A Medley of Potpourri

Wednesday, August 27, 2025

Power station

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Power_station

A power station, also referred to as a power plant and sometimes generating station or generating plant, is an industrial facility for the generation of electric power. Power stations are generally connected to an electrical grid.

Many power stations contain one or more generators, rotating machine that converts mechanical power into three-phase electric power. The relative motion between a magnetic field and a conductor creates an electric current.

The energy source harnessed to turn the generator varies widely. Most power stations in the world burn fossil fuels such as coal, oil, and natural gas to generate electricity. Low-carbon power sources include nuclear power, and use of renewables such as solar, wind, geothermal, and hydroelectric.

History

In early 1871 Belgian inventor Zénobe Gramme invented a generator powerful enough to produce power on a commercial scale for industry.

In 1878, a hydroelectric power station was designed and built by William, Lord Armstrong at Cragside, England. It used water from lakes on his estate to power Siemens dynamos. The electricity supplied power to lights, heating, produced hot water, ran an elevator as well as labor-saving devices and farm buildings.

In January 1882 the world's first public coal-fired power station, the Edison Electric Light Station, was built in London, a project of Thomas Edison organized by Edward Johnson. A Babcock & Wilcox boiler powered a 93 kW (125 horsepower) steam engine that drove a 27-tonne (27-long-ton) generator. This supplied electricity to premises in the area that could be reached through the culverts of the viaduct without digging up the road, which was the monopoly of the gas companies. The customers included the City Temple and the Old Bailey. Another important customer was the Telegraph Office of the General Post Office, but this could not be reached through the culverts. Johnson arranged for the supply cable to be run overhead, via Holborn Tavern and Newgate.

In September 1882 in New York, the Pearl Street Station was established by Edison to provide electric lighting in the lower Manhattan Island area. The station ran until destroyed by fire in 1890. The station used reciprocating steam engines to turn direct-current generators. Because of the DC distribution, the service area was small, limited by voltage drop in the feeders. In 1886 George Westinghouse began building an alternating current system that used a transformer to step up voltage for long-distance transmission and then stepped it back down for indoor lighting, a more efficient and less expensive system which is similar to modern systems. The war of the currents eventually resolved in favor of AC distribution and utilization, although some DC systems persisted to the end of the 20th century. DC systems with a service radius of a mile (kilometer) or so were necessarily smaller, less efficient of fuel consumption, and more labor-intensive to operate than much larger central AC generating stations.

AC systems used a wide range of frequencies depending on the type of load; lighting load using higher frequencies, and traction systems and heavy motor load systems preferring lower frequencies. The economics of central station generation improved greatly when unified light and power systems, operating at a common frequency, were developed. The same generating plant that fed large industrial loads during the day, could feed commuter railway systems during rush hour and then serve lighting load in the evening, thus improving the system load factor and reducing the cost of electrical energy overall. Many exceptions existed, generating stations were dedicated to power or light by the choice of frequency, and rotating frequency changers and rotating converters were particularly common to feed electric railway systems from the general lighting and power network.

Throughout the first few decades of the 20th century central stations became larger, using higher steam pressures to provide greater efficiency, and relying on interconnections of multiple generating stations to improve reliability and cost. High-voltage AC transmission allowed hydroelectric power to be conveniently moved from distant waterfalls to city markets. The advent of the steam turbine in central station service, around 1906, allowed great expansion of generating capacity. Generators were no longer limited by the power transmission of belts or the relatively slow speed of reciprocating engines, and could grow to enormous sizes. For example, Sebastian Ziani de Ferranti planned what would have reciprocating steam engine ever built for a proposed new central station, but scrapped the plans when turbines became available in the necessary size. Building power systems out of central stations required combinations of engineering skill and financial acumen in equal measure. Pioneers of central station generation include George Westinghouse and Samuel Insull in the United States, Ferranti and Charles Hesterman Merz in UK, and many others.

Thermal power stations

2024 world electricity generation by source in terawatt-hours (TWh). Total generation was 30.85 petawatt-hours.

Coal 10,587 (34.4%)
Natural gas 6,796 (22.1%)
Hydro 4,417 (14.4%)
Nuclear 2,765 (8.99%)
Wind 2,497 (8.12%)
Solar 2,130 (6.92%)
Other 1,569 (5.10%)

In thermal power stations, mechanical power is produced by a heat engine that transforms thermal energy, often from combustion of a fuel, into rotational energy. Most thermal power stations produce steam, so they are sometimes called steam power stations. Not all thermal energy can be transformed into mechanical power, according to the second law of thermodynamics; therefore, there is always heat lost to the environment. If this loss is employed as useful heat, for industrial processes or district heating, the power plant is referred to as a cogeneration power plant or CHP (combined heat-and-power) plant. In countries where district heating is common, there are dedicated heat plants called heat-only boiler stations. An important class of power stations in the Middle East uses by-product heat for the desalination of water.

The efficiency of a thermal power cycle is limited by the maximum working fluid temperature produced. The efficiency is not directly a function of the fuel used. For the same steam conditions, coal-, nuclear- and gas power plants all have the same theoretical efficiency. Overall, if a system is on constantly (base load) it will be more efficient than one that is used intermittently (peak load). Steam turbines generally operate at higher efficiency when operated at full capacity.

Besides use of reject heat for process or district heating, one way to improve overall efficiency of a power plant is to combine two different thermodynamic cycles in a combined cycle plant. Most commonly, exhaust gases from a gas turbine are used to generate steam for a boiler and a steam turbine. The combination of a "top" cycle and a "bottom" cycle produces higher overall efficiency than either cycle can attain alone.

In 2018, Inter RAO UES and State Grid Archived 21 December 2021 at the Wayback Machine planned to build an 8-GW thermal power plant, which's the largest coal-fired power plant construction project in Russia.

Classification

By heat source

Fossil-fuel power stations may also use a steam turbine generator or in the case of natural gas-fired power plants may use a combustion turbine. A coal-fired power station produces heat by burning coal in a steam boiler. The steam drives a steam turbine and generator that then produces electricity. The waste products of combustion include ash, sulfur dioxide, nitrogen oxides, and carbon dioxide. Some of the gases can be removed from the waste stream to reduce pollution.
Nuclear power plants use the heat generated in a nuclear reactor's core (by the fission process) to create steam which then operates a steam turbine and generator. About 20 percent of electric generation in the US is produced by nuclear power plants.
Geothermal power plants use steam extracted from hot underground rocks. These rocks are heated by the decay of radioactive material in the Earth's core.
Biomass-fuelled power plants may be fuelled by waste from sugar cane, municipal solid waste, landfill methane, or other forms of biomass.
In integrated steel mills, blast furnace exhaust gas is a low-cost, although low-energy-density, fuel.
Waste heat from industrial processes is occasionally concentrated enough to use for power generation, usually in a steam boiler and turbine.
Solar thermal electric plants use sunlight to boil water and produce steam which turns the generator.
Hydrogen power plants can use green hydrogen from electrolysis to help balance supply and demand from Variable renewable energy sources.

By prime mover

A prime mover is a machine that converts energy of various forms into energy of motion.

Steam turbine plants use the dynamic pressure generated by expanding steam to turn the blades of a turbine. Almost all large non-hydro plants use this system. About 90 percent of all electric power produced in the world is through use of steam turbines.
Gas turbine plants use the dynamic pressure from flowing gases (air and combustion products) to directly operate the turbine. Natural-gas fuelled (and oil fueled) combustion turbine plants can start rapidly and so are used to supply "peak" energy during periods of high demand, though at higher cost than base-loaded plants. These may be comparatively small units, and sometimes completely unmanned, being remotely operated. This type was pioneered by the UK, Princetown being the world's first, commissioned in 1959.
Combined cycle plants have both a gas turbine fired by natural gas, and a steam boiler and steam turbine which use the hot exhaust gas from the gas turbine to produce electricity. This greatly increases the overall efficiency of the plant, and many new baseload power plants are combined cycle plants fired by natural gas.
Internal combustion reciprocating engines are used to provide power for isolated communities and are frequently used for small cogeneration plants. Hospitals, office buildings, industrial plants, and other critical facilities also use them to provide backup power in case of a power outage. These are usually fuelled by diesel oil, heavy oil, natural gas, and landfill gas.
Microturbines, Stirling engine and internal combustion reciprocating engines are low-cost solutions for using opportunity fuels, such as landfill gas, digester gas from water treatment plants and waste gas from oil production.

By duty

Power plants that can be dispatched (scheduled) to provide energy to a system include:

Base load power plants run nearly continually to provide that component of system load that does not vary during a day or week. Baseload plants can be highly optimized for low fuel cost, but may not start or stop quickly during changes in system load. Examples of base-load plants would include large modern coal-fired and nuclear generating stations, or hydro plants with a predictable supply of water.
Peaking power plants meet the daily peak load, which may only be for one or two hours each day. While their incremental operating cost is always higher than base load plants, they are required to ensure security of the system during load peaks. Peaking plants include simple cycle gas turbines and reciprocating internal combustion engines, which can be started up rapidly when system peaks are predicted. Hydroelectric plants may also be designed for peaking use.
Load following power plants can economically follow the variations in the daily and weekly load, at lower cost than peaking plants and with more flexibility than baseload plants.

Non-dispatchable plants include such sources as wind and solar energy; while their long-term contribution to system energy supply is predictable, on a short-term (daily or hourly) base their energy must be used as available since generation cannot be deferred. Contractual arrangements ("take or pay") with independent power producers or system interconnections to other networks may be effectively non-dispatchable.

Cooling towers

All thermal power plants produce waste heat energy as a byproduct of the useful electrical energy produced. The amount of waste heat energy equals or exceeds the amount of energy converted into useful electricity. Gas-fired power plants can achieve as much as 65% conversion efficiency, while coal and oil plants achieve around 30–49%. The waste heat produces a temperature rise in the atmosphere, which is small compared to that produced by greenhouse-gas emissions from the same power plant. Natural draft wet cooling towers at many nuclear power plants and large fossil-fuel-fired power plants use large hyperboloid chimney-like structures (as seen in the image at the right) that release the waste heat to the ambient atmosphere by the evaporation of water.

However, the mechanical induced-draft or forced-draft wet cooling towers in many large thermal power plants, nuclear power plants, fossil-fired power plants, petroleum refineries, petrochemical plants, geothermal, biomass and waste-to-energy plants use fans to provide air movement upward through down coming water and are not hyperboloid chimney-like structures. The induced or forced-draft cooling towers are typically rectangular, box-like structures filled with a material that enhances the mixing of the upflowing air and the down-flowing water.

In areas with restricted water use, a dry cooling tower or directly air-cooled radiators may be necessary, since the cost or environmental consequences of obtaining make-up water for evaporative cooling would be prohibitive. These coolers have lower efficiency and higher energy consumption to drive fans, compared to a typical wet, evaporative cooling tower.

Air-cooled condenser (ACC)

Power plants can use an air-cooled condenser, traditionally in areas with a limited or expensive water supply. Air-cooled condensers serve the same purpose as a cooling tower (heat dissipation) without using water. They consume additional auxiliary power and thus may have a higher carbon footprint compared to a traditional cooling tower.

Once-through cooling systems

Electric companies often prefer to use cooling water from the ocean or a lake, river, or cooling pond instead of a cooling tower. This single pass or once-through cooling system can save the cost of a cooling tower and may have lower energy costs for pumping cooling water through the plant's heat exchangers. However, the waste heat can cause thermal pollution as the water is discharged. Power plants using natural bodies of water for cooling are designed with mechanisms such as fish screens, to limit intake of organisms into the cooling machinery. These screens are only partially effective and as a result billions of fish and other aquatic organisms are killed by power plants each year. For example, the cooling system at the Indian Point Energy Center in New York kills over a billion fish eggs and larvae annually. A further environmental impact is that aquatic organisms which adapt to the warmer discharge water may be injured if the plant shuts down in cold weather.

Water consumption by power stations is a developing issue.

In recent years, recycled wastewater, or grey water, has been used in cooling towers. The Calpine Riverside and the Calpine Fox power stations in Wisconsin as well as the Calpine Mankato power station in Minnesota are among these facilities.

Power from renewable energy

Power stations can generate electrical energy from renewable energy sources.

Hydroelectric power station

In a hydroelectric power station water flows through turbines using hydropower to generate hydroelectricity. Power is captured from the gravitational force of water falling through penstocks to water turbines connected to generators. The amount of power available is a combination of height and water flow. A wide range of Dams may be built to raise the water level, and create a lake for storing water. Hydropower is produced in 150 countries, with the Asia-Pacific region generating 32 percent of global hydropower in 2010. China is the largest hydroelectricity producer, with 721 terawatt-hours of production in 2010, representing around 17 percent of domestic electricity use.

Solar

Solar energy can be turned into electricity either directly in solar cells, or in a concentrating solar power plant by focusing the light to run a heat engine.

A solar photovoltaic power plant converts sunlight into direct current electricity using the photoelectric effect. Inverters change the direct current into alternating current for connection to the electrical grid. This type of plant does not use rotating machines for energy conversion.

Solar thermal power plants use either parabolic troughs or heliostats to direct sunlight onto a pipe containing a heat transfer fluid, such as oil. The heated oil is then used to boil water into steam, which turns a turbine that drives an electrical generator. The central tower type of solar thermal power plant uses hundreds or thousands of mirrors, depending on size, to direct sunlight onto a receiver on top of a tower. The heat is used to produce steam to turn turbines that drive electrical generators.

Wind

Wind turbines can be used to generate electricity in areas with strong, steady winds, sometimes offshore. Many different designs have been used in the past, but almost all modern turbines being produced today use a three-bladed, upwind design. Grid-connected wind turbines now being built are much larger than the units installed during the 1970s. They thus produce power more cheaply and reliably than earlier models. With larger turbines (on the order of one megawatt), the blades move more slowly than older, smaller, units, which makes them less visually distracting and safer for birds.

Marine

Marine energy or marine power (also sometimes referred to as ocean energy or ocean power) refers to the energy carried by ocean waves, tides, salinity, and ocean temperature differences. The movement of water in the world's oceans creates a vast store of kinetic energy, or energy in motion. This energy can be harnessed to generate electricity to power homes, transport and industries.

The term marine energy encompasses both wave power—power from surface waves, and tidal power—obtained from the kinetic energy of large bodies of moving water. Offshore wind power is not a form of marine energy, as wind power is derived from the wind, even if the wind turbines are placed over water.

The oceans have a tremendous amount of energy and are close to many if not most concentrated populations. Ocean energy has the potential of providing a substantial amount of new renewable energy around the world.

Osmosis

Salinity gradient energy is called pressure-retarded osmosis. In this method, seawater is pumped into a pressure chamber that is at a pressure lower than the difference between the pressures of saline water and fresh water. Freshwater is also pumped into the pressure chamber through a membrane, which increases both the volume and pressure of the chamber. As the pressure differences are compensated, a turbine is spun creating energy. This method is being specifically studied by the Norwegian utility Statkraft, which has calculated that up to 25 TWh/yr would be available from this process in Norway. Statkraft has built the world's first prototype osmotic power plant on the Oslo fjord which was opened on 24 November 2009. In January 2014, however, Statkraft announced not to continue this pilot.

Biomass

Biomass energy can be produced from combustion of waste green material to heat water into steam and drive a steam turbine. Bioenergy can also be processed through a range of temperatures and pressures in gasification, pyrolysis or torrefaction reactions. Depending on the desired end product, these reactions create more energy-dense products (syngas, wood pellets, biocoal) that can then be fed into an accompanying engine to produce electricity at a much lower emission rate when compared with open burning.

Storage power stations

It is possible to store energy and produce electrical power at a later time as in pumped-storage hydroelectricity, thermal energy storage, flywheel energy storage, battery storage power station and so on.

Pumped storage

The world's largest form of storage for excess electricity, pumped-storage is a reversible hydroelectric plant. They are a net consumer of energy but provide storage for any source of electricity, effectively smoothing peaks and troughs in electricity supply and demand. Pumped storage plants typically use "spare" electricity during off peak periods to pump water from a lower reservoir to an upper reservoir. Because the pumping takes place "off peak", electricity is less valuable than at peak times. This less valuable "spare" electricity comes from uncontrolled wind power and base load power plants such as coal, nuclear and geothermal, which still produce power at night even though demand is very low. During daytime peak demand, when electricity prices are high, the storage is used for peaking power, where water in the upper reservoir is allowed to flow back to a lower reservoir through a turbine and generator. Unlike coal power stations, which can take more than 12 hours to start up from cold, a hydroelectric generator can be brought into service in a few minutes, ideal to meet a peak load demand. Two substantial pumped storage schemes are in South Africa, Palmiet Pumped Storage Scheme and another in the Drakensberg, Ingula Pumped Storage Scheme.

Typical power output

The power generated by a power station is measured in multiples of the watt, typically megawatts (10⁶ watts) or gigawatts (10⁹ watts). Power stations vary greatly in capacity depending on the type of power plant and on historical, geographical and economic factors.

Many of the largest operational onshore wind farms are located in China. As of 2022, the Roscoe Wind Farm is the largest onshore wind farm in the world, producing 8000 MW of power, followed by the Zhang Jiakou (3000 MW). As of January 2022, the Hornsea Wind Farm in United Kingdom is the largest offshore wind farm in the world at 1218 MW, followed by Walney Wind Farm in United Kingdom at 1026 MW.

In 2021, the worldwide installed capacity of power plants increased by 347 GW. Solar and wind power plant capacities rose by 80% in one year. As of 2022, the largest photovoltaic (PV) power plants in the world are led by Bhadla Solar Park in India, rated at 2245 MW.

Solar thermal power stations in the U.S. have the following output:

Ivanpah Solar Power Facility is the largest of the country with an output of 392 MW

The Koeberg Nuclear Power Station, South Africa

Large coal-fired, nuclear, and hydroelectric power stations can generate hundreds of megawatts to multiple gigawatts. Some examples:

The Koeberg Nuclear Power Station in South Africa has a rated capacity of 1860 megawatts.

The coal-fired Ratcliffe-on-Soar Power Station in the UK has a rated capacity of 2 gigawatts.

The Aswan Dam hydro-electric plant in Egypt has a capacity of 2.1 gigawatts.

The Three Gorges Dam hydro-electric plant in China has a capacity of 22.5 gigawatts.

Gas turbine power plants can generate tens to hundreds of megawatts. Some examples:

The Indian Queens simple-cycle, or open cycle gas turbine (OCGT), peaking power station in Cornwall UK, with a single gas turbine is rated 140 megawatts.

The Medway Power Station, a combined-cycle gas turbine (CCGT) power station in Kent, UK, with two gas turbines and one steam turbine, is rated 700 megawatts.

The rated capacity of a power station is nearly the maximum electrical power that the power station can produce. Some power plants are run at almost exactly their rated capacity all the time, as a non-load-following base load power plant, except at times of scheduled or unscheduled maintenance.

However, many power plants usually produce much less power than their rated capacity.

In some cases a power plant produces much less power than its rated capacity because it uses an intermittent energy source. Operators try to pull maximum available power from such power plants, because their marginal cost is practically zero, but the available power varies widely—in particular, it may be zero during heavy storms at night.

In some cases operators deliberately produce less power for economic reasons. The cost of fuel to run a load following power plant may be relatively high, and the cost of fuel to run a peaking power plant is even higher—they have relatively high marginal costs. Operators keep power plants turned off ("operational reserve") or running at minimum fuel consumption ("spinning reserve") most of the time. Operators feed more fuel into load following power plants only when the demand rises above what lower-cost plants (i.e., intermittent and base load plants) can produce, and then feed more fuel into peaking power plants only when the demand rises faster than the load following power plants can follow.

Output metering

Not all of the generated power of a plant is necessarily delivered into a distribution system. Power plants typically also use some of the power themselves, in which case the generation output is classified into gross generation, and net generation.

Gross generation or gross electric output is the total amount of electricity generated by a power plant over a specific period of time. It is measured at the generating terminal and is measured in kilowatt-hours (kW·h), megawatt-hours (MW·h), gigawatt-hours (GW·h) or for the largest power plants terawatt-hours (TW·h). It includes the electricity used in the plant auxiliaries and in the transformers.

Gross generation = net generation + usage within the plant (also known as in-house loads)

Net generation is the amount of electricity generated by a power plant that is transmitted and distributed for consumer use. Net generation is less than the total gross power generation as some power produced is consumed within the plant itself to power auxiliary equipment such as pumps, motors and pollution control devices. Thus

Net generation = gross generation − usage within the plant (a.k.a. in-house loads)

Operations

This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (July 2021) (Learn how and when to remove this message)

Operating staff at a power station have several duties. Operators are responsible for the safety of the work crews that frequently do repairs on the mechanical and electrical equipment. They maintain the equipment with periodic inspections and log temperatures, pressures and other important information at regular intervals. Operators are responsible for starting and stopping the generators depending on need. They are able to synchronize and adjust the voltage output of the added generation with the running electrical system, without upsetting the system. They must know the electrical and mechanical systems to troubleshoot problems in the facility and add to the reliability of the facility. Operators must be able to respond to an emergency and know the procedures in place to deal with it.

Tuesday, August 26, 2025

Ludwig Boltzmann

From Wikipedia, the free encyclopedia

Ludwig Boltzmann
Boltzmann in 1902
Born	Ludwig Eduard Boltzmann 20 February 1844 Vienna, Austrian Empire, German Confederation
Died	5 September 1906 (aged 62) Tybein, Princely County of Gorizia and Gradisca, Austria-Hungary
Resting place	Vienna Central Cemetery
Alma mater	University of Vienna (PhD; Dr. habil., 1869)
Known for	Boltzmann distribution (1868) Boltzmann equation (1872) Introducing the H-theorem (1872) Boltzmann's entropy formula (1875) Expanding the equipartition theorem (1876) Describing canonical ensemble (1884) Stefan–Boltzmann law (1884)
Spouse	Henriette von Aigentler (m. 1876)
Children	4
Awards	ForMemRS (1899)
Scientific career
Fields	Statistical physics Thermodynamics
Institutions	University of Graz (1869–1873, 1876–1890) University of Vienna (1873–1876, 1894–1900, 1902–1906) University of Munich (1890–1894) University of Leipzig (1900–1902)
Thesis	Über die mechanische Bedeutung des zweiten Hauptsatzes der mechanischen Wärmetheorie (1866)
Doctoral advisor	Josef Stefan
Doctoral students	Ignaz Schütz (1894) Paul Ehrenfest (1904) Philipp Frank (1907)
Other notable students	Svante Arrhenius Gustav Herglotz Lise Meitner Walther Nernst Karl Přibram
Signature

Ludwig Eduard Boltzmann (/ˈbɔːltsˌmɑːn/ BAWLTS-mahn or /ˈboʊltsmən/ BOHLTS-muhn; German: [ˈluːtvɪç ˈeːduaʁt ˈbɔltsman]; 20 February 1844 – 5 September 1906) was an Austrian mathematician and theoretical physicist. His greatest achievements were the development of statistical mechanics and the statistical explanation of the second law of thermodynamics. In 1877 he provided the current definition of entropy, $S = k_{B} \ln Ω$ , where Ω is the number of microstates whose energy equals the system's energy, interpreted as a measure of the statistical disorder of a system. Max Planck named the constant $k B$ the Boltzmann constant.

Statistical mechanics is one of the pillars of modern physics. It describes how macroscopic observations (such as temperature and pressure) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas, in classical thermodynamics, the only available option would be to measure and tabulate such quantities for various materials.

Biography

Childhood and education

Boltzmann was born in Erdberg, a suburb of Vienna into a Catholic family. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg. Boltzmann was home-schooled until the age of ten, and then attended high school in Linz, Upper Austria. When Boltzmann was 15, his father died.

Starting in 1863, Boltzmann studied mathematics and physics at the University of Vienna. He received his doctorate in 1866 and his venia legendi in 1869. Boltzmann worked closely with Josef Stefan, director of the institute of physics. It was Stefan who introduced Boltzmann to Maxwell's work.

Academic career

In 1869 at age 25, thanks to a letter of recommendation written by Josef Stefan, Boltzmann was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and in 1871 with Gustav Kirchhoff and Hermann von Helmholtz in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876.

Ludwig Boltzmann and co-workers in Graz, 1887: (standing, from the left) Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger

In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to audit lectures unofficially. Boltzmann supported her decision to appeal, which was successful. On 17 July 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and Else (1891); and a son, Arthur Ludwig (1881). Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz were Svante Arrhenius and Walther Nernst. He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature.

Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria, Germany in 1890.

In 1894, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna.

Final years and death

Boltzmann spent a great deal of effort in his final years defending his theories. He did not get along with some of his colleagues in Vienna, particularly Ernst Mach, who became a professor of philosophy and history of sciences in 1895. That same year Georg Helm and Wilhelm Ostwald presented their position on energetics at a meeting in Lübeck. They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate. In 1900, Boltzmann went to the University of Leipzig, on the invitation of Wilhelm Ostwald. Ostwald offered Boltzmann the professorial chair in physics, which became vacant when Gustav Heinrich Wiedemann died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902. In 1903, Boltzmann, together with Gustav von Escherich and Emil Müller, founded the Austrian Mathematical Society. His students included Karl Přibram, Paul Ehrenfest and Lise Meitner.

In Vienna, Boltzmann taught physics and also lectured on philosophy. Boltzmann's lectures on natural philosophy were very popular and received considerable attention. His first lecture was an enormous success: people stood all the way down the staircase outside the largest available lecture hall, and the Emperor invited him to a reception.

In 1905, he gave an invited course of lectures in the summer session at the University of California in Berkeley, which he described in a popular essay A German professor's trip to El Dorado.

In May 1906, Boltzmann's deteriorating mental condition (described in a letter by the Dean as "a serious form of neurasthenia") forced him to resign his position. His symptoms indicate he experienced what might today be diagnosed as bipolar disorder. Four months later he died by suicide on 5 September 1906, by hanging himself while on vacation with his wife and daughter in Duino, near Trieste (then Austria).He is buried in the Viennese Zentralfriedhof. His tombstone bears the inscription of Boltzmann's entropy formula: $S = k \cdot \log W$ .

Philosophy

Boltzmann's kinetic theory of gases seemed to presuppose the reality of atoms and molecules, but almost all German philosophers and many scientists like Ernst Mach and the physical chemist Wilhelm Ostwald disbelieved their existence. Boltzmann had been exposed to molecular theory by James Clerk Maxwell’s paper, "Illustrations of the Dynamical Theory of Gases," which described temperature as dependent on the speed of the molecules. This inspired Boltzmann to embrace atomism, introducing statistics into physics and extending the theory.

Boltzmann wrote treatises on philosophy such as "On the question of the objective existence of processes in inanimate nature" (1897). He was a realist. In his work "On Thesis of Schopenhauer's", Boltzmann refers to his philosophy as materialism and says further: "Idealism asserts that only the ego exists, the various ideas, and seeks to explain matter from them. Materialism starts from the existence of matter and seeks to explain sensations from it."

Physics

Boltzmann's most important scientific contributions were in the kinetic theory of gases based upon the Second law of thermodynamics. This was important because Newtonian mechanics did not differentiate between past and future motion, but Rudolf Clausius’ invention of entropy to describe the second law was based on disgregation or dispersion at the molecular level so that the future was one-directional. Boltzmann was twenty-five years of age when he came upon James Clerk Maxwell's work on the kinetic theory of gases which hypothesized that temperature was caused by collision of molecules. Maxwell used statistics to create a curve of molecular kinetic energy distribution from which Boltzmann clarified and developed the ideas of kinetic theory and entropy based upon statistical atomic theory creating the Maxwell–Boltzmann distribution as a description of molecular speeds in a gas. It was Boltzmann who derived the first equation to model the dynamic evolution of the probability distribution Maxwell and he had created. Boltzmann's key insight was that dispersion occurred due to the statistical probability of increased molecular "states". Boltzmann went beyond Maxwell by applying his distribution equation to not solely gases, but also liquids and solids. Boltzmann also extended his theory in his 1877 paper beyond Carnot, Rudolf Clausius, James Clerk Maxwell and Lord Kelvin by demonstrating that entropy is contributed to by heat, spatial separation, and radiation. Maxwell–Boltzmann statistics and the Boltzmann distribution remain central in the foundations of classical statistical mechanics. They are also applicable to other phenomena that do not require quantum statistics and provide insight into the meaning of temperature.

He made multiple attempts to explain the second law of thermodynamics, with the attempts ranging over many areas. He tried Helmholtz's monocycle model, a pure ensemble approach like Gibbs, a pure mechanical approach like ergodic theory, the combinatorial argument, the Stoßzahlansatz, etc.

Boltzmann's 1898 I₂ molecule diagram showing atomic "sensitive region" (α, β) overlap

Most chemists, since the discoveries of John Dalton in 1808, and James Clerk Maxwell in Scotland and Josiah Willard Gibbs in the United States, shared Boltzmann's belief in atoms and molecules, but much of the physics establishment did not share this belief until decades later. Boltzmann had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908–1909), based on Einstein's theoretical studies of 1905, confirmed the values of the Avogadro constant and the Boltzmann constant, convincing the world that the tiny particles really exist.

To quote Planck, "The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases". This famous formula for entropy S is $S = k_{B} \ln W$ where $k$ _B is the Boltzmann constant, and ln is the natural logarithm. $W$ (for Wahrscheinlichkeit, a German word meaning "probability") is the probability of occurrence of a macrostate or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system – the number of (unobservable) "ways" in the (observable) thermodynamic state of a system that can be realized by assigning different positions and momenta to the various molecules. Boltzmann's paradigm was an ideal gas of $N$ identical particles, of which $N i$ are in the $i$ th microscopic condition (range) of position and momentum. $W$ can be counted using the formula for permutations $W = N! \prod_{i} \frac{1}{N_{i}!}$ where $i$ ranges over all possible molecular conditions, and where $!$ denotes factorial. The "correction" in the denominator account for indistinguishable particles in the same condition.

Boltzmann could also be considered one of the forerunners of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete, although Boltzmann used this as a mathematical device with no physical meaning.

An alternative to Boltzmann's formula for entropy, above, is the information entropy definition introduced in 1948 by Claude Shannon. Shannon's definition was intended for use in communication theory but is applicable in all areas. It reduces to Boltzmann's expression when all the probabilities are equal, but can, of course, be used when they are not. Its virtue is that it yields immediate results without resorting to factorials or Stirling's approximation. Similar formulas are found, however, as far back as the work of Boltzmann, and explicitly in Gibbs (see reference).

Boltzmann equation

The Boltzmann equation was developed to describe the dynamics of an ideal gas. $\frac{\partial f}{\partial t} + v \frac{\partial f}{\partial x} + \frac{F}{m} \frac{\partial f}{\partial v} = \frac{\partial f}{\partial t} {\frac{}{} |}_{c o l l i s i o n}$ where $ƒ$ represents the distribution function of single-particle position and momentum at a given time (see the Maxwell–Boltzmann distribution), $F$ is a force, $m$ is the mass of a particle, $t$ is the time and $v$ is an average velocity of particles.

This equation describes the temporal and spatial variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle phase space. (See Hamiltonian mechanics.) The first term on the left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions.

In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate boundary conditions. This first-order differential equation has a deceptively simple appearance, since $f$ can represent an arbitrary single-particle distribution function. Also, the force acting on the particles depends directly on the velocity distribution function $f$ . The Boltzmann equation is notoriously difficult to integrate. David Hilbert spent years trying to solve it without any real success.

The form of the collision term assumed by Boltzmann was approximate. However, for an ideal gas the standard Chapman–Enskog solution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for an ideal gas only under shock wave conditions.

Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation – his famous H-theorem. However the key assumption he made in formulating the collision term was "molecular chaos", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with Loschmidt and others over Loschmidt's paradox ultimately ended in his failure.

Finally, in the 1970s E. G. D. Cohen and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, nonequilibrium statistical mechanics for dense gases and liquids focuses on the Green–Kubo relations, the fluctuation theorem, and other approaches instead.

Second thermodynamics law as a law of disorder

The idea that the second law of thermodynamics or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") is due to Boltzmann's view of the second law of thermodynamics.

In particular, it was Boltzmann's attempt to reduce it to a stochastic collision function, or law of probability following from the random collisions of mechanical particles. Following Maxwell, Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder or the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials or gradients). The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable. Because there are so many more possible disordered states than ordered ones, a system will almost always be found either in the state of maximum disorder – the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium – or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction", Boltzmann concluded, is thus "the most improbable case conceivable...an infinitely improbable configuration of energy."

Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered pack of cards under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.) The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary dice, with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system must move to one of the more probable states.

Legacy and impact on modern science

Ludwig Boltzmann's contributions to physics and philosophy have left a lasting impact on modern science. His pioneering work in statistical mechanics and thermodynamics laid the foundation for some of the most fundamental concepts in physics. For instance, Max Planck in quantizing resonators in his Black Body theory of radiation used the Boltzmann constant to describe the entropy of the system to arrive at his formula in 1900. However, Boltzmann's work was not always readily accepted during his lifetime, and he faced opposition from some of his contemporaries, particularly in regard to the existence of atoms and molecules. Nevertheless, the validity and importance of his ideas were eventually recognized, and they have since become cornerstones of modern physics. Here, we delve into some aspects of Boltzmann's legacy and his influence on various areas of science.

Atomic theory and the existence of atoms and molecules

Boltzmann's kinetic theory of gases was one of the first attempts to explain macroscopic properties, such as pressure and temperature, in terms of the behaviour of individual atoms and molecules. Although many chemists were already accepting the existence of atoms and molecules, the broader physics community took some time to embrace this view. Boltzmann's long-running dispute with the editor of a prominent German physics journal over the acceptance of atoms and molecules underscores the initial resistance to this idea.

It was only after experiments, such as Jean Perrin's studies of colloidal suspensions, confirmed the values of the Avogadro constant and the Boltzmann constant that the existence of atoms and molecules gained wider acceptance. Boltzmann's kinetic theory played a crucial role in demonstrating the reality of atoms and molecules and explaining various phenomena in gases, liquids, and solids.

Statistical mechanics and the Boltzmann constant

Statistical mechanics, which Boltzmann pioneered, connects macroscopic observations with microscopic behaviors. His statistical explanation of the second law of thermodynamics was a significant achievement, and he provided the current definition of entropy ( $S = k_{B} \ln Ω$ ), where $k B$ is the Boltzmann constant and Ω is the number of microstates corresponding to a given macrostate.

Max Planck later named the constant $k B$ as the Boltzmann constant in honor of Boltzmann's contributions to statistical mechanics. The Boltzmann constant is now a fundamental constant in physics and across many scientific disciplines.

Boltzmann equation and modern uses

Because the Boltzmann equation is practical in solving problems in rarefied or dilute gases, it has been used in many diverse areas of technology. It has been used to calculate Space Shuttle re-entry in the upper atmosphere. It is the basis for Neutron transport theory, and ion transport in Semiconductors.

Influence on quantum mechanics

Boltzmann's work in statistical mechanics laid the groundwork for understanding the statistical behavior of particles in systems with a large number of degrees of freedom. In his paper published in 1877, he used discrete energy levels of physical systems as a mathematical device and went on to show that the same approach could be applied to continuous systems. This might be seen as a forerunner to the development of quantum mechanics. One biographer of Boltzmann says that Boltzmann’s approach “pav[ed] the way for Planck.”

Quantization of energy levels became a fundamental postulate in quantum mechanics, leading to groundbreaking theories like quantum electrodynamics and quantum field theory. Thus, Boltzmann's early insights into the quantization of energy levels had a profound influence on the development of quantum physics.

Awards and honours

In 1885 he became a member of the Imperial Austrian Academy of Sciences and in 1887 he became the President of the University of Graz. He was elected a member of the Royal Swedish Academy of Sciences in 1888 and a Foreign Member of the Royal Society (ForMemRS) in 1899. He was awarded honorary membership of the Manchester Literary and Philosophical Society in 1892. Numerous things are named in his honour.

Search This Blog