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Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a particular energy level is known as the degree of degeneracy (or simply the degeneracy) of the level.
Using the Fermi gas as a model, it is possible to calculate the Chandrasekhar limit, i.e. the maximum mass any star may acquire (without significant thermally generated pressure) before collapsing into a black hole or a neutron star. The latter, is a star mainly composed of neutrons, where the collapse is also avoided by neutron degeneracy ...
A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac , each of whom derived the distribution independently in 1926. [ 1 ] [ 2 ] Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics .
The heat capacity is = = . In general, consider the extensive variable X and intensive variable Y where X and Y form a pair of conjugate variables . In ensembles where Y is fixed (and X is allowed to fluctuate), then the average value of X will be: X = ± ∂ ln Z ∂ β Y . {\displaystyle \langle X\rangle =\pm {\frac {\partial \ln Z ...
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.
This will be the case for photons and massive particles in mutual equilibrium and the resulting distribution will be the Planck distribution. Notes A much simpler way to think of Bose–Einstein distribution function is to consider that n particles are denoted by identical balls and g shells are marked by g-1 line partitions.
By the equipartition theorem, internal energy per mole of gas equals c v T, where T is absolute temperature and the specific heat at constant volume is c v = (f)(R/2). R = 8.314 J/(K mol) is the universal gas constant, and "f" is the number of thermodynamic (quadratic) degrees of freedom, counting the number of ways in which energy can occur.
The lake retention time for a body of water with the volume 2,000 m 3 (71,000 cu ft) and the exit flow of 100 m 3 /h (3,500 cu ft/h) is 20 hours.. Lake retention time (also called the residence time of lake water, or the water age or flushing time) is a calculated quantity expressing the mean time that water (or some dissolved substance) spends in a particular lake.