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Bioleaching

Bioleaching is the extraction or liberation of metals from their ores through the use of living organisms. Bioleaching is one of several applications within biohydrometallurgy and several methods are used to treat ores or concentrates containing copper, zinc, lead, arsenic, antimony, nickel, molybdenum, gold, silver, and cobalt.

Bioleaching falls into two broad categories. The first, is the use of microorganisms to oxidize refractory minerals to release valuable metals such and gold and silver. Most commonly the minerals that are the target of oxidization are pyrite and arsenopyrite.

The second category is leaching of sulphide minerals to release the associated metal, for example, leaching of pentlandite to release nickel, or the leaching of chalcocite, covellite or chalcopyrite to release copper.

Process
Bioleaching can involve numerous ferrous iron and sulfur oxidizing bacteria, including Acidithiobacillus ferrooxidans (formerly known as Thiobacillus ferrooxidans) and Acidithiobacillus thiooxidans  (formerly known as Thiobacillus thiooxidans). As a general principle, in one proposed method of bacterial leaching known as Indirect Leaching, Fe3+ ions are used to oxidize the ore. This step is entirely independent of microbes. The role of the bacteria is further oxidation of the ore, but also the regeneration of the chemical oxidant Fe3+ from Fe2+. For example, bacteria catalyse the breakdown of the mineral pyrite (FeS2) by oxidising the sulfur and metal (in this case ferrous iron, (Fe2+)) using oxygen. This yields soluble products that can be further purified and refined to yield the desired metal.

Pyrite leaching (FeS2): In the first step, disulfide is spontaneously oxidized to thiosulfate by ferric ion (Fe3+), which in turn is reduced to give ferrous ion (Fe2+):
 * (1)  $$\mathrm{FeS_2 + 6 \ Fe^{\,3+} + 3 \ H_2O \longrightarrow 7 \ Fe^{\,2+} + S_2O_3^{\,2-} + 6 \ H^+}$$    spontaneous

The ferrous ion is then oxidized by bacteria using oxygen:
 * (2)  $$\mathrm{4 \ Fe^{\,2+} + \ O_2 + 4 \ H^+ \longrightarrow 4 \ Fe^{\,3+} + 2 \ H_2O}$$    (iron oxidizers)

Thiosulfate is also oxidized by bacteria to give sulfate:
 * (3)  $$\mathrm{S_2O_3^{\,2-} + 2 \ O_2 + H_2O \longrightarrow 2 \ SO_4^{\,2-} + 2 \ H^+}$$    (sulfur oxidizers)

The ferric ion produced in reaction (2) oxidized more sulfide as in reaction (1), closing the cycle and given the net reaction:
 * (4) $$\mathrm{2 \ FeS_2 + 7 \ O_2 + 2 \ H_2O \longrightarrow 2 \ Fe^{\,2+} + 4 \ SO_4^{\,2-} + 4 \ H^+}$$

The net products of the reaction are soluble ferrous sulfate and sulfuric acid.

The microbial oxidation process occurs at the cell membrane of the bacteria. The electrons pass into the cells and are used in biochemical processes to produce energy for the bacteria while reducing oxygen to water. The critical reaction is the oxidation of sulfide by ferric iron. The main role of the bacterial step is the regeneration of this reactant.

The process for copper is very similar, but the efficiency and kinetics depend on the copper mineralogy. The most efficient minerals are supergene minerals such as chalcocite, Cu2S and covellite, CuS. The main copper mineral chalcopyrite (CuFeS2) is not leached very efficiently, which is why the dominant copper-producing technology remains flotation, followed by smelting and refining. The leaching of CuFeS2 follows the two stages of being dissolved and then further oxidised, with Cu2+ ions being left in solution.

Chalcopyrite leaching:
 * (1)  $$\mathrm{CuFeS_2 + 4 \ Fe^{\,3+} \longrightarrow Cu^{\,2+} + 5 \ Fe^{\,2+} + 2 \ S_0}$$    spontaneous
 * (2)  $$\mathrm{4 \ Fe^{\,2+} + O_2 + 4 \ H^+ \longrightarrow 4 \ Fe^{\,3+} + 2 \ H_2O}$$    (iron oxidizers)
 * (3)  $$\mathrm{2 \ S^0 + 3 \ O_2 + 2 \ H_2O \longrightarrow 2 \ SO_4^{\,2-} + 4 \ H^+}$$    (sulfur oxidizers)

net reaction:
 * (4) $$\mathrm{CuFeS_2 + 4 \ O_2 \longrightarrow Cu^{\,2+} + Fe^{\,2+} + 2 \ SO_4^{\,2-}}$$

In general, sulfides are first oxidized to elemental sulfur, whereas disulfides are oxidized to give thiosulfate, and the processes above can be applied to other sulfidic ores. Bioleaching of non-sulfidic ores such as pitchblende also uses ferric iron as an oxidant (e.g., UO2 + 2 Fe3+ ==> UO22+ + 2 Fe2+). In this case, the sole purpose of the bacterial step is the regeneration of Fe3+. Sulfidic iron ores can be added to speed up the process and provide a source of iron. Bioleaching of non-sulfidic ores by layering of waste sulfides and elemental sulfur, colonized by Acidithiobacillus spp., has been accomplished, which provides a strategy for accelerated leaching of materials that do not contain sulfide minerals.

Further processing
The dissolved copper (Cu2+) ions are removed from the solution by ligand exchange solvent extraction, which leaves other ions in the solution. The copper is removed by bonding to a ligand, which is a large molecule consisting of a number of smaller groups, each possessing a lone electron pair. The ligand-copper complex is extracted from the solution using an organic solvent such as kerosene:

 * Cu2+(aq) + 2LH(organic) → CuL2(organic) + 2H+(aq)

The ligand donates electrons to the copper, producing a complex - a central metal atom (copper) bonded to the ligand. Because this complex has no charge, it is no longer attracted to polar water molecules and dissolves in the kerosene, which is then easily separated from the solution. Because the initial reaction is reversible, it is determined by pH. Adding concentrated acid reverses the equation, and the copper ions go back into an aqueous solution.

Then the copper is passed through an electro-winning process to increase its purity: An electric current is passed through the resulting solution of copper ions. Because copper ions have a 2+ charge, they are attracted to the negative cathodes and collect there.

The copper can also be concentrated and separated by displacing the copper with Fe from scrap iron:

 * Cu2+(aq) + Fe(s) → Cu(s) + Fe2+(aq)

The electrons lost by the iron are taken up by the copper. Copper is the oxidising agent (it accepts electrons), and iron is the reducing agent (it loses electrons).

Traces of precious metals such as gold may be left in the original solution. Treating the mixture with sodium cyanide in the presence of free oxygen dissolves the gold. The gold is removed from the solution by adsorbing (taking it up on the surface) to charcoal.

With fungi
Several species of fungi can be used for bioleaching. Fungi can be grown on many different substrates, such as electronic scrap, catalytic converters, and fly ash from municipal waste incineration. Experiments have shown that two fungal strains (Aspergillus niger, Penicillium simplicissimum) were able to mobilize Cu and Sn by 65%, and Al, Ni, Pb, and Zn by more than 95%. Aspergillus niger can produce some organic acids such as citric acid. This form of leaching does not rely on microbial oxidation of metal but rather uses microbial metabolism as source of acids that directly dissolve the metal.

Economic feasibility
Bioleaching is in general simpler and, therefore, cheaper to operate and maintain than traditional processes, since fewer specialists are needed to operate complex chemical plants. And low concentrations are not a problem for bacteria because they simply ignore the waste that surrounds the metals, attaining extraction yields of over 90% in some cases. These microorganisms actually gain energy by breaking down minerals into their constituent elements. The company simply collects the ions out of the solution after the bacteria have finished.

Bioleaching can be used to extract metals from low concentration ores such as gold that are too poor for other technologies. It can be used to partially replace the extensive crushing and grinding that translates to prohibitive cost and energy consumption in a conventional process. Because the lower cost of bacterial leaching outweighs the time it takes to extract the metal.

High concentration ores, such as copper, are more economical to smelt rather bioleach due to the slow speed of the bacterial leaching process compared to smelting. The slow speed of bioleaching introduces a significant delay in cash flow for new mines. Nonetheless, at the largest copper mine of the world, Escondida in Chile the process seems to be favorable.

Economically it is also very expensive and many companies once started can not keep up with the demand and end up in debt.

In space
In 2020 scientists showed, with an experiment with different gravity environments on the ISS, that microorganisms could be employed to mine useful elements from basaltic rocks via bioleaching in space.

Environmental impact
The process is more environmentally friendly than traditional extraction methods. For the company this can translate into profit, since the necessary limiting of sulfur dioxide emissions during smelting is expensive. Less landscape damage occurs, since the bacteria involved grow naturally, and the mine and surrounding area can be left relatively untouched. As the bacteria breed in the conditions of the mine, they are easily cultivated and recycled.

Toxic chemicals are sometimes produced in the process. Sulfuric acid and H+ ions that have been formed can leak into the ground and surface water turning it acidic, causing environmental damage. Heavy ions such as iron, zinc, and arsenic leak during acid mine drainage. When the pH of this solution rises, as a result of dilution by fresh water, these ions precipitate, forming "Yellow Boy" pollution. For these reasons, a setup of bioleaching must be carefully planned, since the process can lead to a biosafety failure. Unlike other methods, once started, bioheap leaching cannot be quickly stopped, because leaching would still continue with rainwater and natural bacteria. Projects like Finnish Talvivaara proved to be environmentally and economically disastrous.

title: Bioleaching


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Bouldering

Bouldering is a form of free climbing that is performed on small rock formations or artificial rock walls without the use of ropes or harnesses. While bouldering can be done without any equipment, most climbers use climbing shoes to help secure footholds, chalk to keep their hands dry and to provide a firmer grip, and bouldering mats to prevent injuries from falls. Unlike free solo climbing, which is also performed without ropes, bouldering problems (the sequence of moves that a climber performs to complete the climb) are usually less than 6 m tall. Traverses, which are a form of boulder problem, require the climber to climb horizontally from one end to another. Artificial climbing walls allow boulderers to climb indoors in areas without natural boulders. In addition, bouldering competitions take place in both indoor and outdoor settings.

The sport was originally a method of training for roped climbs and mountaineering, so climbers could practice specific moves at a safe distance from the ground. Additionally, the sport served to build stamina and increase finger strength. Throughout the 20th century, bouldering evolved into a separate discipline. Individual problems are assigned ratings based on difficulty. Although there have been various rating systems used throughout the history of bouldering, modern problems usually use either the V-scale or the Fontainebleau scale.

The growing popularity of bouldering has caused several environmental concerns, including soil erosion and trampled vegetation, as climbers often hike off-trail to reach bouldering sites. This has caused some landowners to restrict access or prohibit bouldering altogether.

Outdoor bouldering

The characteristics of boulder problems depend largely on the type of rock being climbed. For example, granite often features long cracks and slabs while sandstone rocks are known for their steep overhangs and frequent horizontal breaks. Limestone and volcanic rock are also used for bouldering.

There are many prominent bouldering areas throughout the United States, including Hueco Tanks in Texas, Mount Blue Sky in Colorado, The Appalachian Mountains in The Eastern United States, and The Buttermilks in Bishop, California. Squamish, British Columbia is one of the most popular bouldering areas in Canada. Europe is also home to a number of bouldering sites, such as Fontainebleau in France, Meschia in Italy, Albarracín in Spain, and various mountains throughout Switzerland. Africa's most prominent bouldering areas include the more established Rocklands, South Africa, the newer Oukaïmeden in Morocco or more recently opened areas like Chimanimani in Zimbabwe.

Indoor bouldering

Artificial climbing walls are used to simulate boulder problems in an indoor environment, usually at climbing gyms. These walls are constructed with wooden panels, polymer cement panels, concrete shells, or precast molds of actual rock walls. Holds, usually made of plastic, are then bolted onto the wall to create problems. Some problems use steep overhanging surfaces which force the climber to support much of their weight using their upper body strength. Other problems are set on flat walls; Instead of requiring upper body strength, these problems create difficulty by requiring the climber to execute a series of predetermined movements to complete the route. The IFSC Climbing World Championships have noticeably included more of such problems in their competitions as of late.

Climbing gyms often feature multiple problems within the same section of wall. Historically, the most common method route-setters used to designate the intended problem was by placing colored tape next to each hold. For example, red tape would indicate one bouldering problem while green tape would be used to set a different problem in the same area. Today, it is more common for problems and grades to be designated using a set color of plastic hold to indicate problems and their difficulty levels. Using colored holds to set has certain advantages, the most notable of which are that it makes it more obvious where the holds for a problem are, and that there is no chance of tape being accidentally kicked off footholds. Smaller, resource-poor climbing gyms may prefer taped problems because large, expensive holds can be used in multiple routes by marking them with more than one color of tape. The tape indicates the hold(s) that the athlete should grab first.

Indoor bouldering requires very little in terms of equipment: at minimum, climbing shoes; at maximum, a chalk bag, chalk, a brush, and climbing shoes.

Grading

Bouldering problems are assigned numerical difficulty ratings by route-setters and climbers. The two most widely used rating systems are the V-scale and the Fontainebleau system.

The V-scale, which originated in the United States, is an open-ended rating system with higher numbers indicating a higher degree of difficulty. The V1 rating indicates that a problem can be completed by a novice climber in good physical condition after several attempts. The scale begins at V0, and as of 2013, the highest V rating that has been assigned to a bouldering problem is V17. Some climbing gyms also use a VB grade to indicate beginner problems.

The Fontainebleau scale follows a similar system, with each numerical grade divided into three ratings with the letters a, b, and c. For example, Fontainebleau 7A roughly corresponds with V6, while Fontainebleau 7C+ is equivalent to V10. In both systems, grades are further differentiated by appending "+" to indicate a small increase in difficulty. Despite this level of specificity, ratings of individual problems are often controversial, as ability level is not the only factor that affects how difficult a problem may be for a particular climber. Height, arm length, flexibility, and other body characteristics can also affect difficulty.

Highball bouldering
Highball bouldering is defined as climbing high, difficult, long, and tall boulders, using the same protection as standard bouldering. This form of bouldering adds an additional requirement of mental focus to the existing test of physical strength and skill. Highballing, like most of climbing, is open to interpretation. Most climbers say anything above 15 ft is a highball and can range in height up to 35-40 ft where highball bouldering then turns into free soloing.

Highball bouldering may have begun in 1961 when John Gill, without top-rope rehearsal, bouldered a steep face on a 37 ft granite spire called The Thimble. The difficulty level of this ascent (V4/5 or 5.12a) was extraordinary for that time. Gill's achievement initiated a wave of climbers making ascents of large boulders. Later, with the introduction and evolution of crash pads, climbers were able to push the limits of highball bouldering ever higher.

In 2002 Jason Kehl completed the first highball at double-digit V-difficulty, called Evilution, a 55 ft boulder in the Buttermilks of California, earning the grade of V12. This climb marked the beginning of a new generation of highball climbing that pushed not only height but great difficulty. It is not unusual for climbers to rehearse such risky problems on top-rope, although this practice is not a settled issue.

Important milestone ascents in this style include:

 * Ambrosia, V11, a 55 ft boulder in Bishop, California, climbed by Kevin Jorgeson in 2015.
 * Too Big to Flail, V10, another 55 ft line in Bishop, California, climbed by Alex Honnold in 2016.
 * Livin' Large, V15, a 35 ft boulder in Rocklands, South Africa, found and established by Nalle Hukkataival in 2009.
 * The Process, V16, a 55 ft boulder in Bishop, California, first climbed by Daniel Woods in 2015.

Competition bouldering

Traditionally, competition in bouldering was informal, with climbers working out problems near the limits of their abilities, then challenging their peers to repeat these accomplishments. However, modern climbing gyms allow for a more formal competitive structure.

The International Federation of Sport Climbing (IFSC) employs an indoor format (although competitions can also take place in an outdoor setting ) that breaks the competition into three rounds: qualifications, semi-finals, and finals. The rounds feature different sets of four to six boulder problems, and each competitor has a fixed amount of time to attempt each problem. At the end of each round, competitors are ranked by the number of completed problems with ties settled by the total number of attempts taken to solve the problems.

Some competitions only permit climbers a fixed number of attempts at each problem with a timed rest period in between. In an open-format competition, all climbers compete simultaneously, and are given a fixed amount of time to complete as many problems as possible. More points are awarded for more difficult problems, while points are deducted for multiple attempts on the same problem.

In 2012, the IFSC submitted a proposal to the International Olympic Committee (IOC) to include lead climbing in the 2020 Summer Olympics. The proposal was later revised to an "overall" competition, which would feature bouldering, lead climbing, and speed climbing. In May 2013, the IOC announced that climbing would not be added to the 2020 Olympic program.

In 2016, the International Olympic Committee (IOC) officially approved climbing as an Olympic sport "in order to appeal to younger audiences." The Olympics featured the earlier proposed overall competition. Medalists competed in all three categories for a best overall score. The score is calculated by the multiplication of the positions that the climbers have attained in each discipline of climbing.

History
Rock climbing first appeared as a sport in the late 1800s. Early records describe climbers engaging in what is now referred to as bouldering, not as a separate discipline, but as a playful form of training for larger ascents. It was during this time that the words "bouldering" and "problem" first appeared in British climbing literature. Oscar Eckenstein was an early proponent of the activity in the British Isles. In the early 20th century, the Fontainebleau area of France established itself as a prominent climbing area, where some of the first dedicated bleausards (or "boulderers") emerged. One of those athletes, Pierre Allain, invented the specialized shoe used for rock climbing.

Modern bouldering
In the late 1950s through the 1960s, American mathematician John Gill pushed the sport further and contributed several important innovations, distinguishing bouldering as a separate discipline in the process. Gill previously pursued gymnastics, a sport which had an established scale of difficulty for movements and body positions, and shifted the focus of bouldering from reaching the summit to navigating a set of holds. Gill developed a rating system that was closed-ended: B1 problems were as difficult as the most challenging roped routes of the time, B2 problems were more difficult, and B3 problems had been completed once.

Gill introduced chalk as a method of keeping the climber's hands dry, promoted a dynamic climbing style, and emphasized the importance of strength training to complement skill. As Gill improved in ability and influence, his ideas became the norm.

In the 1980s, two important training tools emerged. One important training tool was bouldering mats, also referred to as "crash pads", which protected against injuries from falling and enabled boulderers to climb in areas that would have been too dangerous otherwise. The second important tool was indoor climbing walls, which helped spread the sport to areas without outdoor climbing and allowed serious climbers to train year-round.

As the sport grew in popularity, new bouldering areas were developed throughout Europe and the United States, and more athletes began participating in bouldering competitions. The visibility of the sport greatly increased in the early 2000s, as YouTube videos and climbing blogs helped boulderers around the world to quickly learn techniques, find hard problems, and announce newly completed projects.

Notable ascents
Notable boulder climbs are chronicled by the climbing media to track progress in boulder climbing standards and levels of technical difficulty; in contrast, the hardest traditional climbing routes tend to be of lower technical difficulty due to the additional burden of having to place protection during the course of the climb, and due to the lack of any possibility of using natural protection on the most extreme climbs.

As of November 2022, the world's hardest bouldering routes are Burden of Dreams by Nalle Hukkataival and Return of the Sleepwalker by Daniel Woods, both at proposed grades of. There are a number of routes with a confirmed climbing grade of, the first of which was Gioia by Christian Core in 2008 (and confirmed by Adam Ondra in 2011).

As of December 2021, female climbers Josune Bereziartu, Ashima Shiraishi, and Kaddi Lehmann have repeated boulder problems at the boulder grade. On July 28, 2023, Katie Lamb repeated Box Therapy at Rocky Mountain National Park, which at the time was graded making Katie the first female to climb 8C+. However, after Brooke Raboutou repeated the climb In October 2023 along with consensus of first ascensionist Daniel Woods and second acenstionist Drew Ruana, the boulder was ultimately downgraded to. This made Katie Lamb the fourth female to climb and Brooke the fifth.

Equipment
Unlike other climbing sports, bouldering can be performed safely and effectively with very little equipment, an aspect which makes the discipline highly appealing, but opinions differ. While bouldering pioneer John Sherman asserted that "The only gear really needed to go bouldering is boulders," others suggest the use of climbing shoes and a chalkbag – a small pouch where ground-up chalk is kept – as the bare minimum, and more experienced boulderers typically bring multiple pairs of climbing shoes, chalk, brushes, crash pads, and a skincare kit.

Climbing shoes have the most direct impact on performance. Besides protecting the climber's feet from rough surfaces, climbing shoes are designed to help the climber secure footholds. Climbing shoes typically fit much tighter than other athletic footwear and often curl the toes downwards to enable precise footwork. They are manufactured in a variety of different styles to perform in different situations. For example, High-top shoes provide better protection for the ankle, while low-top shoes provide greater flexibility and freedom of movement. Stiffer shoes excel at securing small edges, whereas softer shoes provide greater sensitivity. The front of the shoe, called the "toe box", can be asymmetric, which performs well on overhanging rocks, or symmetric, which is better suited for vertical problems and slabs.

To absorb sweat, most boulderers use gymnastics chalk on their hands, stored in a chalkbag, which can be tied around the waist (also called sport climbing chalkbags), allowing the climber to reapply chalk during the climb. There are also versions of floor chalkbags (also called bouldering chalkbags), which are usually bigger than sport climbing chalkbags and are meant to be kept on the floor while climbing; this is because boulders do not usually have so many movements as to require chalking up more than once. Different sizes of brushes are used to remove excess chalk and debris from boulders in between climbs; they are often attached to the end of a long straight object in order to reach higher holds. Crash pads, also referred to as bouldering mats, are foam cushions placed on the ground to protect climbers from injury after falling.

Boulder problems are generally shorter than 20 ft from ground to top. This makes the sport significantly safer than free solo climbing, which is also performed without ropes, but with no upper limit on the height of the climb. However, minor injuries are common in bouldering, particularly sprained ankles and wrists. Two factors contribute to the frequency of injuries in bouldering: first, boulder problems typically feature more difficult moves than other climbing disciplines, making falls more common. Second, without ropes to arrest the climber's descent, every fall will cause the climber to hit the ground.

To prevent injuries, boulderers position crash pads near the boulder to provide a softer landing, as well as one or more spotters (people watching out for the climber to fall in convenient position) to help redirect the climber towards the pads. Upon landing, boulderers employ falling techniques similar to those used in gymnastics: spreading the impact across the entire body to avoid bone fractures, and positioning limbs to allow joints to move freely throughout the impact.

Techniques
Although every type of rock climbing requires a high level of strength and technique, bouldering is the most dynamic form of the sport, requiring the highest level of power and placing considerable strain on the body. Training routines that strengthen fingers and forearms are useful in preventing injuries such as tendonitis and ruptured ligaments.

However, as with other forms of climbing, bouldering technique begins with proper footwork. Leg muscles are significantly stronger than arm muscles; thus, proficient boulderers use their arms to maintain balance and body positioning as much as possible, relying on their legs to push them up the rock. Boulderers also keep their arms straight with their shoulders engaged whenever feasible, allowing their bones to support their body weight rather than their muscles.

Bouldering movements are described as either "static" or "dynamic". Static movements are those that are performed slowly, with the climber's position controlled by maintaining contact on the boulder with the other three limbs. Dynamic movements use the climber's momentum to reach holds that would be difficult or impossible to secure statically, with an increased risk of falling if the movement is not performed accurately.

Environmental impact
Bouldering can damage vegetation that grows on rocks, such as moss and lichens. This can occur as a result of the climber intentionally cleaning the boulder, or unintentionally from repeated use of handholds and footholds. Vegetation on the ground surrounding the boulder can also be damaged from overuse, particularly by climbers laying down crash pads. Soil erosion can occur when boulderers trample vegetation while hiking off of established trails, or when they unearth small rocks near the boulder in an effort to make the landing zone safer in case of a fall. The repeated use of white climbing chalk can damage the rock surface of boulders and cliffs, particularly sandstone and other porous rock types, and the scrubbing of rocks to remove chalk can also degrade the rock surface. In order to prevent chalk from damaging the surface of the rock, it is important to remove it gently with a brush after a rock climbing session. Other environmental concerns include littering, improperly disposed feces, and graffiti. These issues have caused some land managers to prohibit bouldering, as was the case in Tea Garden, a popular bouldering area in Rocklands, South Africa.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Bouldering


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Boiling point

The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.

The boiling point of a liquid varies depending upon the surrounding environmental pressure. A liquid in a partial vacuum, i.e., under a lower pressure, has a lower boiling point than when that liquid is at atmospheric pressure. Because of this, water boils at 100°C (or with scientific precision: 99.97 C) under standard pressure at sea level, but at 93.4 C at 1905 m altitude. For a given pressure, different liquids will boil at different temperatures.

The normal boiling point (also called the atmospheric boiling point or the atmospheric pressure boiling point) of a liquid is the special case in which the vapor pressure of the liquid equals the defined atmospheric pressure at sea level, one atmosphere. At that temperature, the vapor pressure of the liquid becomes sufficient to overcome atmospheric pressure and allow bubbles of vapor to form inside the bulk of the liquid. The standard boiling point has been defined by IUPAC since 1982 as the temperature at which boiling occurs under a pressure of one bar.

The heat of vaporization is the energy required to transform a given quantity (a mol, kg, pound, etc.) of a substance from a liquid into a gas at a given pressure (often atmospheric pressure).

Liquids may change to a vapor at temperatures below their boiling points through the process of evaporation. Evaporation is a surface phenomenon in which molecules located near the liquid's edge, not contained by enough liquid pressure on that side, escape into the surroundings as vapor. On the other hand, boiling is a process in which molecules anywhere in the liquid escape, resulting in the formation of vapor bubbles within the liquid.

Saturation temperature and pressure

A saturated liquid contains as much thermal energy as it can without boiling (or conversely a saturated vapor contains as little thermal energy as it can without condensing).

Saturation temperature means boiling point. The saturation temperature is the temperature for a corresponding saturation pressure at which a liquid boils into its vapor phase. The liquid can be said to be saturated with thermal energy. Any addition of thermal energy results in a phase transition.

If the pressure in a system remains constant (isobaric), a vapor at saturation temperature will begin to condense into its liquid phase as thermal energy (heat) is removed. Similarly, a liquid at saturation temperature and pressure will boil into its vapor phase as additional thermal energy is applied.

The boiling point corresponds to the temperature at which the vapor pressure of the liquid equals the surrounding environmental pressure. Thus, the boiling point is dependent on the pressure. Boiling points may be published with respect to the NIST, USA standard pressure of 101.325 kPa (or 1 atm), or the IUPAC standard pressure of 100.000 kPa. At higher elevations, where the atmospheric pressure is much lower, the boiling point is also lower. The boiling point increases with increased pressure up to the critical point, where the gas and liquid properties become identical. The boiling point cannot be increased beyond the critical point. Likewise, the boiling point decreases with decreasing pressure until the triple point is reached. The boiling point cannot be reduced below the triple point.

If the heat of vaporization and the vapor pressure of a liquid at a certain temperature are known, the boiling point can be calculated by using the Clausius–Clapeyron equation, thus:

 * $$T_\text{B} = \left(\frac{1}{T_0} - \frac{R\,\ln \frac{P}{P_0}}{\Delta H_\text{vap}}\right)^{-1}$$

where:
 * $$T_\text{B}$$ is the boiling point at the pressure of interest,
 * $$R$$ is the ideal gas constant,
 * $$P$$ is the vapor pressure of the liquid,
 * $$P_0$$ is some pressure where the corresponding $$T_0$$ is known (usually data available at 1 atm or 100 kPa),
 * $$\Delta H_\text{vap}$$ is the heat of vaporization of the liquid,
 * $$T_0$$ is the boiling temperature,
 * $$\ln$$ is the natural logarithm.

Saturation pressure is the pressure for a corresponding saturation temperature at which a liquid boils into its vapor phase. Saturation pressure and saturation temperature have a direct relationship: as saturation pressure is increased, so is saturation temperature.

If the temperature in a system remains constant (an isothermal system), vapor at saturation pressure and temperature will begin to condense into its liquid phase as the system pressure is increased. Similarly, a liquid at saturation pressure and temperature will tend to flash into its vapor phase as system pressure is decreased.

There are two conventions regarding the standard boiling point of water: The normal boiling point is 99.97 °C at a pressure of 1 atm (i.e., 101.325 kPa). The IUPAC-recommended standard boiling point of water at a standard pressure of 100 kPa (1 bar) is 99.61 °C. For comparison, on top of Mount Everest, at 8848 m elevation, the pressure is about 34 kPa and the boiling point of water is 71 °C. The Celsius temperature scale was defined until 1954 by two points: 0 °C being defined by the water freezing point and 100 °C being defined by the water boiling point at standard atmospheric pressure.

Relation between the normal boiling point and the vapor pressure of liquids

The higher the vapor pressure of a liquid at a given temperature, the lower the normal boiling point (i.e., the boiling point at atmospheric pressure) of the liquid.

The vapor pressure chart to the right has graphs of the vapor pressures versus temperatures for a variety of liquids. As can be seen in the chart, the liquids with the highest vapor pressures have the lowest normal boiling points.

For example, at any given temperature, methyl chloride has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point (−24.2 °C), which is where the vapor pressure curve of methyl chloride (the blue line) intersects the horizontal pressure line of one atmosphere (atm) of absolute vapor pressure.

The critical point of a liquid is the highest temperature (and pressure) it will actually boil at.

See also Vapour pressure of water.

Boiling point of chemical elements
The element with the lowest boiling point is helium. Both the boiling points of rhenium and tungsten exceed 5000 K at standard pressure; because it is difficult to measure extreme temperatures precisely without bias, both have been cited in the literature as having the higher boiling point.

Boiling point as a reference property of a pure compound
As can be seen from the above plot of the logarithm of the vapor pressure vs. the temperature for any given pure chemical compound, its normal boiling point can serve as an indication of that compound's overall volatility. A given pure compound has only one normal boiling point, if any, and a compound's normal boiling point and melting point can serve as characteristic physical properties for that compound, listed in reference books. The higher a compound's normal boiling point, the less volatile that compound is overall, and conversely, the lower a compound's normal boiling point, the more volatile that compound is overall. Some compounds decompose at higher temperatures before reaching their normal boiling point, or sometimes even their melting point. For a stable compound, the boiling point ranges from its triple point to its critical point, depending on the external pressure. Beyond its triple point, a compound's normal boiling point, if any, is higher than its melting point. Beyond the critical point, a compound's liquid and vapor phases merge into one phase, which may be called a superheated gas. At any given temperature, if a compound's normal boiling point is lower, then that compound will generally exist as a gas at atmospheric external pressure. If the compound's normal boiling point is higher, then that compound can exist as a liquid or solid at that given temperature at atmospheric external pressure, and will so exist in equilibrium with its vapor (if volatile) if its vapors are contained. If a compound's vapors are not contained, then some volatile compounds can eventually evaporate away in spite of their higher boiling points.

In general, compounds with ionic bonds have high normal boiling points, if they do not decompose before reaching such high temperatures. Many metals have high boiling points, but not all. Very generally—with other factors being equal—in compounds with covalently bonded molecules, as the size of the molecule (or molecular mass) increases, the normal boiling point increases. When the molecular size becomes that of a macromolecule, polymer, or otherwise very large, the compound often decomposes at high temperature before the boiling point is reached. Another factor that affects the normal boiling point of a compound is the polarity of its molecules. As the polarity of a compound's molecules increases, its normal boiling point increases, other factors being equal. Closely related is the ability of a molecule to form hydrogen bonds (in the liquid state), which makes it harder for molecules to leave the liquid state and thus increases the normal boiling point of the compound. Simple carboxylic acids dimerize by forming hydrogen bonds between molecules. A minor factor affecting boiling points is the shape of a molecule. Making the shape of a molecule more compact tends to lower the normal boiling point slightly compared to an equivalent molecule with more surface area.

Most volatile compounds (anywhere near ambient temperatures) go through an intermediate liquid phase while warming up from a solid phase to eventually transform to a vapor phase. By comparison to boiling, a sublimation is a physical transformation in which a solid turns directly into vapor, which happens in a few select cases such as with carbon dioxide at atmospheric pressure. For such compounds, a sublimation point is a temperature at which a solid turning directly into vapor has a vapor pressure equal to the external pressure.

Impurities and mixtures
In the preceding section, boiling points of pure compounds were covered. Vapor pressures and boiling points of substances can be affected by the presence of dissolved impurities (solutes) or other miscible compounds, the degree of effect depending on the concentration of the impurities or other compounds. The presence of non-volatile impurities such as salts or compounds of a volatility far lower than the main component compound decreases its mole fraction and the solution's volatility, and thus raises the normal boiling point in proportion to the concentration of the solutes. This effect is called boiling point elevation. As a common example, salt water boils at a higher temperature than pure water.

In other mixtures of miscible compounds (components), there may be two or more components of varying volatility, each having its own pure component boiling point at any given pressure. The presence of other volatile components in a mixture affects the vapor pressures and thus boiling points and dew points of all the components in the mixture. The dew point is a temperature at which a vapor condenses into a liquid. Furthermore, at any given temperature, the composition of the vapor is different from the composition of the liquid in most such cases. In order to illustrate these effects between the volatile components in a mixture, a boiling point diagram is commonly used. Distillation is a process of boiling and [usually] condensation which takes advantage of these differences in composition between liquid and vapor phases.

title: Boiling point


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Big Bang

The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. It was first proposed as a physical theory in 1931 by Roman Catholic priest and physicist Georges Lemaître when he suggested the universe emerged from a "primeval atom". Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The uniformity of the universe, known as the flatness problem, is explained through cosmic inflation: a sudden and very rapid expansion of space during the earliest moments.

Crucially, these models are compatible with the Hubble–Lemaître law—the observation that the farther away a galaxy is, the faster it is moving away from Earth. Extrapolating this cosmic expansion backward in time using the known laws of physics, the models describe an increasingly concentrated cosmos preceded by a singularity in which space and time lose meaning (typically named "the Big Bang singularity"). Physics lacks a widely accepted theory of quantum gravity that can model the earliest conditions of the Big Bang. In 1964 the CMB was discovered, which convinced many cosmologists that the competing steady-state model of cosmic evolution was falsified, since the Big Bang models predict a uniform background radiation caused by high temperatures and densities in the distant past. A wide range of empirical evidence strongly favors the Big Bang event, which is now essentially universally accepted. Detailed measurements of the expansion rate of the universe place the Big Bang singularity at an estimated $13.787$ billion years ago, which is considered the age of the universe.

There remain aspects of the observed universe that are not yet adequately explained by the Big Bang models. After its initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, and later atoms. The unequal abundances of matter and antimatter that allowed this to occur is an unexplained effect known as baryon asymmetry. These primordial elements—mostly hydrogen, with some helium and lithium—later coalesced through gravity, forming early stars and galaxies. Astronomers observe the gravitational effects of an unknown dark matter surrounding galaxies. Most of the gravitational potential in the universe seems to be in this form, and the Big Bang models and various observations indicate that this excess gravitational potential is not created by baryonic matter, such as normal atoms. Measurements of the redshifts of supernovae indicate that the expansion of the universe is accelerating, an observation attributed to an unexplained phenomenon known as dark energy.

Features of the models
The Big Bang models offer a comprehensive explanation for a broad range of observed phenomena, including the abundances of the light elements, the CMB, large-scale structure, and Hubble's law. The models depend on two major assumptions: the universality of physical laws and the cosmological principle. The universality of physical laws is one of the underlying principles of the theory of relativity. The cosmological principle states that on large scales the universe is homogeneous and isotropic—appearing the same in all directions regardless of location.

These ideas were initially taken as postulates, but later efforts were made to test each of them. For example, the first assumption has been tested by observations showing that the largest possible deviation of the fine-structure constant over much of the age of the universe is of order 10−5. Also, general relativity has passed stringent tests on the scale of the Solar System and binary stars.

The large-scale universe appears isotropic as viewed from Earth. If it is indeed isotropic, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred (or special) observer or vantage point. To this end, the cosmological principle has been confirmed to a level of 10−5 via observations of the temperature of the CMB. At the scale of the CMB horizon, the universe has been measured to be homogeneous with an upper bound on the order of 10% inhomogeneity, as of 1995.

Horizons
An important feature of the Big Bang spacetime is the presence of particle horizons. Since the universe has a finite age, and light travels at a finite speed, there may be events in the past whose light has not yet had time to reach earth. This places a limit or a past horizon on the most distant objects that can be observed. Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never "catch up" to very distant objects. This defines a future horizon, which limits the events in the future that we will be able to influence. The presence of either type of horizon depends on the details of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric that describes the expansion of the universe.

Our understanding of the universe back to very early times suggests that there is a past horizon, though in practice our view is also limited by the opacity of the universe at early times. So our view cannot extend further backward in time, though the horizon recedes in space. If the expansion of the universe continues to accelerate, there is a future horizon as well.

Thermalization
Some processes in the early universe occurred too slowly, compared to the expansion rate of the universe, to reach approximate thermodynamic equilibrium. Others were fast enough to reach thermalization. The parameter usually used to find out whether a process in the very early universe has reached thermal equilibrium is the ratio between the rate of the process (usually rate of collisions between particles) and the Hubble parameter. The larger the ratio, the more time particles had to thermalize before they were too far away from each other.

Timeline
According to the Big Bang models, the universe at the beginning was very hot and very compact, and since then it has been expanding and cooling.

Singularity
In the absence of a perfect cosmological principle, extrapolation of the expansion of the universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. This irregular behavior, known as the gravitational singularity, indicates that general relativity is not an adequate description of the laws of physics in this regime. Models based on general relativity alone cannot fully extrapolate toward the singularity. In some proposals, such as the emergent Universe models, the singularity is replaced by another cosmological epoch. A different approach identifies the initial singularity as a singularity predicted by some models of the Big Bang theory to have existed before the Big Bang event.

This primordial singularity is itself sometimes called "the Big Bang", but the term can also refer to a more generic early hot, dense phase of the universe. In either case, "the Big Bang" as an event is also colloquially referred to as the "birth" of our universe since it represents the point in history where the universe can be verified to have entered into a regime where the laws of physics as we understand them (specifically general relativity and the Standard Model of particle physics) work. Based on measurements of the expansion using Type Ia supernovae and measurements of temperature fluctuations in the cosmic microwave background, the time that has passed since that event—known as the "age of the universe"—is 13.8 billion years.

Despite being extremely dense at this time—far denser than is usually required to form a black hole—the universe did not re-collapse into a singularity. Commonly used calculations and limits for explaining gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not apply to rapidly expanding space such as the Big Bang. Since the early universe did not immediately collapse into a multitude of black holes, matter at that time must have been very evenly distributed with a negligible density gradient.

Inflation and baryogenesis
The earliest phases of the Big Bang are subject to much speculation, given the lack of available data. In the most common models the universe was filled homogeneously and isotropically with a very high energy density and huge temperatures and pressures, and was very rapidly expanding and cooling. The period up to 10−43 seconds into the expansion, the Planck epoch, was a phase in which the four fundamental forces—the electromagnetic force, the strong nuclear force, the weak nuclear force, and the gravitational force, were unified as one. In this stage, the characteristic scale length of the universe was the Planck length, $1.6 m$, and consequently had a temperature of approximately 1032 degrees Celsius. Even the very concept of a particle breaks down in these conditions. A proper understanding of this period awaits the development of a theory of quantum gravity. The Planck epoch was succeeded by the grand unification epoch beginning at 10−43 seconds, where gravitation separated from the other forces as the universe's temperature fell.

At approximately 10−37 seconds into the expansion, a phase transition caused a cosmic inflation, during which the universe grew exponentially, unconstrained by the light speed invariance, and temperatures dropped by a factor of 100,000. This concept is motivated by the flatness problem, where the density of matter and energy is very close to the critical density needed to produce a flat universe. That is, the shape of the universe has no overall geometric curvature due to gravitational influence. Microscopic quantum fluctuations that occurred because of Heisenberg's uncertainty principle were "frozen in" by inflation, becoming amplified into the seeds that would later form the large-scale structure of the universe. At a time around 10−36 seconds, the electroweak epoch begins when the strong nuclear force separates from the other forces, with only the electromagnetic force and weak nuclear force remaining unified.

Inflation stopped locally at around 10−33 to 10−32 seconds, with the observable universe's volume having increased by a factor of at least 1078. Reheating followed as the inflaton field decayed, until the universe obtained the temperatures required for the production of a quark–gluon plasma as well as all other elementary particles. Temperatures were so high that the random motions of particles were at relativistic speeds, and particle–antiparticle pairs of all kinds were being continuously created and destroyed in collisions. At some point, an unknown reaction called baryogenesis violated the conservation of baryon number, leading to a very small excess of quarks and leptons over antiquarks and antileptons—of the order of one part in 30 million. This resulted in the predominance of matter over antimatter in the present universe.

Cooling
The universe continued to decrease in density and fall in temperature, hence the typical energy of each particle was decreasing. Symmetry-breaking phase transitions put the fundamental forces of physics and the parameters of elementary particles into their present form, with the electromagnetic force and weak nuclear force separating at about 10−12 seconds.

After about 10−11 seconds, the picture becomes less speculative, since particle energies drop to values that can be attained in particle accelerators. At about 10−6 seconds, quarks and gluons combined to form baryons such as protons and neutrons. The small excess of quarks over antiquarks led to a small excess of baryons over antibaryons. The temperature was no longer high enough to create either new proton–antiproton or neutron–antineutron pairs. A mass annihilation immediately followed, leaving just one in 108 of the original matter particles and none of their antiparticles. A similar process happened at about 1 second for electrons and positrons. After these annihilations, the remaining protons, neutrons and electrons were no longer moving relativistically and the energy density of the universe was dominated by photons (with a minor contribution from neutrinos).

A few minutes into the expansion, when the temperature was about a billion kelvin and the density of matter in the universe was comparable to the current density of Earth's atmosphere, neutrons combined with protons to form the universe's deuterium and helium nuclei in a process called Big Bang nucleosynthesis (BBN). Most protons remained uncombined as hydrogen nuclei.

As the universe cooled, the rest energy density of matter came to gravitationally dominate that of the photon radiation. The recombination epoch began after about 379,000 years, when the electrons and nuclei combined into atoms (mostly hydrogen), which were able to emit radiation. This relic radiation, which continued through space largely unimpeded, is known as the cosmic microwave background.

Structure formation
After the recombination epoch, the slightly denser regions of the uniformly distributed matter gravitationally attracted nearby matter and thus grew even denser, forming gas clouds, stars, galaxies, and the other astronomical structures observable today. The details of this process depend on the amount and type of matter in the universe. The four possible types of matter are known as cold dark matter (CDM), warm dark matter, hot dark matter, and baryonic matter. The best measurements available, from the Wilkinson Microwave Anisotropy Probe (WMAP), show that the data is well-fit by a Lambda-CDM model in which dark matter is assumed to be cold. (Warm dark matter is ruled out by early reionization.) This CDM is estimated to make up about 23% of the matter/energy of the universe, while baryonic matter makes up about 4.6%.

In an "extended model" which includes hot dark matter in the form of neutrinos, then the "physical baryon density" $$\Omega _\text{b} h^2$$ is estimated at 0.023. (This is different from the 'baryon density' $$\Omega _\text{b}$$ expressed as a fraction of the total matter/energy density, which is about 0.046.) The corresponding cold dark matter density $$\Omega _\text{c} h^2$$ is about 0.11, and the corresponding neutrino density $$\Omega _\text{v} h^2$$ is estimated to be less than 0.0062.

Cosmic acceleration
Independent lines of evidence from Type Ia supernovae and the CMB imply that the universe today is dominated by a mysterious form of energy known as dark energy, which appears to homogeneously permeate all of space. Observations suggest that 73% of the total energy density of the present day universe is in this form. When the universe was very young it was likely infused with dark energy, but with everything closer together, gravity predominated, braking the expansion. Eventually, after billions of years of expansion, the declining density of matter relative to the density of dark energy allowed the expansion of the universe to begin to accelerate.

Dark energy in its simplest formulation is modeled by a cosmological constant term in Einstein field equations of general relativity, but its composition and mechanism are unknown. More generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both through observation and theory.

All of this cosmic evolution after the inflationary epoch can be rigorously described and modeled by the lambda-CDM model of cosmology, which uses the independent frameworks of quantum mechanics and general relativity. There are no easily testable models that would describe the situation prior to approximately 10−15 seconds. Understanding this earliest of eras in the history of the universe is one of the greatest unsolved problems in physics.

Etymology
English astronomer Fred Hoyle is credited with coining the term "Big Bang" during a talk for a March 1949 BBC Radio broadcast, saying: "These theories were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past." However, it did not catch on until the 1970s.

It is popularly reported that Hoyle, who favored an alternative "steady-state" cosmological model, intended this to be pejorative, but Hoyle explicitly denied this and said it was just a striking image meant to highlight the difference between the two models. Helge Kragh writes that the evidence for the claim that it was meant as a pejorative is "unconvincing", and mentions a number of indications that it was not a pejorative.

The term itself has been argued to be a misnomer because it evokes an explosion. The argument is that whereas an explosion suggests expansion into a surrounding space, the Big Bang only describes the intrinsic expansion of the contents of the universe. Another issue pointed out by Santhosh Mathew is that bang implies sound, which is not an important feature of the model. An attempt to find a more suitable alternative was not successful.

Development
The Big Bang models developed from observations of the structure of the universe and from theoretical considerations. In 1912, Vesto Slipher measured the first Doppler shift of a "spiral nebula" (spiral nebula is the obsolete term for spiral galaxies), and soon discovered that almost all such nebulae were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it was highly controversial whether or not these nebulae were "island universes" outside our Milky Way. Ten years later, Alexander Friedmann, a Russian cosmologist and mathematician, derived the Friedmann equations from the Einstein field equations, showing that the universe might be expanding in contrast to the static universe model advocated by Albert Einstein at that time.

In 1924, American astronomer Edwin Hubble's measurement of the great distance to the nearest spiral nebulae showed that these systems were indeed other galaxies. Starting that same year, Hubble painstakingly developed a series of distance indicators, the forerunner of the cosmic distance ladder, using the 100 in Hooker telescope at Mount Wilson Observatory. This allowed him to estimate distances to galaxies whose redshifts had already been measured, mostly by Slipher. In 1929, Hubble discovered a correlation between distance and recessional velocity—now known as Hubble's law.

Independently deriving Friedmann's equations in 1927, Georges Lemaître, a Belgian physicist and Roman Catholic priest, proposed that the recession of the nebulae was due to the expansion of the universe. He inferred the relation that Hubble would later observe, given the cosmological principle. In 1931, Lemaître went further and suggested that the evident expansion of the universe, if projected back in time, meant that the further in the past the smaller the universe was, until at some finite time in the past all the mass of the universe was concentrated into a single point, a "primeval atom" where and when the fabric of time and space came into existence.

In the 1920s and 1930s, almost every major cosmologist preferred an eternal steady-state universe, and several complained that the beginning of time implied by the Big Bang imported religious concepts into physics; this objection was later repeated by supporters of the steady-state theory. This perception was enhanced by the fact that the originator of the Big Bang concept, Lemaître, was a Roman Catholic priest. Arthur Eddington agreed with Aristotle that the universe did not have a beginning in time, viz., that matter is eternal. A beginning in time was "repugnant" to him. Lemaître, however, disagreed: "If the world has begun with a single quantum, the notions of space and time would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time."

During the 1930s, other ideas were proposed as non-standard cosmologies to explain Hubble's observations, including the Milne model, the oscillatory universe (originally suggested by Friedmann, but advocated by Albert Einstein and Richard C. Tolman) and Fritz Zwicky's tired light hypothesis.

After World War II, two distinct possibilities emerged. One was Fred Hoyle's steady-state model, whereby new matter would be created as the universe seemed to expand. In this model the universe is roughly the same at any point in time. The other was Lemaître's Big Bang theory, advocated and developed by George Gamow, who introduced BBN and whose associates, Ralph Alpher and Robert Herman, predicted the CMB. Ironically, it was Hoyle who coined the phrase that came to be applied to Lemaître's theory, referring to it as "this big bang idea" during a BBC Radio broadcast in March 1949. For a while, support was split between these two theories. Eventually, the observational evidence, most notably from radio source counts, began to favor Big Bang over steady state. The discovery and confirmation of the CMB in 1964 secured the Big Bang as the best theory of the origin and evolution of the universe.

In 1968 and 1970, Roger Penrose, Stephen Hawking, and George F. R. Ellis published papers where they showed that mathematical singularities were an inevitable initial condition of relativistic models of the Big Bang. Then, from the 1970s to the 1990s, cosmologists worked on characterizing the features of the Big Bang universe and resolving outstanding problems. In 1981, Alan Guth made a breakthrough in theoretical work on resolving certain outstanding theoretical problems in the Big Bang models with the introduction of an epoch of rapid expansion in the early universe he called "inflation". Meanwhile, during these decades, two questions in observational cosmology that generated much discussion and disagreement were over the precise values of the Hubble Constant and the matter-density of the universe (before the discovery of dark energy, thought to be the key predictor for the eventual fate of the universe).

In the mid-1990s, observations of certain globular clusters appeared to indicate that they were about 15 billion years old, which conflicted with most then-current estimates of the age of the universe (and indeed with the age measured today). This issue was later resolved when new computer simulations, which included the effects of mass loss due to stellar winds, indicated a much younger age for globular clusters.

Significant progress in Big Bang cosmology has been made since the late 1990s as a result of advances in telescope technology as well as the analysis of data from satellites such as the Cosmic Background Explorer (COBE), the Hubble Space Telescope and WMAP. Cosmologists now have fairly precise and accurate measurements of many of the parameters of the Big Bang model, and have made the unexpected discovery that the expansion of the universe appears to be accelerating.

Observational evidence
The earliest and most direct observational evidence of the validity of the theory are the expansion of the universe according to Hubble's law (as indicated by the redshifts of galaxies), discovery and measurement of the cosmic microwave background and the relative abundances of light elements produced by Big Bang nucleosynthesis (BBN). More recent evidence includes observations of galaxy formation and evolution, and the distribution of large-scale cosmic structures, These are sometimes called the "four pillars" of the Big Bang models.

Precise modern models of the Big Bang appeal to various exotic physical phenomena that have not been observed in terrestrial laboratory experiments or incorporated into the Standard Model of particle physics. Of these features, dark matter is currently the subject of most active laboratory investigations. Remaining issues include the cuspy halo problem and the dwarf galaxy problem of cold dark matter. Dark energy is also an area of intense interest for scientists, but it is not clear whether direct detection of dark energy will be possible. Inflation and baryogenesis remain more speculative features of current Big Bang models. Viable, quantitative explanations for such phenomena are still being sought. These are unsolved problems in physics.

Hubble's law and the expansion of the universe
Observations of distant galaxies and quasars show that these objects are redshifted: the light emitted from them has been shifted to longer wavelengths. This can be seen by taking a frequency spectrum of an object and matching the spectroscopic pattern of emission or absorption lines corresponding to atoms of the chemical elements interacting with the light. These redshifts are uniformly isotropic, distributed evenly among the observed objects in all directions. If the redshift is interpreted as a Doppler shift, the recessional velocity of the object can be calculated. For some galaxies, it is possible to estimate distances via the cosmic distance ladder. When the recessional velocities are plotted against these distances, a linear relationship known as Hubble's law is observed: $$v = H_0D$$ where
 * $$v$$ is the recessional velocity of the galaxy or other distant object,
 * $$D$$ is the proper distance to the object, and
 * $$H_0$$ is Hubble's constant, measured to be $70.4$ km/s/Mpc by the WMAP.

Hubble's law implies that the universe is uniformly expanding everywhere. This cosmic expansion was predicted from general relativity by Friedmann in 1922 and Lemaître in 1927, well before Hubble made his 1929 analysis and observations, and it remains the cornerstone of the Big Bang model as developed by Friedmann, Lemaître, Robertson, and Walker.

The theory requires the relation $$v = HD$$ to hold at all times, where $$D$$ is the proper distance, $$v$$ is the recessional velocity, and $$v$$, $$H$$, and $$D$$ vary as the universe expands (hence we write $$H_0$$ to denote the present-day Hubble "constant"). For distances much smaller than the size of the observable universe, the Hubble redshift can be thought of as the Doppler shift corresponding to the recession velocity $$v$$. For distances comparable to the size of the observable universe, the attribution of the cosmological redshift becomes more ambiguous, although its interpretation as a kinematic Doppler shift remains the most natural one.

An unexplained discrepancy with the determination of the Hubble constant is known as Hubble tension. Techniques based on observation of the CMB suggest a lower value of this constant compared to the quantity derived from measurements based on the cosmic distance ladder.

Cosmic microwave background radiation

In 1964, Arno Penzias and Robert Wilson serendipitously discovered the cosmic background radiation, an omnidirectional signal in the microwave band. Their discovery provided substantial confirmation of the big-bang predictions by Alpher, Herman and Gamow around 1950. Through the 1970s, the radiation was found to be approximately consistent with a blackbody spectrum in all directions; this spectrum has been redshifted by the expansion of the universe, and today corresponds to approximately 2.725 K. This tipped the balance of evidence in favor of the Big Bang model, and Penzias and Wilson were awarded the 1978 Nobel Prize in Physics.

The surface of last scattering corresponding to emission of the CMB occurs shortly after recombination, the epoch when neutral hydrogen becomes stable. Prior to this, the universe comprised a hot dense photon-baryon plasma sea where photons were quickly scattered from free charged particles. Peaking at around $372 kyr$, the mean free path for a photon becomes long enough to reach the present day and the universe becomes transparent.

In 1989, NASA launched COBE, which made two major advances: in 1990, high-precision spectrum measurements showed that the CMB frequency spectrum is an almost perfect blackbody with no deviations at a level of 1 part in 104, and measured a residual temperature of 2.726 K (more recent measurements have revised this figure down slightly to 2.7255 K); then in 1992, further COBE measurements discovered tiny fluctuations (anisotropies) in the CMB temperature across the sky, at a level of about one part in 105. John C. Mather and George Smoot were awarded the 2006 Nobel Prize in Physics for their leadership in these results.

During the following decade, CMB anisotropies were further investigated by a large number of ground-based and balloon experiments. In 2000–2001, several experiments, most notably BOOMERanG, found the shape of the universe to be spatially almost flat by measuring the typical angular size (the size on the sky) of the anisotropies.

In early 2003, the first results of the Wilkinson Microwave Anisotropy Probe were released, yielding what were at the time the most accurate values for some of the cosmological parameters. The results disproved several specific cosmic inflation models, but are consistent with the inflation theory in general. The Planck space probe was launched in May 2009. Other ground and balloon-based cosmic microwave background experiments are ongoing.

Abundance of primordial elements
Using Big Bang models, it is possible to calculate the expected concentration of the isotopes helium-4 (4He), helium-3 (3He), deuterium (2H), and lithium-7 (7Li) in the universe as ratios to the amount of ordinary hydrogen. The relative abundances depend on a single parameter, the ratio of photons to baryons. This value can be calculated independently from the detailed structure of CMB fluctuations. The ratios predicted (by mass, not by abundance) are about 0.25 for 4He:H, about 10−3 for 2H:H, about 10−4 for 3He:H, and about 10−9 for 7Li:H.

The measured abundances all agree at least roughly with those predicted from a single value of the baryon-to-photon ratio. The agreement is excellent for deuterium, close but formally discrepant for 4He, and off by a factor of two for 7Li (this anomaly is known as the cosmological lithium problem); in the latter two cases, there are substantial systematic uncertainties. Nonetheless, the general consistency with abundances predicted by BBN is strong evidence for the Big Bang, as the theory is the only known explanation for the relative abundances of light elements, and it is virtually impossible to "tune" the Big Bang to produce much more or less than 20–30% helium. Indeed, there is no obvious reason outside of the Big Bang that, for example, the young universe before star formation, as determined by studying matter supposedly free of stellar nucleosynthesis products, should have more helium than deuterium or more deuterium than 3He, and in constant ratios, too.

Galactic evolution and distribution
Detailed observations of the morphology and distribution of galaxies and quasars are in agreement with the current Big Bang models. A combination of observations and theory suggest that the first quasars and galaxies formed within a billion years after the Big Bang, and since then, larger structures have been forming, such as galaxy clusters and superclusters.

Populations of stars have been aging and evolving, so that distant galaxies (which are observed as they were in the early universe) appear very different from nearby galaxies (observed in a more recent state). Moreover, galaxies that formed relatively recently appear markedly different from galaxies formed at similar distances but shortly after the Big Bang. These observations are strong arguments against the steady-state model. Observations of star formation, galaxy and quasar distributions and larger structures, agree well with Big Bang simulations of the formation of structure in the universe, and are helping to complete details of the theory.

Primordial gas clouds
In 2011, astronomers found what they believe to be pristine clouds of primordial gas by analyzing absorption lines in the spectra of distant quasars. Before this discovery, all other astronomical objects have been observed to contain heavy elements that are formed in stars. Despite being sensitive to carbon, oxygen, and silicon, these three elements were not detected in these two clouds. Since the clouds of gas have no detectable levels of heavy elements, they likely formed in the first few minutes after the Big Bang, during BBN.

Other lines of evidence
The age of the universe as estimated from the Hubble expansion and the CMB is now in agreement with other estimates using the ages of the oldest stars, both as measured by applying the theory of stellar evolution to globular clusters and through radiometric dating of individual Population II stars. It is also in agreement with age estimates based on measurements of the expansion using Type Ia supernovae and measurements of temperature fluctuations in the cosmic microwave background. The agreement of independent measurements of this age supports the Lambda-CDM (ΛCDM) model, since the model is used to relate some of the measurements to an age estimate, and all estimates turn agree. Still, some observations of objects from the relatively early universe (in particular quasar APM 08279+5255) raise concern as to whether these objects had enough time to form so early in the ΛCDM model.

The prediction that the CMB temperature was higher in the past has been experimentally supported by observations of very low temperature absorption lines in gas clouds at high redshift. This prediction also implies that the amplitude of the Sunyaev–Zel'dovich effect in clusters of galaxies does not depend directly on redshift. Observations have found this to be roughly true, but this effect depends on cluster properties that do change with cosmic time, making precise measurements difficult.

Future observations
Future gravitational-wave observatories might be able to detect primordial gravitational waves, relics of the early universe, up to less than a second after the Big Bang.

Problems and related issues in physics
As with any theory, a number of mysteries and problems have arisen as a result of the development of the Big Bang models. Some of these mysteries and problems have been resolved while others are still outstanding. Proposed solutions to some of the problems in the Big Bang model have revealed new mysteries of their own. For example, the horizon problem, the magnetic monopole problem, and the flatness problem are most commonly resolved with inflation theory, but the details of the inflationary universe are still left unresolved and many, including some founders of the theory, say it has been disproven. What follows are a list of the mysterious aspects of the Big Bang concept still under intense investigation by cosmologists and astrophysicists.

Baryon asymmetry
It is not yet understood why the universe has more matter than antimatter. It is generally assumed that when the universe was young and very hot it was in statistical equilibrium and contained equal numbers of baryons and antibaryons. However, observations suggest that the universe, including its most distant parts, is made almost entirely of normal matter, rather than antimatter. A process called baryogenesis was hypothesized to account for the asymmetry. For baryogenesis to occur, the Sakharov conditions must be satisfied. These require that baryon number is not conserved, that C-symmetry and CP-symmetry are violated and that the universe depart from thermodynamic equilibrium. All these conditions occur in the Standard Model, but the effects are not strong enough to explain the present baryon asymmetry.

Dark energy
Measurements of the redshift–magnitude relation for type Ia supernovae indicate that the expansion of the universe has been accelerating since the universe was about half its present age. To explain this acceleration, general relativity requires that much of the energy in the universe consists of a component with large negative pressure, dubbed "dark energy".

Dark energy, though speculative, solves numerous problems. Measurements of the cosmic microwave background indicate that the universe is very nearly spatially flat, and therefore according to general relativity the universe must have almost exactly the critical density of mass/energy. But the mass density of the universe can be measured from its gravitational clustering, and is found to have only about 30% of the critical density. Since theory suggests that dark energy does not cluster in the usual way it is the best explanation for the "missing" energy density. Dark energy also helps to explain two geometrical measures of the overall curvature of the universe, one using the frequency of gravitational lenses, and the other using the characteristic pattern of the large-scale structure--baryon acoustic oscillations--as a cosmic ruler.

Negative pressure is believed to be a property of vacuum energy, but the exact nature and existence of dark energy remains one of the great mysteries of the Big Bang. Results from the WMAP team in 2008 are in accordance with a universe that consists of 73% dark energy, 23% dark matter, 4.6% regular matter and less than 1% neutrinos. According to theory, the energy density in matter decreases with the expansion of the universe, but the dark energy density remains constant (or nearly so) as the universe expands. Therefore, matter made up a larger fraction of the total energy of the universe in the past than it does today, but its fractional contribution will fall in the far future as dark energy becomes even more dominant.

The dark energy component of the universe has been explained by theorists using a variety of competing theories including Einstein's cosmological constant but also extending to more exotic forms of quintessence or other modified gravity schemes. A cosmological constant problem, sometimes called the "most embarrassing problem in physics", results from the apparent discrepancy between the measured energy density of dark energy, and the one naively predicted from Planck units.

Dark matter
During the 1970s and the 1980s, various observations showed that there is not sufficient visible matter in the universe to account for the apparent strength of gravitational forces within and between galaxies. This led to the idea that up to 90% of the matter in the universe is dark matter that does not emit light or interact with normal baryonic matter. In addition, the assumption that the universe is mostly normal matter led to predictions that were strongly inconsistent with observations. In particular, the universe today is far more lumpy and contains far less deuterium than can be accounted for without dark matter. While dark matter has always been controversial, it is inferred by various observations: the anisotropies in the CMB, galaxy cluster velocity dispersions, large-scale structure distributions, gravitational lensing studies, and X-ray measurements of galaxy clusters.

Indirect evidence for dark matter comes from its gravitational influence on other matter, as no dark matter particles have been observed in laboratories. Many particle physics candidates for dark matter have been proposed, and several projects to detect them directly are underway.

Additionally, there are outstanding problems associated with the currently favored cold dark matter model which include the dwarf galaxy problem and the cuspy halo problem. Alternative theories have been proposed that do not require a large amount of undetected matter, but instead modify the laws of gravity established by Newton and Einstein; yet no alternative theory has been as successful as the cold dark matter proposal in explaining all extant observations.

Horizon problem
The horizon problem results from the premise that information cannot travel faster than light. In a universe of finite age this sets a limit—the particle horizon—on the separation of any two regions of space that are in causal contact. The observed isotropy of the CMB is problematic in this regard: if the universe had been dominated by radiation or matter at all times up to the epoch of last scattering, the particle horizon at that time would correspond to about 2 degrees on the sky. There would then be no mechanism to cause wider regions to have the same temperature.

A resolution to this apparent inconsistency is offered by inflation theory in which a homogeneous and isotropic scalar energy field dominates the universe at some very early period (before baryogenesis). During inflation, the universe undergoes exponential expansion, and the particle horizon expands much more rapidly than previously assumed, so that regions presently on opposite sides of the observable universe are well inside each other's particle horizon. The observed isotropy of the CMB then follows from the fact that this larger region was in causal contact before the beginning of inflation.

Heisenberg's uncertainty principle predicts that during the inflationary phase there would be quantum thermal fluctuations, which would be magnified to a cosmic scale. These fluctuations served as the seeds for all the current structures in the universe. Inflation predicts that the primordial fluctuations are nearly scale invariant and Gaussian, which has been confirmed by measurements of the CMB.

A related issue to the classic horizon problem arises because in most standard cosmological inflation models, inflation ceases well before electroweak symmetry breaking occurs, so inflation should not be able to prevent large-scale discontinuities in the electroweak vacuum since distant parts of the observable universe were causally separate when the electroweak epoch ended.

Magnetic monopoles
The magnetic monopole objection was raised in the late 1970s. Grand unified theories (GUTs) predicted topological defects in space that would manifest as magnetic monopoles. These objects would be produced efficiently in the hot early universe, resulting in a density much higher than is consistent with observations, given that no monopoles have been found. This problem is resolved by cosmic inflation, which removes all point defects from the observable universe, in the same way that it drives the geometry to flatness.

Flatness problem

The flatness problem (also known as the oldness problem) is an observational problem associated with a FLRW. The universe may have positive, negative, or zero spatial curvature depending on its total energy density. Curvature is negative if its density is less than the critical density; positive if greater; and zero at the critical density, in which case space is said to be flat. Observations indicate the universe is consistent with being flat.

The problem is that any small departure from the critical density grows with time, and yet the universe today remains very close to flat. Given that a natural timescale for departure from flatness might be the Planck time, 10−43 seconds, the fact that the universe has reached neither a heat death nor a Big Crunch after billions of years requires an explanation. For instance, even at the relatively late age of a few minutes (the time of nucleosynthesis), the density of the universe must have been within one part in 1014 of its critical value, or it would not exist as it does today.

Misconceptions
One of the common misconceptions about the Big Bang model is that it fully explains the origin of the universe. However, the Big Bang model does not describe how energy, time, and space were caused, but rather it describes the emergence of the present universe from an ultra-dense and high-temperature initial state. It is misleading to visualize the Big Bang by comparing its size to everyday objects. When the size of the universe at Big Bang is described, it refers to the size of the observable universe, and not the entire universe.

Another common misconception is that the Big Bang must be understood as the expansion of space and not in terms of the contents of space exploding apart. In fact, either description can be accurate. The expansion of space (implied by the FLRW metric) is only a mathematical convention, corresponding to a choice of coordinates on spacetime. There is no generally covariant sense in which space expands.

The recession speeds associated with Hubble's law are not velocities in a relativistic sense (for example, they are not related to the spatial components of 4-velocities). Therefore, it is not remarkable that according to Hubble's law, galaxies farther than the Hubble distance recede faster than the speed of light. Such recession speeds do not correspond to faster-than-light travel.

Many popular accounts attribute the cosmological redshift to the expansion of space. This can be misleading because the expansion of space is only a coordinate choice. The most natural interpretation of the cosmological redshift is that it is a Doppler shift.

Implications
Given current understanding, scientific extrapolations about the future of the universe are only possible for finite durations, albeit for much longer periods than the current age of the universe. Anything beyond that becomes increasingly speculative. Likewise, at present, a proper understanding of the origin of the universe can only be subject to conjecture.

Pre–Big Bang cosmology
The Big Bang explains the evolution of the universe from a starting density and temperature that is well beyond humanity's capability to replicate, so extrapolations to the most extreme conditions and earliest times are necessarily more speculative. Lemaître called this initial state the "primeval atom" while Gamow called the material "ylem". How the initial state of the universe originated is still an open question, but the Big Bang model does constrain some of its characteristics. For example, if specific laws of nature were to come to existence in a random way, inflation models show, some combinations of these are far more probable, partly explaining why our Universe is rather stable. Another possible explanation for the stability of the Universe could be a hypothetical multiverse, which assumes every possible universe to exist, and thinking species could only emerge in those stable enough. A flat universe implies a balance between gravitational potential energy and other energy forms, requiring no additional energy to be created.

The Big Bang theory, built upon the equations of classical general relativity, indicates a singularity at the origin of cosmic time, and such an infinite energy density may be a physical impossibility. However, the physical theories of general relativity and quantum mechanics as currently realized are not applicable before the Planck epoch, and correcting this will require the development of a correct treatment of quantum gravity. Certain quantum gravity treatments, such as the Wheeler–DeWitt equation, imply that time itself could be an emergent property. As such, physics may conclude that time did not exist before the Big Bang.

While it is not known what could have preceded the hot dense state of the early universe or how and why it originated, or even whether such questions are sensible, speculation abounds on the subject of "cosmogony".

Some speculative proposals in this regard, each of which entails untested hypotheses, are:
 * The simplest models, in which the Big Bang was caused by quantum fluctuations. That scenario had very little chance of happening, but, according to the totalitarian principle, even the most improbable event will eventually happen. It took place instantly, in our perspective, due to the absence of perceived time before the Big Bang.
 * Emergent Universe models, which feature a low-activity past-eternal era before the Big Bang, resembling ancient ideas of a cosmic egg and birth of the world out of primordial chaos.
 * Models in which the whole of spacetime is finite, including the Hartle–Hawking no-boundary condition. For these cases, the Big Bang does represent the limit of time but without a singularity. In such a case, the universe is self-sufficient.
 * Brane cosmology models, in which inflation is due to the movement of branes in string theory; the pre-Big Bang model; the ekpyrotic model, in which the Big Bang is the result of a collision between branes; and the cyclic model, a variant of the ekpyrotic model in which collisions occur periodically. In the latter model the Big Bang was preceded by a Big Crunch and the universe cycles from one process to the other.
 * Eternal inflation, in which universal inflation ends locally here and there in a random fashion, each end-point leading to a bubble universe, expanding from its own big bang.

Proposals in the last two categories see the Big Bang as an event in either a much larger and older universe or in a multiverse.

Ultimate fate of the universe
Before observations of dark energy, cosmologists considered two scenarios for the future of the universe. If the mass density of the universe were greater than the critical density, then the universe would reach a maximum size and then begin to collapse. It would become denser and hotter again, ending with a state similar to that in which it started—a Big Crunch.

Alternatively, if the density in the universe were equal to or below the critical density, the expansion would slow down but never stop. Star formation would cease with the consumption of interstellar gas in each galaxy; stars would burn out, leaving white dwarfs, neutron stars, and black holes. Collisions between these would result in mass accumulating into larger and larger black holes. The average temperature of the universe would very gradually asymptotically approach absolute zero—a Big Freeze. Moreover, if protons are unstable, then baryonic matter would disappear, leaving only radiation and black holes. Eventually, black holes would evaporate by emitting Hawking radiation. The entropy of the universe would increase to the point where no organized form of energy could be extracted from it, a scenario known as heat death.

Modern observations of accelerating expansion imply that more and more of the currently visible universe will pass beyond our event horizon and out of contact with us. The eventual result is not known. The ΛCDM model of the universe contains dark energy in the form of a cosmological constant. This theory suggests that only gravitationally bound systems, such as galaxies, will remain together, and they too will be subject to heat death as the universe expands and cools. Other explanations of dark energy, called phantom energy theories, suggest that ultimately galaxy clusters, stars, planets, atoms, nuclei, and matter itself will be torn apart by the ever-increasing expansion in a so-called Big Rip.

Religious and philosophical interpretations
As a description of the origin of the universe, the Big Bang has significant bearing on religion and philosophy. As a result, it has become one of the liveliest areas in the discourse between science and religion. Some believe the Big Bang implies a creator, while others argue that Big Bang cosmology makes the notion of a creator superfluous.

title: Big Bang


text:
Talk:Bookbinding/Archive 1

I'm normally doing book binding in Swedish, so I'm not sure about the terminology in English. Please help! --Pinkunicorn

Am I not understanding? Most hardbound books I own don't have marbled paper or any other fancy decoration on the inside covers. --Larry Sanger - No, I'm being unclear. When I'm talking about marbled paper and so on, I'm talking about hand-bound books. The first half of the article is about binding types in general. There should be a heading or something in the middle. And I was talking about marbled paper on the cover, not on the inside. It's not uncommon to use marbled paper for the flyleaf as well, though.

Also, are you sure that they're really hardbound? ;-) --Pinkunicorn

title: Talk:Bookbinding/Archive 1


text:
Bock

Bock is a strong German beer, usually a dark lager.

History
The style now known as Bock was first brewed in the 14th century in the Hanseatic town of Einbeck in Lower Saxony.

The style was later adopted in Bavaria by Munich brewers in the 17th century. Due to their Bavarian accent, citizens of Munich pronounced "Einbeck" as "ein Bock" ("a billy goat"), and thus the beer became known as "Bock". A goat often appears on bottle labels.

Bock is historically associated with special occasions, often religious festivals such as Christmas, Easter, or Lent (Lentenbock). Bock has a long history of being brewed and consumed by Bavarian monks as a source of nutrition during times of fasting.

Styles
Substyles of Bock include:

 * Maibock (May Bock), a paler, more hopped version generally made for consumption at spring festivals. Due to its lighter colour, it is also referred to as Heller Bock; from German hell (bright, light in colour).
 * Doppelbock (Double Bock), a stronger and maltier version
 * Eisbock (Ice Bock), a much stronger version made by partially freezing the beer and removing the ice that forms
 * Weizenbock (Wheat Bock), a wheat beer made from 40 to 60% wheat

Traditionally Bock is a sweet, relatively strong (6.3–7.6% by volume), lightly hopped lager registering between 20 and 30 International Bitterness Units (IBUs). The beer should be clear, with colour ranging from light copper to brown, and a bountiful, persistent off-white head. The aroma should be malty and toasty, possibly with hints of alcohol, but no detectable hops or fruitiness. The mouthfeel is smooth, with low to moderate carbonation and no astringency. The taste is rich and toasty, sometimes with a bit of caramel. The low-to-undetectable presence of hops provides just enough bitterness so that the sweetness is not cloying and the aftertaste is muted.

Maibock
The Maibock style – also known as Heller Bock or Lente Bock in the Netherlands – is a strong pale lager, lighter in colour and with more hop presence.

Colour can range from deep gold to light amber with a large, creamy, persistent white head, and moderate to moderately high carbonation, while alcohol content ranges from 6.3% to 8.1% by volume. The flavour is typically less malty than a traditional Bock, and may be drier, hoppier, and more bitter, but still with a relatively low hop flavour, with a mild spicy or peppery quality from the hops, increased carbonation and alcohol content.

Doppelbock
Doppelbock or Double Bock is a stronger version of traditional Bock that was first brewed in Munich by the Paulaner Friars, a Franciscan order founded by St. Francis of Paula.

Historically, Doppelbock was high in alcohol and sweetness. The story is told that it served as "liquid bread" for the Friars during times of fasting when solid food was not permitted. However, historian Mark Dredge, in his book A Brief History of Lager, says that this story is myth and that the monks produced Doppelbock to supplement their order's vegetarian diet all year.

Today, Doppelbock is still strong – ranging from 7% to 12% or more by volume. It is clear, with colour ranging from dark gold, for the paler version, to dark brown with ruby highlights for a darker version. It has a large, creamy, persistent head (although head retention may be impaired by alcohol in the stronger versions). The aroma is intensely malty, with some toasty notes, and possibly some alcohol presence as well; darker versions may have a chocolate-like or fruity aroma. The flavour is very rich and malty, with noticeable alcoholic strength, and little or no detectable hops (16–26 IBUs).

Paler versions may have a drier finish. The monks who originally brewed Doppelbock named their beer "Salvator" (literally "Savior", but actually a malapropism for "Sankt Vater", "St. Father", originally brewed for the feast of St. Francis of Paola on 2 April which often falls in Lent), which today is trademarked by Paulaner.

Brewers of modern Doppelbock often add "-ator" to their beer's name as a signpost of the style; there are 200 "-ator" Doppelbock names registered with the German patent office.

The following are representative examples of the style: Paulaner Salvator, Ayinger Celebrator, Weihenstephaner Korbinian, Andechser Doppelbock Dunkel, Spaten Optimator, Augustiner Brau Maximator, Tucher Bajuvator, Weltenburger Kloster Asam-Bock, Capital Autumnal Fire, EKU 28, Eggenberg Urbock 23º, Bell's Consecrator, Moretti La Rossa, Samuel Adams Double Bock, Tröegs Tröegenator Double Bock, Wasatch Brewery Devastator, Great Lakes Doppelrock, Abita Andygator, Wolverine State Brewing Company Predator, Burly Brewing's Burlynator, Monteith's Doppel Bock, and Christian Moerlein Emancipator Doppelbock.

Eisbock

Eisbock is a traditional specialty beer of the Kulmbach district of Bavaria, made by partially freezing a Doppelbock and removing the water ice to concentrate the flavour and alcohol content, which ranges from 8.6% to 14.3% by volume.

It is clear, with a colour ranging from deep copper to dark brown in colour, often with ruby highlights. Although it can pour with a thin off-white head, head retention is frequently impaired by the higher alcohol content. The aroma is intense, with no hop presence, but frequently can contain fruity notes, especially of prunes, raisins, and plums. Mouthfeel is full and smooth, with significant alcohol, although this should not be hot or sharp. The flavour is rich and sweet, often with toasty notes, and sometimes hints of chocolate, always balanced by a significant alcohol presence.

The following are representative examples of the style: Colorado Team Brew "Warning Sign", Kulmbacher Reichelbräu Eisbock, Eggenberg, Schneider Aventinus Eisbock, Urbock Dunkel Eisbock, Franconia Brewing Company Ice Bock 17%.

The strongest ice beer, Strength in Numbers, was a one-time collaboration in 2020 between Schorschbrau of Germany and BrewDog of Scotland, who had competed with each other in the early years of the 21st century to produce the world's strongest beer. Strength in Numbers was created using traditional ice distillation, reaching a final strength of 57.8% ABV.

Weizenbock
Weizenbock is a style that replaces some of the barley in the grain bill with 40–60% wheat. It was first produced in Bavaria in 1907 by G. Schneider & Sohn and was named Aventinus after 16th-century Bavarian historian Johannes Aventinus. The style combines darker Munich malts and top-fermenting wheat beer yeast, brewed at the strength of a Doppelbock.

title: Bock