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Equation of State01:07

Equation of State

1.7K
The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and...
1.7K
Clausius-Clapeyron Equation02:35

Clausius-Clapeyron Equation

56.5K
The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
56.5K
Van der Waals Equation01:10

Van der Waals Equation

4.0K
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...
4.0K
Ideal Gas Equation01:17

Ideal Gas Equation

6.7K
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.
6.7K
Molecular Comparison of Gases, Liquids, and Solids02:26

Molecular Comparison of Gases, Liquids, and Solids

40.9K
Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no regular arrangement (no fixed shape); in a gas, they are far apart with no regular arrangement (no fixed shape). Particles in a solid vibrate about fixed positions (cannot flow) and do not generally move in relation to one another; in a liquid, they move past each other (can flow) but remain in essentially constant contact; in a gas, they move...
40.9K
Energy Conservation and Bernoulli's Equation01:16

Energy Conservation and Bernoulli's Equation

8.9K
Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
8.9K

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Related Experiment Video

Updated: Jun 18, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

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Generally applicable physics-based equation of state for liquids.

J E Proctor1, Kostya Trachenko2

  • 1Materials and Physics Research Group, University of Salford, Manchester M5 4WT, United Kingdom.

Reports on Progress in Physics. Physical Society (Great Britain)
|August 2, 2024
PubMed
Summary
This summary is machine-generated.

Researchers developed a new physics-based equation of state (EOS) for liquids, linking macroscopic properties to microscopic molecular behavior. This generally applicable (GAP) EOS offers a significant advancement for understanding liquid and supercritical fluid behavior under extreme conditions.

Keywords:
Grüneisenequation of statefluidsliquids

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Area of Science:

  • Thermodynamics and Statistical Mechanics
  • Condensed Matter Physics
  • Planetary Science and Geophysics

Background:

  • Existing physics-based equations of state (EOS) are well-established for solids and gases, but not for liquids due to inherent theoretical complexities.
  • Current liquid EOS models are often empirical, complex, and contain physically meaningless parameters, limiting their predictive power for planetary interiors and industrial processes.
  • A fundamental gap exists in theoretical frameworks for describing liquid behavior under high pressure and temperature conditions.

Purpose of the Study:

  • To develop a generally applicable, physics-based equation of state (EOS) for liquids and supercritical fluids at liquid-like densities.
  • To establish a direct link between macroscopic thermodynamic properties (EOS) and microscopic liquid dynamics (molecular hopping frequency).
  • To provide a more accurate and physically grounded model for fluid behavior relevant to extreme environments.

Main Methods:

  • Development of a new generally applicable (GAP) equation of state explicitly dependent on internal energy.
  • Integration of molecular hopping frequency (liquid relaxation time) as a key microscopic input to determine internal energy.
  • Validation against experimental data through various testing methods, including isochoric studies, and comparison with solid and gas EOS models.

Main Results:

  • The developed GAP EOS demonstrates good agreement with available experimental data for liquids and supercritical fluids.
  • The GAP EOS successfully links macroscopic pressure-volume-temperature (PVT) properties to microscopic liquid relaxation times.
  • The model shows similarities to solid EOS (Mie-Grüneisen) in condensed phases but fundamental differences compared to gas EOS.

Conclusions:

  • The new generally applicable (GAP) EOS provides a robust, physics-based framework for describing liquid behavior, overcoming limitations of previous models.
  • The inclusion of a semi-empirical term for static energy and the Grüneisen parameter are necessary components, similar to solid-state physics.
  • Further experimental data is crucial to refine and extend the applicability of liquid EOS models.