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Related Concept Videos

Ideal Gas Equation01:17

Ideal Gas Equation

The ideal gas equation is an equation of state that relates the state variables pressure, volume, temperature, and the number of moles of a hypothetical gas. This equation is a combination of four empirical laws, namely Boyle’s Law, Charles’s Law, Avogadro’s Law, and Gay-Lussac’s Law. When the proportionalities of the above four empirical laws are combined, it results in a single proportionality constant known as the universal gas constant.
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
Gas Laws: Boyle's, Gay-Lussac, Charles', Avogadro's, and Ideal Gas Law03:19

Gas Laws: Boyle's, Gay-Lussac, Charles', Avogadro's, and Ideal Gas Law

Through experiments, scientists established the mathematical relationships between pairs of variables, such as pressure and temperature, pressure and volume, volume and temperature, and volume and moles, that hold for an ideal gas.
The Van der Waals Equation01:26

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
Kinetic Theory of an Ideal Gas01:12

Kinetic Theory of an Ideal Gas

A mole is defined as the amount of any substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. An Italian scientist Amedeo Avogadro (1776–1856) formed the  hypothesis that equal volumes of gas at equal pressure and temperature contain equal numbers of molecules, independent of the type of gas. Later, the hypothesis was developed to form the SI unit for measuring the amount of any substance.
The number of molecules in one mole is called Avogadro's number...

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Related Experiment Video

Updated: May 27, 2026

Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames
10:29

Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames

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Boltzmann equations for a binary one-dimensional ideal gas.

A D Boozer1

  • 1Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA. boozer@unm.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
PubMed
Summary
This summary is machine-generated.

This study derives Boltzmann and anti-Boltzmann equations for a one-dimensional binary ideal gas. It rigorously proves time-asymmetric assumptions for large N, clarifying the origin of time asymmetry in Boltzmann's H theorem.

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Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry
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Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames
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Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry
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Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry

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Area of Science:

  • Statistical Mechanics
  • Theoretical Physics
  • Dynamical Systems

Background:

  • The Boltzmann H theorem explains the irreversibility of macroscopic systems from microscopic laws.
  • Understanding the origin of time asymmetry in statistical mechanics remains a complex challenge.
  • Ideal gas models provide a foundational framework for studying thermodynamic behavior.

Purpose of the Study:

  • To derive time-asymmetric Boltzmann and anti-Boltzmann equations for a one-dimensional binary ideal gas.
  • To rigorously investigate the validity of time-asymmetric assumptions in the context of statistical mechanics.
  • To clarify the origins of time asymmetry in Boltzmann's H theorem.

Main Methods:

  • Development of a time-reversal invariant dynamical model for a binary ideal gas in one dimension.
  • Introduction of time-asymmetric assumptions to derive Boltzmann and anti-Boltzmann equations.
  • Derivation of an exact expression for the N-molecule velocity distribution function for specific initial states.
  • Rigorous mathematical proof of the validity of time-asymmetric assumptions in the large N limit.

Main Results:

  • Successfully derived Boltzmann and anti-Boltzmann equations describing single-molecule velocity distribution functions.
  • Obtained an exact N-molecule velocity distribution function for a special class of initial states.
  • Provided a rigorous proof that time-asymmetric assumptions are valid in the limit of large N.
  • Offered new insights into the origin of time asymmetry in Boltzmann's H theorem.

Conclusions:

  • The study successfully derives and validates time-asymmetric equations for an ideal gas model.
  • The findings provide a rigorous foundation for understanding the emergence of irreversibility in physical systems.
  • This work contributes to resolving subtle issues concerning the time asymmetry inherent in statistical mechanics.