Search results
Results from the WOW.Com Content Network
Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation – his famous H-theorem. However the key assumption he made in formulating the collision term was " molecular chaos ", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law.
Boltzmann's distribution is an exponential distribution. Boltzmann factor (vertical axis) as a function of temperature T for several energy differences ε i − ε j.. In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution [1]) is a probability distribution or probability measure that gives the probability that a system will be in a certain ...
The Boltzmann equation can be used to determine how physical quantities change, such as heat energy and momentum, when a fluid is in transport. One may also derive other properties characteristic to fluids such as viscosity , thermal conductivity , and electrical conductivity (by treating the charge carriers in a material as a gas). [ 2 ]
In practice, information entropy is almost always calculated using base-2 logarithms, but this distinction amounts to nothing other than a change in units. One nat is about 1.44 shannons. For a simple compressible system that can only perform volume work, the first law of thermodynamics becomes = +.
Boltzmann in his original publication writes the symbol E (as in entropy) for its statistical function. [1] Years later, Samuel Hawksley Burbury, one of the critics of the theorem, [7] wrote the function with the symbol H, [8] a notation that was subsequently adopted by Boltzmann when referring to his "H-theorem". [9]
Although Boltzmann first linked entropy and probability in 1877, the relation was never expressed with a specific constant until Max Planck first introduced k, and gave a more precise value for it (1.346 × 10 −23 J/K, about 2.5% lower than today's figure), in his derivation of the law of black-body radiation in 1900–1901. [11]
The Boltzmann–Matano method is used to convert the partial differential equation resulting from Fick's law of diffusion into a more easily solved ordinary differential equation, which can then be applied to calculate the diffusion coefficient as a function of concentration.
The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan , who empirically derived the relationship, and Ludwig Boltzmann who derived the law theoretically.