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    Derivation of the Sackur-Tetrode equation

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    Derive the formula for the entropy of an ideal monoatomic gas using the microcanonical ensemble. This formula is known as the Sackur-Tetrode equation.

    © BrainMass Inc. brainmass.com October 9, 2019, 6:49 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/derivation-of-the-sackur-tetrode-equation-99036

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    documentclass[a4paper]{article}
    usepackage{amsmath,amssymb}
    newcommand{haak}[1]{!left(#1right)}
    newcommand{rhaak}[1]{!left [#1right]}
    newcommand{lhaak}[1]{left | #1right |}
    newcommand{ahaak}[1]{!left{#1right}}
    newcommand{gem}[1]{leftlangle #1rightrangle}
    newcommand{gemc}[2]{leftlangleleftlangleleft. #1right | #2
    rightranglerightrangle}
    newcommand{geml}[1]{leftlangle #1right.}
    newcommand{gemr}[1]{left. #1rightrangle}
    newcommand{haakl}[1]{left(#1right.}
    newcommand{haakr}[1]{left.#1right)}
    newcommand{rhaakl}[1]{left[#1right.}
    newcommand{rhaakr}[1]{left.#1right]}
    newcommand{lhaakl}[1]{left |#1right.}
    newcommand{lhaakr}[1]{left.#1right |}
    newcommand{ket}[1]{lhaakl{gemr{#1}}}
    newcommand{bra}[1]{lhaakr{geml{#1}}}
    newcommand{braket}[3]{gem{#1lhaak{#2}#3}}
    newcommand{floor}[1]{leftlfloor #1rightrfloor}
    newcommand{half}{frac{1}{2}}
    newcommand{kwart}{frac{1}{4}}
    renewcommand{imath}{text{i}}

    begin{document}
    section{Sackur-Tetrode equation}
    The entropy of an ideal mono atomic gas is given by the Sackur-Tetrode equation:
    begin{equation}label{result}
    S=N kahaak{logrhaak{frac{V}{N}haak{frac{E}{N}}^{frac{3}{2}}}+frac{5}{2}+frac{3}{2}loghaak{frac{4pi m}{3 ...

    Solution Summary

    We derive the Sackur-Tetrode equation for the entropy of a monoatomic ideal gas using the microcanonical ensemble.

    $2.19