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Matter organizes into various phases or states of matter depending on its constituents and external factors like pressure and temperature. Except at extreme temperatures and pressures, atoms form the three classical states of matter: solid, liquid and gas.
Forms of matter that are not composed of molecules and are organized by different forces can also be considered different states of matter. Superfluids (like Fermionic condensate) and the quark–gluon plasma are examples. In a chemical equation, the state of matter of the chemicals may be shown as (s) for solid, (l) for liquid, and (g) for gas.
A typical phase diagram.The solid green line applies to most substances; the dashed green line gives the anomalous behavior of water. In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. [1]
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The remaining variable, as well as other quantities such as the internal energy and the entropy, would be expressed as state functions of these three variables. The state functions satisfy certain universal constraints, expressed in the laws of thermodynamics, and they depend on the peculiarities of the materials that compose the concrete system.
1611 – Johannes Kepler first states the Kepler conjecture about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing ( face-centered cubic ) and hexagonal close packing arrangements.
The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
The path or series of states through which a system passes from an initial equilibrium state to a final equilibrium state [1] and can be viewed graphically on a pressure-volume (P-V), pressure-temperature (P-T), and temperature-entropy (T-s) diagrams. [2] There are an infinite number of possible paths from an initial point to an end point in a ...