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Adiabatic Processes for an Ideal Gas01:18

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When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
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Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is,
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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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Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

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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.
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Work Done in an Adiabatic Process01:20

Work Done in an Adiabatic Process

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Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position. The temperature, pressure, and volume of the resulting gas-air mixture are 20 °C, 1.00 x 105 N/m2, and 240 cm3 , respectively. The mixture is then compressed adiabatically to a volume of 40 cm3. Note that, in the actual operation of an automobile engine, the compression is not...
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Van der Waals Equation01:10

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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.
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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Potential-Driven Adiabatic Connection in Density Functional Theory.

Andreas Savin1

  • 1Laboratoire de Chimie Théorique, UMR 7616, CNRS and Université Pierre et Marie, Curie-Paris VI, 4, place Jussieu, F-75252 Paris Cedex 5, France.

Journal of Chemical Theory and Computation
|November 27, 2015
PubMed
Summary
This summary is machine-generated.

Density functional approximations (DFAs) do not introduce extra errors by altering the density. Modeling exchange-correlation holes for all densities prevents this issue, paving the way for new DFT approximations.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Density Functional Theory (DFT) relies on the assumption that the electron density of a model system matches the exact density.
  • Approximations to the exact density might be expected to introduce additional errors by distorting the density.

Purpose of the Study:

  • To investigate whether approximations to the exact density in DFT introduce supplementary errors.
  • To explore a novel technique for constructing new DFT approximations.

Main Methods:

  • Utilizing a potential-driven adiabatic connection technique.
  • Analyzing the behavior of exchange-correlation holes across different densities.

Main Results:

  • Density functional approximations do not introduce supplementary errors by falsifying the density.
  • Modeling exchange-correlation holes for all densities effectively circumvents potential density errors.

Conclusions:

  • The assumption of identical densities in DFT model systems and exact systems is reconciled by approximations.
  • The potential-driven adiabatic connection offers a promising route for developing new, improved DFT approximations.