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01:10Van der Waals Equation
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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.
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...
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02:26Molecular Comparison of Gases, Liquids, and Solids
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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...
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04:01Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
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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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01:07Gauss's Law
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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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01:01Distillation: Vapor–Liquid Equilibria
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01:30Typical Model Studies
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Microscopic determination of correlations in the fluid interfacial region in the presence of liquid-gas asymmetry.
Physical review. E·2019
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Correlation-function structure in square-gradient models of the liquid-gas interface: Exact results and reliable
1Department of Mathematics, Imperial College London, London SW7 2BZ, United Kingdom.
Physical Review. E
|October 3, 2019
Summary
This study validates approximations for fluid interface correlations. These approximations accurately describe the structure factor and pair correlation function across all wave vectors, even near tricritical points.
Area of Science:
- Physical Chemistry
- Statistical Mechanics
- Soft Matter Physics
Background:
- Microscopic structure of density-density correlations in fluid interfaces is crucial for understanding interfacial phenomena.
- Previous work identified resonances in the local structure factor at specific parallel wave vectors (q) for short-ranged forces.
Purpose of the Study:
- To further investigate and validate approximations for the local structure factor and pair correlation function.
- To compare these approximations against analytically solvable models within square-gradient theory.
- To assess the accuracy of these approximations for interfacial systems, including those near tricritical points.
Main Methods:
- Comparison of approximations for local structure factor and pair correlation function.
- Analysis using three new analytically solvable models within square-gradient theory.
- Evaluation against numerical solutions of the Ornstein-Zernike equation for a model near a tricritical point.
Main Results:
- Approximations accurately describe the pair correlation function and structure factor across the entire wave vector spectrum.
- The approximations capture the crossover from Goldstone mode divergence (small q) to bulk-like behavior (large q).
- Approximations are exact for some potentials and highly accurate (within a few percent) for others, including near tricritical points.
Conclusions:
- The validated approximations provide a robust framework for understanding density-density correlations in fluid interfaces.
- These approximations are versatile, accurately describing interfacial behavior across various conditions, including near critical points.
- The findings offer a simplified yet accurate method for analyzing complex interfacial structures.