Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Van der Waals Equation01:10

Van der Waals Equation

4.8K
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...
4.8K
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

1.9K
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
1.9K
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

36.6K
Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws. 
36.6K
Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision02:43

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

35.5K
The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For example, Charles’ law states that volume and temperature are directly related. Gases, therefore, expand when heated at constant pressure. Although gas laws explain how the macroscopic properties change relative to one another, it does not explain the rationale behind it.
35.5K
Ideal Gas Equation01:17

Ideal Gas Equation

7.6K
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.
7.6K
Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules02:34

Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules

35.1K
The test of the kinetic molecular theory (KMT) and its postulates is its ability to explain and describe the behavior of a gas. The various gas laws (Boyle’s, Charles’s, Gay-Lussac’s, Avogadro’s, and Dalton’s laws) can be derived from the assumptions of the KMT, which have led chemists to believe that the assumptions of the theory accurately represent the properties of gas molecules.
35.1K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Inverse Modeling of Heterogeneous Structures in Electron Probe Microanalysis.

Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada·2024
Same author

Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory.

Entropy (Basel, Switzerland)·2020
Same author

Formulation of moment equations for rarefied gases within two frameworks of non-equilibrium thermodynamics: RET and GENERIC.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2020
Same author

Comment on "Thermodynamically admissible 13 moment equations from the Boltzmann equation".

Physical review letters·2010
Same author

Higher-order effects in rarefied channel flows.

Physical review. E, Statistical, nonlinear, and soft matter physics·2008
Same author

H theorem, regularization, and boundary conditions for linearized 13 moment equations.

Physical review letters·2007

Related Experiment Video

Updated: Oct 20, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.4K

Consistent, explicit, and accessible Boltzmann collision operator for polyatomic gases.

Vladimir Djordjić1,2, Milana Pavić-Čolić2, Manuel Torrilhon1

  • 1Applied and Computational Mathematics, RWTH Aachen University, Schinkelstrasse 2, 52062 Aachen, Germany.

Physical Review. E
|September 16, 2021
PubMed
Summary
This summary is machine-generated.

We developed a new Boltzmann collision operator for polyatomic gases, enabling accurate modeling of complex gas dynamics and energy transfer. This approach simplifies calculations for macroscopic properties and recovers established formulas.

More Related Videos

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry
16:11

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry

Published on: June 8, 2022

2.4K
Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

4.7K

Related Experiment Videos

Last Updated: Oct 20, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.4K
Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry
16:11

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry

Published on: June 8, 2022

2.4K
Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

4.7K

Area of Science:

  • Statistical Mechanics
  • Fluid Dynamics
  • Chemical Physics

Background:

  • Accurate modeling of polyatomic gases is crucial for understanding complex fluid dynamics and energy transfer phenomena.
  • Existing Boltzmann collision operators often lack the explicit nonlinearity needed for detailed macroscopic system analysis.
  • The variable hard-sphere model provides a foundation for realistic particle interactions but requires extensions for polyatomic systems.

Purpose of the Study:

  • To propose an explicit, fully nonlinear Boltzmann collision operator for polyatomic gases.
  • To develop a model consistent with monatomic gases and amenable to moment equations and Chapman-Enskog expansion.
  • To enable explicit computation of nonlinear production terms for macroscopic systems.

Main Methods:

  • Development of a continuous internal energy state variable.
  • Polyatomic generalization of the variable hard-sphere model, including frozen collisions.
  • Utilizing a publicly available computer algebra code for explicit computations.

Main Results:

  • An explicit, fully nonlinear Boltzmann collision operator for polyatomic gases with constant heat capacity.
  • The model's consistency with monatomic cases and simplified evaluations for moment equations and Chapman-Enskog expansion.
  • Explicit computation of nonlinear production terms for macroscopic systems of moments.
  • Recovery of the Eucken formula for a specific choice of frozen collisions within the Prandtl number range.

Conclusions:

  • The proposed Boltzmann collision operator offers a robust framework for simulating polyatomic gas dynamics.
  • This model facilitates advanced analysis of macroscopic properties and energy transfer mechanisms.
  • The computational approach allows for explicit calculation of complex nonlinear terms, advancing the field of gas kinetics.