Elevation histogram of the surface of the Earth – approximately 71% of the Earth's surface is covered with water.

The elevation of a geographic location is its height above a fixed reference point^{[citation needed]}, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic system, vertical datum). Elevation, or geometric height, is mainly used when referring to points on the Earth's surface, while altitude or geopotential height is used for points above the surface, such as an aircraft in flight or a spacecraft in orbit, and depth is used for points below the surface.

Less commonly, elevation is measured using the center of the Earth as the reference point. Due to equatorial bulge, there is debate as to which of the summits of Mt. Everest or Chimborazo is at the higher elevation, as the Chimborazo summit is further from the Earth's center while the Mt. Everest summit is higher above mean sea level.

Maps and GIS[link]

Landsat Image over SRTM Elevation by NASA, showing the Cape Peninsula and Cape of Good Hope, South Africa in the foreground.[2]

A topographical map is the main type of map used to depict elevation, often through use of contour lines. In a Geographic Information System (GIS), digital elevation models (DEM) are commonly used to represent the surface (topography) of a place, through a raster (grid) dataset of elevations. Digital terrain models are another way to represent terrain in GIS.

To determine elevation of a place, it must be surveyed, in reference to a ground control point.

Topography[link]

The elevation of a mountain usually refers to its summit. The elevation of a hill also refers to the summit. A valley's elevation is usually taken from the lowest point but is often taken all over the valley.

Global 1-kilometer map[link]

This map is derived from GTOPO30 data that describes the elevation of Earth's terrain at intervals of 30 arcseconds (approximately 1 km). It uses color and shading instead of contour lines to indicate elevation.

Each tile is available at a resolution of 1800 × 1800 pixels (approximate file size 1 MB, 60 pixels = 1 degree, 1 pixel = 1 minute)

Hypsography[link]

Hypsography is the study of the distribution of elevations on the surface of the Earth, although the term is sometimes also applied to other rocky planets such as Mars or Venus. The term originates from the Greek word ὕψος "hypsos" meaning height. Most often it is used only in reference to elevation of land but a complete description of Earth's solid surface requires a description of the seafloor as well. Related to the term hypsometry, the measurement of these elevations of a planet's solid surface are taken relative to mean datum, except for Earth which is taken relative to the sea level.

Hypsography of the Earth. Notice that Earth has two peaks in elevation, one for the continents, the other for the ocean floors.

Temperature[link]

Vertical Distance Comparison

Temperature is less in areas of higher elevation, approximately 6.5 degrees Celsius cooler per 1000 meters.^[1] This is due to less density of air at higher altitudes.

See also[link]

Look up elevation in Wiktionary, the free dictionary.

• Altitude
• Geodesy
  • Geodesy of North America
    • Sea Level Datum of 1929 later National Geodetic Vertical Datum of 1929 (NGVD 29)
    • North American Vertical Datum of 1988 (NAVD 88)
• List of European cities by elevation
• List of highest mountains
• List of highest towns by country
• Normaal Amsterdams Peil
• Normalhöhennull
• Physical geography
• Summit (topography)
• Table of the highest major summits of North America
• Topographic isolation
• Topographic map
• Topographic prominence
• Topography
• Vertical pressure variation

References[link]

External links[link]

• U.S. National Geodetic Survey website
  • Geodetic Glossary @ NGS
  • NGVD 29 to NAVD 88 online elevation converter @ NGS
• United States Geological Survey website
• Geographical Survey Institute
• Downloadable ETOPO2 Raw Data Database (2 minute grid)
• Downloadable ETOPO5 Raw Data Database (5 minute grid)
• Find the elevation of any place
• ELEV

Wikimedia Commons has media related to: Elevation

The melting point of a solid is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends (usually slightly) on pressure and is usually specified at standard pressure. When considered as the temperature of the reverse change from liquid to solid, it is referred to as the freezing point or crystallization point. Because of the ability of some substances to supercool, the freezing point is not considered as a characteristic property of a substance. When the "characteristic freezing point" of a substance is determined, in fact the actual methodology is almost always "the principle of observing the disappearance rather than the formation of ice", that is, the melting point.^[1]

Examples[link]

Melting points (in blue) and boiling points (in pink) of the first eight carboxylic acids (°C)

For most substances, melting and freezing points are approximately equal. For example, the melting point and freezing point of the element mercury is 234.32 kelvin (−38.83 °C or −37.89 °F). However, certain substances possess differing solid-liquid transition temperatures. For example, agar melts at 85 °C (185 °F) and solidifies from 31 °C to 40 °C (89.6 °F to 104 °F); this process is known as hysteresis.

The melting point of ice at 1 atmosphere of pressure is very close ^[2] to 0 °C (32 °F, 273.15 K), this is also known as the ice point. In the presence of nucleating substances the freezing point of water is the same as the melting point, but in the absence of nucleators water can supercool to −42 °C (−43.6 °F, 231 K) before freezing.

The chemical element with the highest melting point is tungsten, at 3683 K (3410 °C, 6170 °F) making it excellent for use as filaments in light bulbs. The often-cited carbon does not melt at ambient pressure but sublimes at about 4000 K; a liquid phase only exists above pressures of 10 MPa and estimated 4300–4700 K. Tantalum hafnium carbide (Ta₄HfC₅) is a refractory compound with a very high melting point of 4488 K (4215 °C, 7619 °F).^[3] At the other end of the scale, helium does not freeze at all at normal pressure, even at temperatures very close to absolute zero; pressures over 20 times normal atmospheric pressure are necessary.

Melting point measurements[link]

Kofler bench with samples for calibration

Many laboratory techniques exist for the determination of melting points. A Kofler bench is a metal strip with a temperature gradient (range from room temperature to 300 °C). Any substance can be placed on a section of the strip revealing its thermal behaviour at the temperature at that point. Differential scanning calorimetry gives information on melting point together with its enthalpy of fusion.

Automatic digital melting point meter M5000

A basic melting point apparatus for the analysis of crystalline solids consists of a oil bath with a transparent window (most basic design: a Thiele tube) and a simple magnifier. The several grains of a solid are placed in a thin glass tube and partially immersed in the oil bath. The oil bath is heated (and stirred) and with the aid of the magnifier (and external light source) melting of the individual crystals at a certain temperature can be observed. In large/small devices, the sample is placed in a heating block, and optical detection is automated.

The measurement can also be made continuously with an operating process. For instance, oil refineries measure the freeze point of diesel fuel online, meaning that the sample is taken from the process and measured automatically. This allows for more frequent measurements as the sample does not have to be manually collected and taken to a remote laboratory.

Thermodynamics[link]

Pressure dependence of water melting point

Not only is heat required to raise the temperature of the solid to the melting point, but the melting itself requires heat called the heat of fusion.

From a thermodynamics point of view, at the melting point the change in Gibbs free energy (ΔG) of the material is zero, but the enthalpy (H) and the entropy (S) of the material are increasing (ΔH, ΔS > 0). Melting phenomenon happens when the Gibbs free energy of the liquid becomes lower than the solid for that material. At various pressures this happens at a specific temperature. It can also be shown that:

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta S = \frac {\Delta H} {T}

Here T, ΔS and ΔH are respectively the temperature at the melting point, change of entropy of melting and the change of enthalpy of melting.

The melting point is sensitive to extremely large changes in pressure, but generally this sensitivity is orders of magnitude less than that for the boiling point, because the solid-liquid transition represents only a small change in volume. ^[4][5] If, as observed in most cases, a substance is more dense in the solid than in the liquid state, the melting point will increase with increases in pressure. Otherwise the reverse behavior occurs. Notably, this is the case of water, as illustrated graphically to the right, but also of Si, Ge, Ga, Bi. With extremely large changes in pressure, substantial changes to the melting point are observed. For example, the melting point of silicon at ambient pressure (0.1 MPa) is 1415 °C, but at pressures in excess of 10 GPa it decreases to 1000 °C.^[6] Melting points are often used to characterize organic and inorganic compounds and to ascertain their purity. The melting point of a pure substance is always higher and has a smaller range than the melting point of an impure substance or, more generally, of mixtures. The higher the quantity of other components, the lower the melting point and the broader will be the melting point range, often referred to as the pasty range. The temperature at which melting begins for a mixture is known as the solidus while the temperature where melting is complete is called the liquidus. Eutectics are special types of mixtures that behave like single phases. They melt sharply at a constant temperature to form a liquid of the same composition. Alternatively, on cooling a liquid with the eutectic composition will solidify as uniformly dispersed, small (fine-grained) mixed crystals with the same composition.

In contrast to crystalline solids, glasses do not possess a melting point; on heating they undergo a smooth glass transition into a viscous liquid. Upon further heating, they gradually soften, which can be characterized by certain softening points.

Freezing-point depression[link]

The freezing point of a solvent is depressed when another compound is added, meaning that a solution has a lower freezing point than a pure solvent. This phenomenon is used in technical applications to avoid freezing, for instance by adding salt or ethylene glycol to water.

Carnelley’s Rule[link]

In organic chemistry Carnelley’s Rule, established in 1882 by Thomas Carnelley, stated that high molecular symmetry is associated with high melting point.^[7] Carnelley based his rule on examination of 15,000 chemical compounds. For example for three structural isomers with molecular formula C₅H₁₂ the melting point increases in the series isopentane −160 °C (113 K) n-pentane −129.8 °C (143 K) and neopentane −18 °C (255 K). Likewise in xylenes and also dichlorobenzenes^{[disambiguation needed ]} the melting point increases in the order meta, ortho and then para. Pyridine has a lower symmetry than benzene hence its lower melting point but the melting point again increases with diazine and triazines. Many cage-like compounds like adamantane and cubane with high symmetry have very high melting points.

A high melting point results from a high heat of fusion, a low entropy of fusion, or a combination of both. In highly symmetrical molecules the crystal phase is densely packed with many efficient intermolecular interactions resulting in a higher enthalpy change on melting.

Predicting the melting point of substances (Lindemann's criterion)[link]

An attempt to predict the bulk melting point of crystalline materials was first made in 1910 by Frederick Lindemann.^[8] The idea behind the theory was the observation that the average amplitude of thermal vibrations increase with increasing temperature. Melting initiates when the amplitude of vibration becomes large enough for adjacent atoms to partly occupy the same space. The Lindemann criterion states that melting is expected when the root mean square vibration amplitude exceeds a threshold value.

Assuming that all atoms in a crystal vibrate with the same frequency ν, the average thermal energy can be estimated using the equipartition theorem as^[9]

Failed to parse (Missing texvc executable; please see math/README to configure.): E = 4\pi^2 m \nu^2~u^2 = k_B T

where m is the atomic mass, ν is the frequency, u is the average vibration amplitude, k_B is the Boltzmann constant, and T is the absolute temperature. If the threshold value of u² is c²a² where c is the Lindemann constant and a is the atomic spacing, then the melting point is estimated as

Failed to parse (Missing texvc executable; please see math/README to configure.): T_m = \cfrac{4\pi^2 m \nu^2 c^2 a^2}{k_B} .

Several other expressions for the estimated melting temperature can be obtained depending on the estimate of the average thermal energy. Another commonly used expression for the Lindemann criterion is^[10]

Failed to parse (Missing texvc executable; please see math/README to configure.): T_m = \cfrac{m \nu^2 c^2 a^2}{k_B} .

From the expression for the Debye frequency for ν, we have

Failed to parse (Missing texvc executable; please see math/README to configure.): T_m = \cfrac{2\pi m c^2 a^2 \theta_D^2 k_B}{h^2}

where θ_D is the Debye temperature and h is the Planck constant. Values of c range from 0.15–0.3 for most materials.^[11]

Open Melting Point Data[link]

In February 2011^[12] Alfa Aesar released over 10,000 melting points of compounds from their catalog as Open Data. This data has been curated and is freely available for download.^[13] This data has been used to create a random forest model for melting point prediction^[14] which is now available as a free to use webservice.^[15] Highly curated and open melting point data is also available from Nature Precedings.^[16]

See also[link]

• List of elements by melting point
• Phases of matter
• Triple point
• Liquidus temperature
• Slip melting point
• Solidus temperature

References[link]

External links[link]

• Melting and boiling point tables vol. 1 by Thomas Carnelley (Harrison, London, 1885–1887)
• Melting and boiling point tables vol. 2 by Thomas Carnelley (Harrison, London, 1885–1887)
• ONS melting point explorer Over 10,000 Open Data melting points.

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Esbjörn Svensson
Esbjörn Svensson, in concert in Ghent, 2007.
Background information
Birth name	Bror Fredrik Esbjörn Svensson
Born	(1964-04-16)April 16, 1964 Skultuna, Sweden
Died	June 14, 2008(2008-06-14) (aged 44) Stockholm, Sweden
Genres	Jazz
Instruments	Piano
Years active	1980–2008
Associated acts	Esbjörn Svensson Trio
Website	www.est-music.com/

Esbjörn Svensson (April 16, 1964 – June 14, 2008) was a jazz Swedish pianist and founder of the jazz group Esbjörn Svensson Trio, commonly known as E.S.T. Svensson became one of Europe's most successful jazz musicians at the turn of the 21st century before dying at the age of 44 in a scuba diving accident.

Early life and work[link]

Svensson was introduced to both classical music and jazz very early in life through his mother, a classical pianist, and his father, a jazz enthusiast, and first showed interest in classical music. In his teenage years, he developed an interest in rock music and started a few garage bands with classmates, before going back to classical music and finally making his way towards jazz. At age 16, Svensson went to a music college, where he took piano lessons. He later studied at the Royal College of Music, Stockholm, for four years.

In 1990, Svensson started his own jazz combo with his childhood friend Magnus Öström on percussion. Both had made their first appearances on stage as sidemen in the Swedish and Danish jazz scene during the 1980s. In 1993, bassist Dan Berglund joined the duo, and the Esbjörn Svensson Trio was born. The trio released its debut album, When Everyone Has Gone, in 1993, and in the following years established itself in the Nordic jazz scene. Svensson was nominated for Swedish Jazz Musician of the Year in 1995 and 1996.

Rise to prominence, success, and death[link]

The trio's international breakthrough came with their 1999 album From Gagarin’s Point Of View, their first album to be released outside Scandinavia. With the release of their albums Good Morning Susie Soho (2000) and Strange Place For Snow (2002), the trio drew the attention of United States audiences. In 2002, they went on a 9-month tour through Europe, the U.S. and Japan. Their subsequent albums, Seven Days Of Falling (2003), Viaticum (2005), and Tuesday Wonderland (2006), were equally well received by critics and fans and resulted in several music industry award nominations as well as making the jazz and pop charts.

E.S.T. was the first European jazz combo to make the front page of the American jazz magazine Down Beat (May 2006 issue). Their last live album, E.S.T. Live in Hamburg, a recording of their fall 2006 concert in Hamburg, Germany, as part of the Tuesday Wonderland Tour, was released in November 2007. Before Svensson's death, the trio was working on the concept of integrating electronic and mechanical sound expansions into a jazz trio context. E.S.T.'s last performance took place in Moscow, Russia, at the Tchaikovsky Hall, on May 30, 2008. In addition to his work with E.S.T., Svensson recorded albums with Nils Landgren and Viktoria Tolstoy.

On June 14, 2008, Svensson went missing during a scuba diving session on Ingarö outside Stockholm, Sweden. His diving companions eventually found him lying unconscious on the seabed. Having sustained serious injuries, he was rushed to Karolinska University Hospital by helicopter, but could not be saved. He was 44 years old, married and the father of two sons.^[1]

Discography[link]

Studio Albums:

• When Everyone Has Gone (1993) Dragon
• Winter in Venice (1997) Superstudio GUL
• EST plays Monk (1996) Superstudio GUL
• From Gagarin's Point of View (1999) Superstudio GUL
• Good Morning Susie Soho (2000) Superstudio GUL
• Strange Place for Snow (2002) Superstudio GUL
• Seven Days of Falling (2003) Superstudio GUL
• Viaticum (2005) Spamboolimbo
• Tuesday Wonderland (2006, Recorded and mixed by Åke Linton at Bohus Sound Recording Studios, Gothenburg, Sweden in March 2006)
• Leucocyte (2008, recorded by Åke Linton at Studios 301, Sydney, Australia)
• 301 (2012, recorded in January 2007 at Studio 301, Sydney, Australia) ACT

Live Albums:

• E.S.T. Live '95 (1995, released in Sweden as Mr. & Mrs. Handkerchief) ACT Music + Vision

• Live in Stockholm (2003) DVD, recorded December 10, 2000 – including videos and an interview
• Live in Hamburg (2007, recorded November 22, 2006)

Compilation Albums

• Somewhere Else Before (U.S. compilation from From Gagarin's Point of View and Good Morning Susie Soho, 2001)
• Retrospective - The Very Best of E.S.T. (2009)

Also appears on

• Beginner's Guide to Scandinavia (3CD, Nascente 2011)

References[link]

External links[link]

• Obituary in The Guardian
• Obituary in The Daily Telegraph
• Photos of Esbjörn Svensson Trio by Luca D'Agostino, 2006
• Photos of Esbjörn Svensson Trio by Emre Boyar, 2005