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Related Concept Videos

Kinetic Theory of an Ideal Gas01:12

Kinetic Theory of an Ideal Gas

A mole is defined as the amount of any substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. An Italian scientist Amedeo Avogadro (1776–1856) formed the  hypothesis that equal volumes of gas at equal pressure and temperature contain equal numbers of molecules, independent of the type of gas. Later, the hypothesis was developed to form the SI unit for measuring the amount of any substance.
The number of molecules in one mole is called Avogadro's number...
Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision02:43

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For example, Charles’ law states that volume and temperature are directly related. Gases, therefore, expand when heated at constant pressure. Although gas laws explain how the macroscopic properties change relative to one another, it does not explain the rationale behind it.
Ideal Gas Equation01:17

Ideal Gas Equation

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.
The Kinetic Model of Gases01:24

The Kinetic Model of Gases

The kinetic model of gases explains the properties of a perfect gas using three main assumptions: molecules move in ceaseless random motion, their size is negligible compared to the distances between them, and they do not interact except during perfectly elastic collisions. The total energy of a gas is the sum of the kinetic energies of all its constituent molecules. The pressure exerted by the gas arises from the continual bombardment of the container walls by billions of colliding molecules.
Van der Waals Equation01:10

Van der Waals Equation

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...
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Universal reference state in a driven homogeneous granular gas.

María Isabel García de Soria1, Pablo Maynar, Emmanuel Trizac

  • 1Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Granular gas dynamics quickly forget initial conditions, reaching a universal state dependent on velocity and renormalized temperature. Velocity statistics require two parameters, not one, to describe the approach to stationarity.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Granular Materials

Background:

  • Homogeneous granular gases are modeled as systems of particles interacting via dissipative collisions.
  • Stochastic thermostats are used to inject energy into granular systems, mimicking external heating.
  • Low-density limits simplify the analysis of granular gas dynamics, focusing on binary collisions.

Purpose of the Study:

  • To investigate the dynamical behavior of a homogeneous granular gas under stochastic heating.
  • To identify universal scaling behaviors in the system's evolution towards a stationary state.
  • To compare theoretical predictions with simulation results for the one-particle distribution function.

Main Methods:

  • Direct Monte Carlo simulations were employed to model the granular gas dynamics.
  • Theoretical analysis was performed at the Boltzmann equation level.
  • The study focused on the low-density limit of the granular gas.

Main Results:

  • The system rapidly loses memory of its initial conditions.
  • A universal scaling regime emerges, dependent on dimensionless velocity and renormalized temperature.
  • Excellent agreement was found between Boltzmann equation predictions and simulation data for the one-particle distribution function.

Conclusions:

  • Granular gas velocity statistics exhibit a two-parameter scaling form, not a single-parameter one.
  • This two-parameter form accounts for the system's distance from stationarity.
  • The findings challenge conventional homogeneous cooling phenomenology by highlighting a more complex scaling behavior.