# Derivation of the Sackur-Tetrode equation

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 ad1c9bdddfhttps://brainmass.com/math/basic-algebra/derivation-of-the-sackur-tetrode-equation-99036

#### Solution Preview

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.