In this equation, the quantum effect is expressed by the -term, and parameter v is the speed of the electrons which obey the Maxwell-Boltzmann distribution
as given in Eq.(8).
The equilibrium distribution function [f.sup.eq] is obtained using the Taylor series expansion of the Maxwell-Boltzmann distribution
function with velocity u up to second order.
By maximizing Q and using (5), one obtains that the Hawking radiation for macroscopic black hole is given by the following Maxwell-Boltzmann distribution
Now we are ready to present application of T(x) in probability and thermodynamics using one of the most important distributions which is called Maxwell-Boltzmann distribution
Note that the Arrhenius equation assumes the Maxwell-Boltzmann distribution
, and the relationship would be different for a Fermi gas.
Gatignol, "How to obtain higher-order multivariate Hermite expansion of Maxwell-Boltzmann distribution
by using Taylor expansion?" Zeitschrift fur Angewandte Mathematik und Physik, vol.
Therefore, the Fermi-Dirac integral can be estimated by the Maxwell-Boltzmann distribution
factor of f(E) = exp([[eta].sub.F]).
He covers a brief history of entropy and the second law of thermodynamics, all you need to know but never dared admit that you already knew, the uniform spatial distribution, the Boltzman distribution, the Maxwell-Boltzmann distribution
, entropy and the second law in the world of marbles, and entropy and the second law in the real world.
(1) and the red side is predominantly determined by the Maxwell-Boltzmann distribution
of kinetic energies.
He showed that the probability for each possible state of motion is an exponential function of the energy required, giving what is now known as the Maxwell-Boltzmann distribution
. Maxwell showed how the phenomena of diffusion, viscosity, and thermal conductivity could be related to molecular transport of mass, momentum, and energy.
For example, in [3, 28], Maxwell-Boltzmann distribution
functions are used to calculate the thermodynamics of photon gas.
A nonthermal plasma is in general any plasma which is not in thermodynamic equilibrium, either because the ion temperature is different from the electron temperature, or because the velocity distribution of one of the species does not follow a Maxwell-Boltzmann distribution
. The effects of dust temperature and dust charge variation in a dusty plasma with nonthermal ions have been investigated by Duan .