Communication
Free
Faster access than browser!

# Boltzmann's entropy formula

In statistical mechanics, Boltzmann's equation is a probability equation relating the entropy S of an ideal gas to the quantity W, the number of real microstates corresponding to the gas' macrostate: where kB is the Boltzmann constant (also written as simply k) and equal to 1.38065 × 10−23 J/K. [1]

## Atom

An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element.

## Boltzmann constant

The Boltzmann constant, which is named after Ludwig Boltzmann, is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas.

## Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

## Edwin Thompson Jaynes

Edwin Thompson Jaynes (July 5, 1922 &ndash; April 30, 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis.

## Entropy

In statistical mechanics, entropy is an extensive property of a thermodynamic system.

## Entropy (statistical thermodynamics)

In classical statistical mechanics, the entropy function earlier introduced by Rudolf Clausius is interpreted as statistical entropy using probability theory.

## Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.

## History of entropy

The concept of entropy developed in response to the observation that a certain amount of functional energy released from combustion reactions is always lost to dissipation or friction and is thus not transformed into useful work.

## Ideal gas

An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interactions are perfectly elastic collisions.

## Identical particles

Identical particles, also called indistinguishable or indiscernible particles, are particles that cannot be distinguished from one another, even in principle.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Josiah Willard Gibbs

Josiah Willard Gibbs (February 11, 1839 &ndash; April 28, 1903) was an American scientist who made important theoretical contributions to physics, chemistry, and mathematics.

## Kinetic theory of gases

The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container.

## Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

## Ludwig Boltzmann

Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion).

## Macroscopic scale

The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible almost practically with the naked eye, without magnifying optical instruments.

## Max Planck

Max Karl Ernst Ludwig Planck, FRS (23 April 1858 &ndash; 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.

## Microstate (statistical mechanics)

In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations.

## Molecule

A molecule is an electrically neutral group of two or more atoms held together by chemical bonds.

## Momentum

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.

## Number

A number is a mathematical object used to count, measure and also label.

## Phase space

In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space.

## Probability

Probability is the measure of the likelihood that an event will occur.

## Probability theory

Probability theory is the branch of mathematics concerned with probability.

## Statistical ensemble (mathematical physics)

In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1902, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in.

## Statistical mechanics

Statistical mechanics is one of the pillars of modern physics.

## Thermodynamic system

A thermodynamic system is the material and radiative content of a macroscopic volume in space, that can be adequately described by thermodynamic state variables such as temperature, entropy, internal energy, and pressure.

## Thermodynamics

Thermodynamics is the branch of physics concerned with heat and temperature and their relation to energy and work.

## References

Hey! We are on Facebook now! »