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Boltzmann Average

  • Page ID
    1873
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    The Boltzmann average (sometimes known as the thermal average) for a given quantity or observable, let us say A, is given by

    \[ \langle A \rangle= \frac{\sum_{i}Ae^{-E_i/k_BT}}{\sum_{i}e^{^{-E_{i}/k_BT}}} \nonumber\]

    where kB is the Boltzmann constant, and T is the temperature. This provides the expected value of the property in question at a given temperature. This equation assumes non-degenerate states.

    • Boltzmann Distribution
      The Maxwell-Boltzmann distribution function is a function f(E) which gives the probability that a system in contact with a thermal bath at temperature T has energy E. This distribution is classical and is used to describe systems with identical but distinguishable particles.
    • Ideal Gas Partition Function
    • Proof that β = 1/kT
    • The Boltzmann constant
      The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. It is named after the Austrian physicist Ludwig Eduard Boltzmann.


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