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Debye | A Wisdom Archive on Debye | | Debye A selection of articles related to Debye | |
| | debye, Debye, Debye - Reference | | | Page 1 » Page 2 « | |
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| ARTICLES RELATED TO Debye | | | | | |  Debye: Encyclopedia II - Peltier–Seebeck effect - Thomson effectThomson effect, named for William Thomson, 1st Baron Kelvin, describes the heating or cooling of a current-carrying conductor with a temperature gradient.
Any current-carrying conductor, with a temperature difference between two points, will either absorb or emit heat, depending on the material.
If a current density J is passed through a homogeneous conductor, heat production per unit volume is
where
ρ is the resistivity of the material
dT/dx is the temperature gradient a ...
See also:Peltier–Seebeck effect, Peltier–Seebeck effect - Seebeck effect, Peltier–Seebeck effect - Thermopower, Peltier–Seebeck effect - Charge carrier diffusion, Peltier–Seebeck effect - Phonon drag, Peltier–Seebeck effect - Peltier effect, Peltier–Seebeck effect - Thomson effect, Peltier–Seebeck effect - Patents Read more here: » Peltier–Seebeck effect: Encyclopedia II - Peltier–Seebeck effect - Thomson effect |
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| | | | | Debye: Encyclopedia II - Peltier-Seebeck effect - Thomson effect Thomson effect, named for William Thomson, 1st Baron Kelvin, describes the heating or cooling of a current-carrying conductor with a temperature gradient.
Any current-carrying conductor, with a temperature difference between two points, will either absorb or emit heat, depending on the material.
If a current density J is passed through a homogeneous conductor, heat production per unit volume is
where
ρ is the resistivity of the material
dT/dx is the temperature gradient alo ...
See also:Peltier-Seebeck effect, Peltier-Seebeck effect - Seebeck effect, Peltier-Seebeck effect - Thermopower, Peltier-Seebeck effect - Charge carrier diffusion, Peltier-Seebeck effect - Phonon drag, Peltier-Seebeck effect - Peltier effect, Peltier-Seebeck effect - Thomson effect, Peltier-Seebeck effect - Patents Read more here: » Peltier-Seebeck effect: Encyclopedia II - Peltier-Seebeck effect - Thomson effect |
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| | | | | | Debye: Encyclopedia II - Bessel function - Asymptotic forms The Bessel functions have the following asymptotic forms. For small arguments 0 < x << 1, one obtains:
where α is non-negative, γ is the Euler-Mascheroni constant (0.5772...), and Γ denotes the gamma function. For large arguments x >> 1, they become:
Asymptotic forms for the other types of Bessel function follow straightforwardly from the above relations. For example, for large x >> 1, the modified Bessel functio ...
See also:Bessel function, Bessel function - Applications, Bessel function - Definitions, Bessel function - Bessel functions of the first kind, Bessel function - Bessel functions of the second kind, Bessel function - Hankel functions, Bessel function - Modified Bessel functions, Bessel function - Spherical Bessel functions, Bessel function - Riccati-Bessel functions, Bessel function - Asymptotic forms, Bessel function - Properties Read more here: » Bessel function: Encyclopedia II - Bessel function - Asymptotic forms |
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| | | | | Debye: Encyclopedia II - Absolute zero - Cryogenics It can be shown from the laws of thermodynamics that absolute zero can never be achieved, though it is possible to reach temperatures arbitrarily close to it through the use of cryocoolers. This is the same principle that ensures no machine can be 100% efficient.
At very low temperatures in the vicinity of absolute zero, matter exhibits many unusual properties including superconductivity, superfluidity, and Bose-Einstein condensation. In order to study such phenomena, scientists have worked to obtain ever lower temperatures.
...
See also:Absolute zero, Absolute zero - Kinetic theory and motion, Absolute zero - Cryogenics, Absolute zero - Thermodynamics near absolute zero, Absolute zero - Absolute temperature scales, Absolute zero - Negative temperatures, Absolute zero - Notes Read more here: » Absolute zero: Encyclopedia II - Absolute zero - Cryogenics |
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| | | | | | Debye: Encyclopedia II - Debye model - Low temperature limit The temperature of a Debye solid is said to be low if , leading to
This definite integral can be evaluated exactly:
In the low temperature limit, the limitations of the Debye model mentioned above do not apply, and it gives a correct relationship between (phononic) heat capacity, temperature, the elastic coefficients, and the volume per atom (the latter ...
See also:Debye model, Debye model - Derivation, Debye model - Debye's derivation, Debye model - Low temperature limit, Debye model - High temperature limit, Debye model - Debye versus Einstein, Debye model - Debye temperature table Read more here: » Debye model: Encyclopedia II - Debye model - Low temperature limit |
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| | | | | | Debye: Encyclopedia II - Bessel function - Applications Bessel's equation arises when finding separable solutions to Laplace's equation and the Helmholtz equation in cylindrical or spherical coordinates, and Bessel functions are therefore especially important for many problems of wave propagation, static potentials, and so on. (For cylindrical problems, one obtains Bessel functions of integer order α = n; for spherical problems, one obtains half integer orders α = n+½.) For example:
electromagnetic waves in a cylindrical waveguide
heat conduction in a cylindrical object.
modes of vibration ...
See also:Bessel function, Bessel function - Applications, Bessel function - Definitions, Bessel function - Bessel functions of the first kind, Bessel function - Bessel functions of the second kind, Bessel function - Hankel functions, Bessel function - Modified Bessel functions, Bessel function - Spherical Bessel functions, Bessel function - Riccati-Bessel functions, Bessel function - Asymptotic forms, Bessel function - Properties Read more here: » Bessel function: Encyclopedia II - Bessel function - Applications |
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| | | | | Debye: Encyclopedia II - Absolute zero - Absolute temperature scales As mentioned, absolute or thermodynamic temperature is conventionally measured in Kelvins (Celsius-size degrees), and increasingly rarely in the Rankine scale (Fahrenheit-size degrees). Absolute temperature is uniquely determined up to a multiplicative constant which specifies the size of the "degree", so the ratios of two absolute temperatures, T2/T1, are the same in all scales. The most transparent definition comes from the classical Maxwell-Boltzmann distribution over energies, or from the quantu ...
See also:Absolute zero, Absolute zero - Kinetic theory and motion, Absolute zero - Cryogenics, Absolute zero - Thermodynamics near absolute zero, Absolute zero - Absolute temperature scales, Absolute zero - Negative temperatures, Absolute zero - Notes Read more here: » Absolute zero: Encyclopedia II - Absolute zero - Absolute temperature scales |
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| | | | | Debye: Encyclopedia II - Debye model - High temperature limit The temperature of a Debye solid is said to be high if T > > TD. if | x | < < 1, leads to
This is the Dulong-Petit law, and is fairly accurate although it does not take into account anharmonicity, which causes the heat capacity to rise further. The total heat capacity of the solid, if it is a conductor or semiconductor, may also con ...
See also:Debye model, Debye model - Derivation, Debye model - Debye's derivation, Debye model - Low temperature limit, Debye model - High temperature limit, Debye model - Debye versus Einstein, Debye model - Debye temperature table Read more here: » Debye model: Encyclopedia II - Debye model - High temperature limit |
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