Related Experiment Video
Updated: Sep 22, 2025
09:46
Protocol for Measuring the Thermal Properties of a Supercooled Synthetic Sand-water-gas-methane Hydrate Sample
Published on: March 21, 2016
9.0K
Eighth-Order Virial Equation of State for Methane from Accurate Two-Body and Nonadditive Three-Body Intermolecular
1Institut für Thermodynamik, Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany.
The Journal of Physical Chemistry. B
|May 18, 2022
Summary
We calculated virial coefficients for methane up to 1200 K using advanced potentials and Monte Carlo methods. Including three-body interactions is crucial for accurate methane equations of state.
Area of Science:
- Thermodynamics
- Physical Chemistry
- Computational Chemistry
Background:
- Accurate equations of state are vital for understanding fluid behavior.
- Methane properties are essential for various industrial applications.
- Previous models lacked sufficient accuracy at higher temperatures and densities.
Purpose of the Study:
- To determine virial coefficients for methane up to 1200 K.
- To develop an analytical eighth-order virial equation of state (VEOS8).
- To assess the impact of nonadditive three-body interactions on methane's thermodynamic properties.
Main Methods:
- Utilized an ab initio-based two-body potential and an empirical nonadditive three-body potential.
- Incorporated nuclear quantum effects via the semiclassical Feynman-Hibbs approach.
- Employed Mayer-sampling Monte Carlo techniques for numerical integration.
Main Results:
- Calculated second to eighth virial coefficients for methane.
- Developed an analytical eighth-order virial equation of state (VEOS8).
- Achieved high agreement between VEOS8 and the Setzmann-Wagner equation of state (SWEOS) when nonadditive interactions were included.
Conclusions:
- Nonadditive three-body interactions are essential for accurate methane equations of state.
- The developed VEOS8 provides a reliable representation of methane properties.
- This study advances the understanding of methane's thermodynamic behavior at elevated temperatures.
Related Concept Videos
01:10Van der Waals Equation
4.6K
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...
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...
4.6K
04:01Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
35.7K
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.
35.7K
03:24Hybridization of Atomic Orbitals I
49.4K
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
49.4K
01:17Ideal Gas Equation
7.4K
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.
7.4K
01:08Spin–Spin Coupling Constant: Overview
1.0K
In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
1.0K
01:20Maxwell-Boltzmann Distribution: Problem Solving
1.8K
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
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
1.8K