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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 *k_B 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 Compact star, stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very density, dense: in an Earth sized volume, it packs a mass that is comparable to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 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 ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Boltzmann Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the molar gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating Johnson–Nyquist noise, thermal noise in resistors. The Boltzmann constant has Dimensional analysis, dimensions of energy divided by temperature, the same as entropy and heat capacity. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 revision of the SI, the Boltzmann constant is one of the seven "Physical constant, defining constants" that have been defined so as to have exact finite decimal values in SI units. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly joules per kelvin, with the effect of defining the SI unit ke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Kelvin
The kelvin (symbol: K) is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By definition, the Celsius scale (symbol °C) and the Kelvin scale have the exact same magnitude; that is, a rise of 1 K is equal to a rise of 1 °C and vice versa, and any temperature in degrees Celsius can be converted to kelvin by adding 273.15. The 19th century British scientist Lord Kelvin first developed and proposed the scale. It was often called the "absolute Celsius" scale in the early 20th century. The kelvin was formally added to the International System of Units in 1954, defining 273.16 K to be the triple point of water. The Celsius, Fahrenheit, and Rankine scales were redefined in terms of the Kelvin scale using this definition. The 2019 revision of the SI now defines the kelvin in terms of energy by setting the Bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Planck Constant
The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum. The constant was postulated by Max Planck in 1900 as a proportionality constant needed to explain experimental black-body radiation. Planck later referred to the constant as the "quantum of Action (physics), action". In 1905, Albert Einstein associated the "quantum" or minimal element of the energy to the electromagnetic wave itself. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". In metrology, the Planck constant 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, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
White Dwarf
A white dwarf is a Compact star, stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very density, dense: in an Earth sized volume, it packs a mass that is comparable to the Sun. No nuclear fusion takes place in a white dwarf; what light it radiates is from its residual heat. The nearest known white dwarf is Sirius B, 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 Jacob Luyten in 1922. White dwarfs are thought to be the final stellar evolution, evolutionary state of stars whose mass is not high enough to become a neutron star or black hole. This includes over 97% of the stars in the Milky Way. After the hydrogen-stellar nucleosynthesis, fusing period of a main sequence, main-sequence star of Stellar mass, lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 abov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
