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Related Concept Videos

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...
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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Van der Waals Interactions01:24

Van der Waals Interactions

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Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.
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Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real 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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Dynamic Equilibrium02:20

Dynamic Equilibrium

50.8K
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

1.1K
When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Nonlinear Economic State Equilibria via van der Waals Modeling.

Max-Olivier Hongler1, Olivier Gallay2, Fariba Hashemi3

  • 1Microengineering Institute, School of Engineering (STI), Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 17, CH-1015 Lausanne, Switzerland.

Entropy (Basel, Switzerland)
|September 27, 2024
PubMed
Summary

This study reinterprets the van der Waals equation for economics, linking gas properties to price, demand, and income. It reveals how price and income elasticity can exhibit critical economic transitions, like product substitution.

Keywords:
non-constant elasticityprice elasticity of demandvan der Waals state equilibrium equation

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Area of Science:

  • Economic modeling
  • Physical chemistry
  • Applied mathematics

Background:

  • The van der Waals equation models real gas behavior.
  • Economic elasticity concepts are crucial for market analysis.

Purpose of the Study:

  • To adapt the van der Waals equation to economic principles.
  • To analyze economic equilibrium and elasticity dynamics.

Main Methods:

  • Reinterpreting physical variables (pressure, volume, temperature) as economic ones (price, demand, income).
  • Applying catastrophe theory to model elasticity singularities.
  • Qualitative and quantitative analysis using diverse economic examples.

Main Results:

  • Economic price (Y) and demand (X) relationships can be modeled using a van der Waals-like equation.
  • Price Elasticity of Demand (PED) and Income Elasticity of Demand (YED) can exhibit cusp-catastrophe singularities.
  • The liquid-gas phase transition analogy illustrates product substitution dynamics.

Conclusions:

  • The van der Waals framework offers novel insights into economic equilibrium and market behavior.
  • This model provides a new perspective on phenomena like consumer choice and market shifts.
  • Empirical validation across different markets (e.g., German electricity) supports the model's relevance.