carbon dioxide emissions. Climate change in the United States.

Business action on climate change. A Compendium of Data on Global Change. Emergent risks and key vulnerabilities archived July 8 , pp. Residential and commercial buildings", Climate Change Mitigation of Climate Change , Sec 6. Emergent risks and key vulnerabilities archived July 8 , p.

United Nations , p. Document available in UN languages and text format. Retrieved 12 December Introductory Chapter , p. Nordhaus , p. Global Climate Projections" , Climate Change Archived from the original on Philosophical Transactions of the Royal Society A.

Real clothes for the Emperor: Facing the challenges of climate change. The Cabot annual lecture, Univ. Video proceedings Archived at the Wayback Machine. Cornell, Sarah; Crucifix, Michel; F.

Donges, Jonathan; Fetzer,, Ingo; J. Proceedings of the National Academy of Sciences. Retrieved 21 August Pacific Northwest National Laboratory. Archived from the original PDF on Nature Reports Climate Change. Retrieved 2 January Mitigation , Sec 2. Much less frequently mentioned are, however, the ultimate drivers of those immediate causes of biotic destruction, namely, human overpopulation and continued population growth, and overconsumption, especially by the rich.

These drivers, all of which trace to the fiction that perpetual growth can occur on a finite planet, are themselves increasing rapidly. Retrieved 15 December The overarching driver of species extinction is human population growth and increasing per capita consumption.

Sustainable Development and Equity". California Air Resources Board. The pivotal role of electricity" PDF. Stern Review on the Economics of Climate Change. IEA urges governments to adopt effective policies based on key design principles to accelerate the exploitation of the large potential for renewable energy 29 September Clean Energy Trends , Clean Edge , p. Global Trends in Sustainable Energy Investment Worldwide electricity production from renewable energy sources.

Retrieved 28 March Reliability, system and transmission costs, and policies" PDF. Sticking to "Promise of Clean Energy " ". Japan crisis puts global nuclear expansion in doubt". Energy supply", Climate Change Bulletin of the Atomic Scientists. A typical MWe light water reactor will generate directly and indirectly — m3 low- and intermediate-level waste per year.

It will also discharge about 20 m3 27 tonnes of used fuel per year, which corresponds to a 75 m3 disposal volume following encapsulation if it is treated as waste. Where that used fuel is reprocessed, only 3 m3 of vitrified waste glass is produced, which is equivalent to a 28 m3 disposal volume following placement in a disposal canister.

Annals of Nuclear Energy. Archived from the original on March 3, Journal of Industrial Ecology. Technology — specific cost and performance parameters" PDF.

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Lenton, Hans Joachim Schellnhuber. The limits to global-warming mitigation by terrestrial carbon removal. Earth's Future , ; https: Retrieved 2 November Retrieved 30 July Retrieved 7 August The economic case for securing indigenous land rights in the Amazon".

Climate benefits, tenure costs: The economic case for securing indigenous land rights in the Amazon PDF. Retrieved 25 August Retrieved 18 July New Scientist, August 5, Retrieved on August 18, , from https: Retrieved May 5, Archived from the original on June 25, Retrieved May 11, Retrieved 4 February Chapin III 7 September Retrieved 2 September Capture and Store it?

Mitigation from a cross-sectoral perspective. Mitigation in the short and medium term until Technical status, future directions, and potential responses. A Greenhouse Gas Showdown". The physical science basis. The Physical Science Basis. Retrieved 8 September The Global Rail Revival". Home and the environment". The Journal of Record. Retrieved 2 March Painting the Town White — and Green. Massachusetts Institute of Technology. Policy Implications of Greenhouse Warming: Mitigation, Adaptation, and the Science Base.

Sources of Greenhouse Gas Emissions". Lang 13 July Retrieved 8 July Thanos Papanicolaou, Kenneth M. Journal of Geophysical Research: The New York Times. Retrieved 21 Oct Perspectives on climate change and sustainability. Impacts, Adaptation and Vulnerability. Equity and Social Considerations.

Economic and Social Dimensions of Climate Change. If you can't stand the heat" , The Economist , special report on "Climate change", 28 November , page World Development Report Development and Climate Change. The energy and climate challenge", in van Vuuren, D. Summary available from the Climate Emergency Institute. Report of the Conference of the Parties on its sixteenth session, held in Cancun from 29 November to 10 December UN Office [ permanent dead link ]. Guardian News and Media Limited.

Limits to Mitigation, in: Renegotiating the global climate stabilization target. Nature Climate Change, 4, , pp. Beyond 'dangerous' climate change: Discussion and conclusions," in: By Adam Corner, 13 Dec. How science is telling us all to revolt. By Naomi Klein, 29 Oct. Going beyond dangerous — Brutal numbers, tenuous hope, or cognitive dissonance? Video of presentation made to UK Dept. Programme, abstracts, presentations, and audio recordings. Archived at the Wayback Machine.

Policies, instruments, and co-operative arrangements. Arbitration and Negotiation Issues". Journal of World Energy Law and Business. A Evaluating the Global Environment Facility: A goodwill gesture or a serious attempt to deliver global benefits? Policy Research Working Paper Series. Y Climate adaptation planning in practice: Archived copy as title link last visited Jan. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

Climate Change and Aviation: Issues, Challenges and Solutions, London. Chapter 6 Archived at the Wayback Machine. Exxonmobil's contribution to global warming revealed. Friends of the Earth Trust. Retrieved May 25, Retrieved December 29, Retrieved 17 December Global warming and climate change.

Brightness temperature Effective temperature Geologic record Hiatus Historical climatology Instrumental record Paleoclimatology Paleotempestology Proxy data Record of the past 1, years Satellite measurements. Attribution of recent climate change Aviation Biofuel Black carbon Carbon dioxide Deforestation Earth's energy budget Earth's radiation balance Ecocide Fossil fuel Global dimming Global warming potential Greenhouse effect Infrared window Greenhouse gases Halocarbons Land use, land-use change, and forestry Radiative forcing Tropospheric ozone Urban heat island.

Environmental ethics Media coverage of climate change Public opinion on climate change Popular culture Scientific opinion on climate change Scientists who disagree with the mainstream assessment Climate change denial Global warming conspiracy theory.

Potential effects and issues. Abrupt climate change Anoxic event Arctic dipole anomaly Arctic haze Arctic methane emissions Climate change and agriculture Climate change and ecosystems Climate change and gender Climate change and poverty Drought Economics of global warming Effects on plant biodiversity Effects on health Effects on humans Effects on marine mammals Environmental migrant Extinction risk from global warming Fisheries and climate change Forest dieback Industry and society Iris hypothesis Megadrought Ocean acidification Ozone depletion Physical impacts Polar stratospheric cloud Regime shift Retreat of glaciers since Runaway climate change Sea level rise Season creep Shutdown of thermohaline circulation.

Carbon capture and storage Efficient energy use Low-carbon economy Nuclear power Renewable energy. Individual action on climate change Simple living. Carbon dioxide removal Carbon sink Climate action Climate Action Plan Climate change mitigation scenarios Climate engineering Individual and political action on climate change Reducing emissions from deforestation and forest degradation Reforestation Urban reforestation.

Damming glacial lakes Desalination Drought tolerance Irrigation investment Rainwater storage Sustainable development Weather modification. Avoiding dangerous climate change Land allocation decision support system.

Glossary Index Climate change Global warming Portal. Anthropocene Earth system governance Ecological modernization Environmental governance Environmentalism Global catastrophic risk Human impact on the environment Planetary boundaries Social sustainability Stewardship Sustainable development. Anthropization Anti-consumerism Earth Overshoot Day Ecological footprint Ethical Over-consumption Simple living Sustainability advertising Sustainability brand Sustainability marketing myopia Sustainable Systemic change resistance Tragedy of the commons.

Birth control Family planning Control Overpopulation Zero growth. Conservation Crisis Efficiency Footprint Reclaimed. Sustainability accounting Sustainability measurement Sustainability metrics and indices Sustainability reporting Standards and certification Sustainable yield.

Global warming portal Energy portal. Retrieved from " https: Climate change mitigation Climate change policy. Uses editors parameter Webarchive template wayback links Pages using web citations with no URL All articles with dead external links Articles with dead external links from September Articles with permanently dead external links CS1 maint: Archived copy as title CS1 maint: The causal effect of thermodynamic absorption on thermodynamic spontaneous emission is not direct, but is only indirect as it affects the internal state of the body.

This means that at thermodynamic equilibrium the amount of every wavelength in every direction of thermal radiation emitted by a body at temperature T , black or not, is equal to the corresponding amount that the body absorbs because it is surrounded by light at temperature T. When the body is black, the absorption is obvious: This means that the black-body curve is the amount of light energy emitted by a black body, which justifies the name.

This is the condition for the applicability of Kirchhoff's law of thermal radiation: In the laboratory, black-body radiation is approximated by the radiation from a small hole in a large cavity, a hohlraum , in an entirely opaque body that is only partly reflective, that is maintained at a constant temperature.

This technique leads to the alternative term cavity radiation. Any light entering the hole would have to reflect off the walls of the cavity multiple times before it escaped, in which process it is nearly certain to be absorbed. Absorption occurs regardless of the wavelength of the radiation entering as long as it is small compared to the hole. The hole, then, is a close approximation of a theoretical black body and, if the cavity is heated, the spectrum of the hole's radiation i.

The radiance or observed intensity is not a function of direction. Therefore, a black body is a perfect Lambertian radiator. Real objects never behave as full-ideal black bodies, and instead the emitted radiation at a given frequency is a fraction of what the ideal emission would be. The emissivity of a material specifies how well a real body radiates energy as compared with a black body. This emissivity depends on factors such as temperature, emission angle, and wavelength. However, it is typical in engineering to assume that a surface's spectral emissivity and absorptivity do not depend on wavelength, so that the emissivity is a constant.

This is known as the gray body assumption. With non-black surfaces, the deviations from ideal black-body behavior are determined by both the surface structure, such as roughness or granularity, and the chemical composition. On a "per wavelength" basis, real objects in states of local thermodynamic equilibrium still follow Kirchhoff's Law: In astronomy , objects such as stars are frequently regarded as black bodies, though this is often a poor approximation. An almost perfect black-body spectrum is exhibited by the cosmic microwave background radiation.

Hawking radiation is the hypothetical black-body radiation emitted by black holes , at a temperature that depends on the mass, charge, and spin of the hole. If this prediction is correct, black holes will very gradually shrink and evaporate over time as they lose mass by the emission of photons and other particles.

A black body radiates energy at all frequencies, but its intensity rapidly tends to zero at high frequencies short wavelengths. According to the Classical Theory of Radiation, if each Fourier mode of the equilibrium radiation in an otherwise empty cavity with perfectly reflective walls is considered as a degree of freedom capable of exchanging energy, then, according to the equipartition theorem of classical physics, there would be an equal amount of energy in each mode. Since there are an infinite number of modes this implies infinite heat capacity infinite energy at any non-zero temperature , as well as an unphysical spectrum of emitted radiation that grows without bound with increasing frequency, a problem known as the ultraviolet catastrophe.

In the higher wavelengths this effect is not that noticeable As hv is very small, allowing nhv to be almost infinitesimally small and thus a very huge number of vibrational modes. But in the lower wavelengths the classical theory predicted the energy emitted as Infinity In the ultraviolet range; hence ultraviolet catastrophe. As all possible vibrational modes including those having energy less than hv were considered, the energy added up to infinity. It even predicted that all bodies would emit maximum energy in the ultraviolet range, clearly against the experimental data which showed a different peak wavelength at different temperatures.

Instead, in quantum theory the numbers of the modes are quantized, cutting off the spectrum at high frequency in agreement with experimental observation and resolving the catastrophe. The modes definitely cannot have more energy than the thermal energy of the substance itself, and by quantization infinitesimally small modes too were not allowed.

Thus for lower wavelengths very few modes were allowed, supporting the data that energy emitted falls on further decreasing the wavelength below the peak wavelength. Notice that there are two factors responsible for the shape of the graph. Firstly, higher wavelengths have larger number of modes associated with them. Secondly, lower wavelengths have more energy associated per mode.

The study of the laws of black bodies and the failure of classical physics to describe them helped establish the foundations of quantum mechanics. Calculating the black-body curve was a major challenge in theoretical physics during the late nineteenth century. The problem was solved in by Max Planck in the formalism now known as Planck's law of black-body radiation. Planck had to assume that the energy of the oscillators in the cavity was quantized, i.

Einstein built on this idea and proposed the quantization of electromagnetic radiation itself in to explain the photoelectric effect.

These theoretical advances eventually resulted in the superseding of classical electromagnetism by quantum electrodynamics. These quanta were called photons and the black-body cavity was thought of as containing a gas of photons.

In addition, it led to the development of quantum probability distributions, called Fermi—Dirac statistics and Bose—Einstein statistics , each applicable to a different class of particles, fermions and bosons. The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan—Boltzmann law.

So, as temperature increases, the glow color changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue.

It will never become invisible—indeed, the radiation of visible light increases monotonically with temperature. The law was formulated by Josef Stefan in and later derived by Ludwig Boltzmann.

Planck's law states that [30]. At oblique angles, the solid angle spans involved do get smaller, resulting in lower aggregate intensities.

Wien's displacement law shows how the spectrum of black-body radiation at any temperature is related to the spectrum at any other temperature. If we know the shape of the spectrum at one temperature, we can calculate the shape at any other temperature. Spectral intensity can be expressed as a function of wavelength or of frequency. Planck's law was also stated above as a function of frequency.

The intensity maximum for this is given by. The human body radiates energy as infrared light. The net power radiated is the difference between the power emitted and the power absorbed:. The total surface area of an adult is about 2 m 2 , and the mid- and far-infrared emissivity of skin and most clothing is near unity, as it is for most nonmetallic surfaces.

The total energy radiated in one day is about 8 MJ , or kcal food calories. There are other important thermal loss mechanisms, including convection and evaporation. Conduction is negligible — the Nusselt number is much greater than unity. Evaporation by perspiration is only required if radiation and convection are insufficient to maintain a steady-state temperature but evaporation from the lungs occurs regardless.

Free-convection rates are comparable, albeit somewhat lower, than radiative rates. Given the approximate nature of many of the assumptions, this can only be taken as a crude estimate. Ambient air motion, causing forced convection, or evaporation reduces the relative importance of radiation as a thermal-loss mechanism.

Application of Wien's law to human-body emission results in a peak wavelength of. For this reason, thermal imaging devices for human subjects are most sensitive in the 7—14 micrometer range. The Sun emits that power equally in all directions. Because of this, the planet is hit with only a tiny fraction of it. The power from the Sun that strikes the planet at the top of the atmosphere is:. Because of its high temperature, the Sun emits to a large extent in the ultraviolet and visible UV-Vis frequency range.

The power absorbed by the planet and its atmosphere is then:. If the planet were a perfect black body, it would emit according to the Stefan—Boltzmann law. The actual temperature of the planet will likely be different, depending on its surface and atmospheric properties.

Ignoring the atmosphere and greenhouse effect, the planet, since it is at a much lower temperature than the Sun, emits mostly in the infrared IR portion of the spectrum. The power emitted by the planet is then:. For a body in radiative exchange equilibrium with its surroundings, the rate at which it emits radiant energy is equal to the rate at which it absorbs it: Substituting the expressions for solar and planet power in equations 1—6 and simplifying yields the estimated temperature of the planet, ignoring greenhouse effect, T P:.

In other words, given the assumptions made, the temperature of a planet depends only on the surface temperature of the Sun, the radius of the Sun, the distance between the planet and the Sun, the albedo and the IR emissivity of the planet.

This is the temperature of the Earth if it radiated as a perfect black body in the infrared, assuming an unchanging albedo and ignoring greenhouse effects which can raise the surface temperature of a body above what it would be if it were a perfect black body in all spectrums [44]. The Earth in fact radiates not quite as a perfect black body in the infrared which will raise the estimated temperature a few degrees above the effective temperature. If we wish to estimate what the temperature of the Earth would be if it had no atmosphere, then we could take the albedo and emissivity of the Moon as a good estimate.

The albedo and emissivity of the Moon are about 0. Estimates of the Earth's average albedo vary in the range 0. Estimates are often based on the solar constant total insolation power density rather than the temperature, size, and distance of the Sun.

For example, using 0. The cosmic microwave background radiation observed today is the most perfect black-body radiation ever observed in nature, with a temperature of about 2. Prior to this time, most matter in the universe was in the form of an ionized plasma in thermal, though not full thermodynamic, equilibrium with radiation.

These particles form a part of the black body spectrum, in addition to the electromagnetic radiation. The relativistic Doppler effect causes a shift in the frequency f of light originating from a source that is moving in relation to the observer, so that the wave is observed to have frequency f':.

Through Planck's law the temperature spectrum of a black body is proportionally related to the frequency of light and one may substitute the temperature T for the frequency in this equation. This is an important effect in astronomy, where the velocities of stars and galaxies can reach significant fractions of c. An example is found in the cosmic microwave background radiation , which exhibits a dipole anisotropy from the Earth's motion relative to this black-body radiation field.

In , Balfour Stewart described his experiments on the thermal radiative emissive and absorptive powers of polished plates of various substances, compared with the powers of lamp-black surfaces, at the same temperature. He wrote "Lamp-black, which absorbs all the rays that fall upon it, and therefore possesses the greatest possible absorbing power, will possess also the greatest possible radiating power.

Stewart measured radiated power with a thermo-pile and sensitive galvanometer read with a microscope. He was concerned with selective thermal radiation, which he investigated with plates of substances that radiated and absorbed selectively for different qualities of radiation rather than maximally for all qualities of radiation.

He discussed the experiments in terms of rays which could be reflected and refracted, and which obeyed the Stokes- Helmholtz reciprocity principle though he did not use an eponym for it. He did not in this paper mention that the qualities of the rays might be described by their wavelengths, nor did he use spectrally resolving apparatus such as prisms or diffraction gratings.

His work was quantitative within these constraints. He made his measurements in a room temperature environment, and quickly so as to catch his bodies in a condition near the thermal equilibrium in which they had been prepared by heating to equilibrium with boiling water.

His measurements confirmed that substances that emit and absorb selectively respect the principle of selective equality of emission and absorption at thermal equilibrium. Stewart offered a theoretical proof that this should be the case separately for every selected quality of thermal radiation, but his mathematics was not rigorously valid.

He proposed that his measurements implied that radiation was both absorbed and emitted by particles of matter throughout depths of the media in which it propagated. He applied the Helmholtz reciprocity principle to account for the material interface processes as distinct from the processes in the interior material. He did not postulate unrealizable perfectly black surfaces. He concluded that his experiments showed that in a cavity in thermal equilibrium, the heat radiated from any part of the interior bounding surface, no matter of what material it might be composed, was the same as would have been emitted from a surface of the same shape and position that would have been composed of lamp-black.

He did not state explicitly that the lamp-black-coated bodies that he used as reference must have had a unique common spectral emittance function that depended on temperature in a unique way. In , not knowing of Stewart's work, Gustav Robert Kirchhoff reported the coincidence of the wavelengths of spectrally resolved lines of absorption and of emission of visible light.

Importantly for thermal physics, he also observed that bright lines or dark lines were apparent depending on the temperature difference between emitter and absorber.





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