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    Thermodynamics: Gas

    Physics

    • Title Home
    • Study Guide
    • Topics
      • Introduction and Summary
      • Ideal Gas
      • Problems
      • Non-Classical Gases
      • Problems
    • Terms and Formulae

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    Thermodynamics: Gas Terms and Formulae

    Terms and Formulae

    Thermodynamics: Gas Terms and Formulae

      Terms

    • Bose Gas

      A Bose gas is a gas consisting of bosons.

    • Boson

      A boson is a particle with integer spin.

    • Classical Regime

      The classical regime is that in which gases behave classically, namely without demonstrating bosonic or fermionic character. We can define the regime as f 1 or nnQ.

    • Degenerate

      Term used for a gas when it is too dense to be considered as being in the classical regime, i.e. n > nQ.

    • Distribution Function

      The distribution function, f, gives the average number of particles in an orbital.

    • Einstein Condensation

      Also known as bose condensation, the effect of boson crowding in the ground orbital.

    • Einstein Condensation Temperature

      The temperature below which Einstein Condensation significantly occurs, given by τâÉá.

    • Equipartition

      A classical shortcut that assigns to one particle energy of τ per degree of freedom in the classical expression of its energy.

    • Fermi Energy

      The Fermi energy is defined as the chemical potential at a temperature of zero: μ(τ = 0) = .

    • Fermi Gas

      A Fermi gas is a gas consisting of fermions.

    • Fermion

      A fermion is a particle with half-integer spin.

    • Heat Capacity

      The heat capacity of a gas is a measure of how much heat the gas can hold. We define the heat capacity at constant volume to be:

      CVâÉá.

      We define the heat capacity at constant pressure to be:

      CpâÉá.

    • Ideal Gas

      A gas of particles that do not interact with each other and are in the classical regime.

    • Quantum Concentration

      The quantum concentration marks the concentration transition between the classical and quantum regimes, and is defined as nQ = .

    • Formulas

       
      The classical distribution function

      f () = e(μ-)/τ = λe-/τ

       
      The chemical potential of an ideal gas

      μ = τ log

       
      The free energy of an ideal gas

      F = Nτlog - 1

       
      The pressure of an ideal gas is given by the ideal gas law

      p =

       
      The entropy of an ideal gas

      σ = Nlog +

       
      The energy of an ideal gas

      U = Nτ

       
      The heat capacities for an ideal gas

      CV = N

      Cp = N

       
      The Fermi-Dirac Distribution function

      f () =

       
      The Fermi energy of a degenerate Fermi gas

      = (3Π2n)2/3

       
      The energy of the ground state of a Fermi gas

      Ugs = N

       
      The Bose-Einstein Distribution Function

      f () =

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