Maxwell—Boltzmann statistics¶

In statistical mechanics, Maxwell—Boltzmann statistics describes the distribution of classical material particles over various energy states in thermal equilibrium. It is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible.

Contents:

  • Energy distribution
    • energy
    • energy_distribution_function
    • equilibrium_temperature
    • law
  • Most probable speed in Maxwell—Boltzmann statistics
    • most_probable_speed
    • equilibrium_temperature
    • molecular_mass
    • law
  • Discrete distribution
    • occupancy_of_state
    • particle_count
    • energy_of_state
    • equilibrium_temperature
    • single_particle_partition_function
    • law
  • Speed distribution
    • speed_distribution_function
    • particle_speed
    • particle_mass
    • equilibrium_temperature
    • law
  • Statistical weight of macrostate
    • statistical_weight
    • particle_count_in_state
    • law
  • Velocity component distribution
    • velocity_component_distribution
    • velocity_component
    • particle_mass
    • equilibrium_temperature
    • law

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        • Energy distribution
        • Most probable speed in Maxwell—Boltzmann statistics
        • Discrete distribution
        • Speed distribution
        • Statistical weight of macrostate
        • Velocity component distribution
      • Relativistic Thermodynamics
      • Average kinetic energy of ideal gas from temperature
      • Average speed in Maxwell—Boltzmann statistics
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      • Canonical partition function of a classical discrete system
      • Change in entropy of ideal gas from volume and temperature
      • Chemical potential is Gibbs energy per particle
      • Chemical potential is particle count derivative of enthalpy
      • Chemical potential is particle count derivative of free energy
      • Chemical potential is particle count derivative of Gibbs energy
      • Chemical potential is particle count derivative of internal energy
      • Chemical potential of ideal gas
      • Classical isochoric molar heat capacity of solids
      • Compressibility factor via intermolecular force potential
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      • Dynamic viscosity of gas from temperature
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      • Enthalpy derivative via volume derivative
      • Enthalpy differential
      • Enthalpy is internal energy plus pressure energy
      • Enthalpy via Gibbs energy
      • Entropy change in reversible process
      • Entropy derivative via volume derivative
      • Entropy from statistical weight
      • Entropy is derivative of free energy
      • Entropy is derivative of Gibbs energy
      • Entropy of independent subsystems is sum of their entropies
      • Fractional volume change via small temperature change
      • Free energy differential
      • Gas mixture pressure from partial pressures
      • Gas pressure change from temperature
      • Gibbs energy differential
      • Gibbs energy via enthalpy
      • Grashof number
      • Heat is heat capacity times temperature change
      • Heat of combustion via mass
      • Heat of vaporization via mass
      • Helmholtz free energy via internal energy
      • Infinitesimal work in quasistatic process
      • Intensive parameters relation
      • Internal energy change of ideal gas via temperature
      • Internal energy change via heat and work
      • Internal energy differential
      • Internal energy of ideal gas via temperature
      • Internal energy via Helmholtz free energy
      • Isentropic speed of sound
      • Isobaric molar heat capacity of ideal gas via adiabatic index
      • Isobaric potential from heat capacity
      • Isobaric potential of temperature dependent heat capacity
      • Isochoric and isobaric heat capacities of homogeneous substance
      • Isochoric and isobaric heat capacities of ideal gas
      • Isochoric molar heat capacity of ideal gas via adiabatic index
      • Isochoric molar heat capacity of ideal gas via degrees of freedom
      • Laplace pressure of spherical shapes
      • Latent heat of fusion via mass
      • Mean free path of random motion
      • Number of impacts on the wall from area and speed
      • Prandtl number via dynamic viscosity and thermal conductivity
      • Pressure and temperature in isochoric process
      • Adiabatic process equation via pressure and volume
      • Pressure and volume in isothermal process
      • Pressure from number density and kinetic energy
      • Pressure of ideal gas from height and temperature
      • Probability of finding ideal gas molecules in volume
      • Probability of ideal gas macrostate
      • Quantum isochoric molar heat capacity of solids
      • Radiance of black body from temperature
      • Radiation power via temperature
      • Rate of energy conduction through slab
      • Relative humidity is ratio of vapor pressure
      • Speed of sound in ideal gas
      • Temperature derivative via volume derivative
      • Temperature is derivative of internal energy
      • Total energy transfer is zero in adiabatically isolated system
      • Total particle count is sum of occupancies
      • Volume and temperature in isobaric process
      • Volumetric and linear expansion coefficients in isotropic materials
      • Volumetric expansion coefficient of ideal gas
      • Work is integral of pressure over volume
      • Work of ideal gas in isobaric process
      • Work of ideal gas in isothermal process
    • Waves
  • Definitions
  • Conditions
  • Physical symbols
  • Physical constants

Related Topics

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    • Laws
      • Thermodynamics
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