# Maxwell-Boltzmann distribution

The Maxwell-Boltzmann distribution plotted at different temperatures reveals that the most probable velocity $v_p$ of ideal gas particles scales with the square root of temperature.

Edit and compile if you like:

% The Maxwell-Boltzmann distribution plotted at different temperatures reveals that the most probable velocity v_p of ideal gas particles scales with the square root of temperature.

\documentclass{standalone}

\usepackage{pgfplots,siunitx}

\def\kB{1.38e-23} % Boltzmann constant
\def\mu{1.66e-27} % unified atomic mass unit/Dalton (symbols: m_u or Da)

\def\maxwellboltzmann#1{4 * pi * (\mu / (2 * pi * \kB * #1))^(3/2) * x^2 * exp(-\mu * x^2 / (2 * \kB * #1))}

\begin{document}

\begin{tikzpicture}

\begin{axis}[
domain = 0:8000,
xlabel = {$v$ [\si{\metre\per\second}]},
ylabel = $P(v)$,
smooth, thick,
axis lines = left,
every tick/.style = {thick},
]

\legend{\SI{100}{\kelvin}, \SI{300}{\kelvin}, \SI{1000}{\kelvin}}

\end{axis}
\end{tikzpicture}

\end{document}