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.

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% 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}
\pgfplotsset{compat=newest}
\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},
    ]
    \addplot[color=red,samples=100]{\maxwellboltzmann{100}};
    \addplot[color=yellow]{\maxwellboltzmann{300}};
    \addplot[color=blue]{\maxwellboltzmann{1000}};
    \legend{\SI{100}{\kelvin}, \SI{300}{\kelvin}, \SI{1000}{\kelvin}}
  \end{axis}
\end{tikzpicture}
\end{document}
 
 
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