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phase diagram

phase diagram, graph that shows the relation between the solid, liquid, and gaseous states of a substance (see states of matter) as a function of the temperature and pressure. The graph is divided into three regions, one for each of the physical states, and it specifies the range of temperatures at which the substance exists in each state for any value of the pressure. For example, a phase diagram for water shows that at a pressure of 1 atmosphere water is a solid up to a temperature of 0°C;, a liquid from 0°C; to 100°C;, and a gas above 100°C;. At a pressure of 0.5 atmospheres, the graph shows that although the melting point of ice remains 0°C;, the boiling point of water is lowered to 82°C;. Each substance has its own phase diagram, which must be determined experimentally. The border between two regions on the graph represents an equilibrium state, such as a melting point or boiling point, at which two states can coexist (see chemical equilibrium). The point at which all three regions meet is called the triple point; at these conditions of temperature and pressure, the solid, liquid, and gaseous states can coexist in equilibrium. The triple-point conditions for water are a temperature of .01°C; and a pressure of .006 atmospheres.

The Columbia Electronic Encyclopedia Copyright © 2004.
Licensed from Columbia University Press

Hertzsprung-Russell diagram

Hertzsprung-Russell diagram [for Ejnar Hertzsprung and H. N. Russell], graph showing the luminosity of a star as a function of its surface temperature. The luminosity, or absolute magnitude, increases upwards on the vertical axis; the temperature (or some temperature-dependent characteristic such as spectral class or color) decreases to the right on the horizontal axis. It is found that the majority of stars lie on a diagonal band that extends from hot stars of high luminosity in the upper left corner to cool stars of low luminosity in the lower right corner. This band is called the main sequence. Stars called white dwarfs lie sparsely scattered in the lower left corner. The giant stars—stars of great luminosity and size (see red giant)—form a thick, approximately horizontal band that joins the main sequence near the middle of the diagonal band. Above the giant stars, there is another sparse horizontal band consisting of the supergiant stars. The stars in the lower right corner of the main sequence are frequently called red dwarfs, and the stars between the main sequence and the giant branch are called subgiants. The significance of the H-R diagram is that stars are concentrated in certain distinct regions instead of being distributed at random. This regularity is an indication that definite laws govern stellar structure and stellar evolution. In population I regions (see stellar populations) like the spiral arms of galaxies or open star clusters, the stars fall almost exclusively on the main sequence. In population II regions like the nuclei of galaxies and globular clusters, the stars are older and have evolved significantly. The most luminous stars have evolved furthest, and an H-R diagram of such a region will show the upper end of the main sequence depopulated and will show a well-developed giant branch. In such a diagram it appears that the main sequence has "burned down" from the top like a candle. Thus, the point at which the main sequence terminates and the giant branch begins is an indication of the age of a star cluster. A modified H-R diagram of the stars in a cluster of unknown distance can be used to determine the absolute magnitude, or luminosity, of the stars. Since the apparent magnitude of a star of given absolute magnitude depends only on the star's distance, the observed apparent magnitude of the stars can be used to calculate the distance to the cluster.

The Columbia Electronic Encyclopedia Copyright © 2004.
Licensed from Columbia University Press

flowchart

Graphical representation of a process, such as a manufacturing operation or a computer operation, indicating the various steps taken as the product moves along the production line or the problem moves through the computer. Individual operations can be represented by closed boxes, with arrows between boxes indicating the order in which the steps are taken and divergent paths determined by variable results.

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Hertzsprung-Russell diagram

or H-R diagram

Graph in which the absolute magnitudes of stars are plotted against their colours (a measure of their temperatures). Of great importance to theories of stellar evolution, it evolved from charts begun independently in 1911 by the Danish astronomer Ejnar Hertzsprung (1873–1967) and the U.S. astronomer Henry Norris Russell (1877–1957). On the diagram, stars are ranked from bottom to top in order of increasing brightness and from right to left by increasing temperature. Stars tend to cluster in certain parts of the diagram, especially along a diagonal line, called the main sequence, which is the locus of hydrogen-burning stars of different masses.

Learn more about Hertzsprung-Russell diagram with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.