Ideal gas

An ideal gas is a theoretical gas composed of many randomly moving point particles that do not interact except when they collide elastically. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. One mole of an ideal gas has a volume of 22.7 L at STP as defined by IUPAC.

At normal conditions such as standard temperature and pressure, most real gases behave qualitatively like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases, and some heavier gases like carbon dioxide can be treated like ideal gases within reasonable tolerances. Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure, as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them.

The ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size become important. It also fails for most heavy gases, such as many refrigerants, and for gases with strong intermolecular forces, notably water vapor. At high pressures, the volume of a real gas is often considerably greater than that of an ideal gas. At low temperatures, the pressure of a real gas is often considerably less than that of an ideal gas. At some point of low temperature and high pressure, real gases undergo a phase transition, such as to a liquid or a solid. The model of an ideal gas, however, does not describe or allow phase transitions. These must be modeled by more complex equations of state. The deviation from the ideal gas behaviour can be described by a dimensionless quantity, the compressibility factor, Z.

Ideal

Ideal may refer to:

In philosophy

In mathematics

In science

Lie algebra

In mathematics, a Lie algebra (/liː/, not /laɪ/) is a vector space together with a non-associative multiplication called "Lie bracket" . It was introduced to study the concept of infinitesimal transformations. Hermann Weyl introduced the term "Lie algebra" (after Sophus Lie) in the 1930s. In older texts, the name "infinitesimal group" is used.

Lie algebras are closely related to Lie groups which are groups that are also smooth manifolds, with the property that the group operations of multiplication and inversion are smooth maps. Any Lie group gives rise to a Lie algebra. Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to covering (Lie's third theorem). This correspondence between Lie groups and Lie algebras allows one to study Lie groups in terms of Lie algebras.

Definitions

A Lie algebra is a vector space over some field F together with a binary operation called the Lie bracket that satisfies the following axioms:

Ideal (album)

Ideal is the eponymous debut album by R&B group Ideal released on August 24, 1999 by Virgin Records US. The first single "Get Gone" was featured on the 1999 compilation album Now That's What I Call Music! 3

The album sold 615,000 units in the U.S., according to Nielsen SoundScan, and was certified Gold by the RIAA. It features the hit single "Get Gone", which reached #13 on the Billboard Hot 100 chart, and the moderately successful third single "Whatever". Allmusic's Heather Phares called Ideal's initial effort a "heartfelt first album" which showcased the "group's smooth, sensuous vocal styling and romantic songwriting.

Track listing

Gas

Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture would contain a variety of pure gases much like the air. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer. The interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image. One type of commonly known gas is steam.

The gaseous state of matter is found between the liquid and plasma states, the latter of which provides the upper temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases which are gaining increasing attention. High-density atomic gases super cooled to incredibly low temperatures are classified by their statistical behavior as either a Bose gas or a Fermi gas. For a comprehensive listing of these exotic states of matter see list of states of matter.

Gas (musician)

Gas is a music project of Wolfgang Voigt (born 1961), a Cologne, Germany-based electronic musician. Voigt cites his youthful LSD experiences in the Königsforst, a German forest situated near his hometown of Köln, as the inspiration behind his work under the name Gas. He has claimed that the intention of the project is to "bring the forest to the disco, or vice-versa".

Aliases and projects

Voigt is known for his numerous, nearly inexhaustible list of one-off projects and aliases. Of these, his best known is arguably Gas, a project that saw the marriage of ambient music and 4/4 techno.

Other names under which Voigt has released music include, but are not limited to, All, Auftrieb, Brom, C.K. Decker, Centrifugal Force, Crocker, Dextro NRG, Dieter Gorny, Digital, Dom, Doppel, Filter, Freiland, Fuchsbau, Gelb, Grungerman, Kafkatrax, Love Inc., M:I:5, Mike Ink, Mint, Panthel, Popacid, Riss, RX7, Split Inc., Strass, Studio 1, Tal, Vinyl Countdown, W.V., Wassermann, and X-Lvis.

Characteristics

Gas (album)

Gas is the debut album by Wolfgang Voigt's Gas project. It is the second release under the Gas name, preceded only by the Modern EP. It was released on 29 November, 1996 on the Mille Plateaux label. Like all Gas albums, the tracks are untitled. Along with Modern, it is unusual in that the artwork does not share the unifying forest theme common to all other Gas releases.

Track listing