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# 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.

#### Solution Preview

documentclass[a4paper]{article}
usepackage{amsmath,amssymb}
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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.

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