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Quantum Concentration
The quantum concentration is the particle concentration (i.e. the number of particles per unit volume) of a system where the interparticle distance is equal to the thermal de Broglie wavelength. Quantum effects become appreciable when the particle concentration is greater than or equal to the quantum concentration, which is defined as: :n_=\left(\frac\right)^ :where: : is the mass of the particles in the system : is the Boltzmann constant : is the temperature as measured in kelvins :\hbar is the reduced Planck constant The quantum concentration for room temperature protons is about 1/cubic-Angstrom. As the quantum concentration depends on temperature, high temperatures will put most systems in the classical limit unless they have a very high density e.g. a White dwarf A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Density (particle Count)
The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density. ''Population density'' is an example of areal number density. The term number concentration (symbol: lowercase ''n'', or ''C'', to avoid confusion with amount of substance indicated by uppercase '' N'') is sometimes used in chemistry for the same quantity, particularly when comparing with other concentrations. Definition Volume number density is the number of specified objects per unit volume: :n = \frac, where ''N'' is the total number of objects in a volume ''V''. Here it is assumed that ''N'' is large enough that rounding of the count to the nearest integer does not introduce much of an error, however ''V'' is chosen to be small enough that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Inter-particle Distance
Mean inter-particle distance (or mean inter-particle separation) is the mean distance between microscopic particles (usually atoms or molecules) in a macroscopic body. Ambiguity From the very general considerations, the mean inter-particle distance is proportional to the size of the per-particle volume 1/n, i.e., : \langle r \rangle \sim 1/n^, where n = N/V is the particle density. However, barring a few simple cases such as the ideal gas model, precise calculations of the proportionality factor are impossible analytically. Therefore, approximate expressions are often used. One such an estimation is the Wigner–Seitz radius : \left( \frac \right)^, which corresponds to the radius of a sphere having per-particle volume 1/n. Another popular definition is : 1/n^, corresponding to the length of the edge of the cube with the per-particle volume 1/n. The two definitions differ by a factor of approximately 1.61, so one has to exercise care if an article fails to define the parameter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal De Broglie Wavelength
In physics, the thermal de Broglie wavelength (\lambda_, sometimes also denoted by \Lambda) is roughly the average de Broglie wavelength of particles in an ideal gas at the specified temperature. We can take the average interparticle spacing in the gas to be approximately where is the volume and is the number of particles. When the thermal de Broglie wavelength is much smaller than the interparticle distance, the gas can be considered to be a classical or Maxwell–Boltzmann gas. On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance, quantum effects will dominate and the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. The critical temperature is the transition point between these two regimes, and at this critical temperature, the thermal wavelength will be approximately equal to the interparticle distance. That is, the quantum nature of the gas will be evident for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven " defining constants" that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly . Roles of the Boltzmann constant Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure and volume is proportional to the product of amount of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907). The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null (zero) point. Historically, the Kelvin scale was developed by shifting the starting point of the much-older Celsius scale down from the melting point of water to absolute zero, and its increments still closely approximate the historic definition of a degree Celsius, but since 2019 the scale has been defined by fixing the Boltzmann constant to be exactly . Hence, one kelvin is equal to a change in the thermodynamic temperature that results in a change of thermal energy by . The temperature in degree Celsius is now defined as the temperature in kelvins minus 273.15, meaning t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planck Constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by h. The reduced Planck constant, or Dirac constant, equal to the constant divided by 2 \pi, is denoted by \hbar. In metrology it is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value The constant was first postulated by Max Planck in 1900 as part of a solution to the ultraviolet catastrophe. At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but the distribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
White Dwarf
A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes from the emission of residual thermal energy; no fusion takes place in a white dwarf. The nearest known white dwarf is at 8.6 light years, the smaller component of the Sirius binary star. There are currently thought to be eight white dwarfs among the hundred star systems nearest the Sun. The unusual faintness of white dwarfs was first recognized in 1910. The name ''white dwarf'' was coined by Willem Luyten in 1922. White dwarfs are thought to be the final evolutionary state of stars whose mass is not high enough to become a neutron star or black hole. This includes over 97% of the other stars in the Milky Way. After the hydrogen- fusing period of a main-sequence star of low or medium mass ends, such a star will expand to a red giant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sackur–Tetrode Equation
The Sackur–Tetrode equation is an expression for the entropy of a monatomic ideal gas. It is named for Hugo Martin Tetrode (1895–1931) and Otto Sackur (1880–1914), who developed it independently as a solution of Boltzmann's gas statistics and entropy equations, at about the same time in 1912. Formula The Sackur–Tetrode equation expresses the entropy S of a monatomic ideal gas in terms of its thermodynamic state—specifically, its volume V, internal energy U, and the number of particles N: : \frac = \ln \left \frac VN \left(\frac\frac UN\right)^\right , where k_\mathrm is the Boltzmann constant, m is the mass of a gas particle and h is the Planck constant. The equation can also be expressed in terms of the thermal wavelength \Lambda: : \frac = \ln\left(\frac\right)+\frac , For a derivation of the Sackur–Tetrode equation, see the Gibbs paradox. For the constraints placed upon the entropy of an ideal gas by thermodynamics alone, see the ideal gas article. The above ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
