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Related Concept Videos

Equation of State01:07

Equation of State

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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...
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Thermodynamic Potentials01:26

Thermodynamic Potentials

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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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Heat Capacities of an Ideal Gas III01:25

Heat Capacities of an Ideal Gas III

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The number of independent ways a gas molecule can move along straight line, rotate, and vibrate is called its degrees of freedom. Supposing d represents the number of degrees of freedom of an ideal gas, the molar heat capacity at constant volume of an ideal gas in terms of d is
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Heat Capacities of an Ideal Gas II01:23

Heat Capacities of an Ideal Gas II

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For a system that undergoes a thermodynamic process at a constant volume condition, the heat absorbed is used only to increase the system's internal energy and not for doing any kind of work. While for a system undergoing a thermodynamic process under a constant pressure condition, the amount of heat absorbed is used not only for increasing the internal energy (as a function of temperature) but also for doing some work. The molar heat capacity is the amount of heat required to increase the...
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Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

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Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...
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Ideal Gas Equation01:17

Ideal Gas Equation

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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.
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Updated: Nov 17, 2025

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
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First-principles equation of state database for warm dense matter computation.

Burkhard Militzer1,2, Felipe González-Cataldo1, Shuai Zhang1,3,4

  • 1Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA.

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|February 19, 2021
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Summary

A new first-principles equation of state (FPEOS) database covers extreme conditions for elements and compounds. This resource enables studying mixtures and predicting maximum shock compression ratios for various materials.

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Area of Science:

  • Condensed Matter Physics
  • Computational Materials Science
  • High-Pressure Physics

Background:

  • Accurate equations of state are crucial for understanding matter under extreme conditions.
  • Simulations provide insights into material properties beyond experimental reach.
  • Existing databases may lack comprehensive coverage of elements and mixtures at high pressures and temperatures.

Purpose of the Study:

  • To develop a first-principles equation of state (FPEOS) database for a wide range of elements and compounds.
  • To provide pressure and internal energy data across broad density-temperature ranges.
  • To investigate the properties of mixtures and predict shock compression behaviors.

Main Methods:

  • Utilized path integral Monte Carlo and density functional molecular dynamics simulations.
  • Performed approximately 5000 first-principles simulations for H, He, B, C, N, O, Ne, Na, Mg, Al, Si, and various compounds.
  • Employed the linear mixing approximation to study mixture properties.

Main Results:

  • Generated an FPEOS database covering densities from 0.5 to 50 g/cm³ and temperatures from 10⁴ to 10⁹ K.
  • Computed isobars, adiabats, and shock Hugoniot curves, including L- and K-shell ionization regimes.
  • Derived Hugoniot curves for mixtures like water, alumina, carbon-oxygen, helium-neon, and CH-silicon, predicting maximum shock compression ratios.

Conclusions:

  • The FPEOS database offers a valuable resource for high-pressure and high-temperature material science.
  • Mixtures can exhibit enhanced shock compression ratios compared to their constituent elements.
  • The study provides insights into trends in mixture properties across different thermodynamic spaces.