Graphics, Figures & Tables ⇒ Maxwell-Boltzmann Distribution Graph

[svend_tveskaeg]

Please ask in physics fora for questions like the last one.

Regarding the graph, I would use pst-plot myself but many people use TikZ these days.

[ghostanime2001]

is there a tikz generated package made for graphing functions of maxwell boltzmann graphs ? I have checked pst-plot but didn't find anything relevant.

[svend_tveskaeg]

There are loads of relevant stuff for you in pst-plot; the graph can be drawn using the \psplot command. (See for example page 8--9 in the manual.) If you are not familiar with RPN notation, you can use the algebraic option for the plot command.

I do not know TikZ so I cannot help with this.

[cgnieder]

This is easily done with the aforementioned pgfplots which is based on TikZ:

Code: Select all

\documentclass{article}

\usepackage{pgfplots}
\pgfplotsset{
  compat = 1.7 ,
  yticklabel style = {/pgf/number format/.cd,fixed,fixed zerofill,precision=4} ,
  samples = 100 ,
  scaled ticks = false 
}

\usepackage{chemmacros}

\usepackage{siunitx}
\sisetup{per-mode=symbol}

\begin{document}

\begin{tikzpicture}
 % parameter:
 \def\kB{1.3806488e-23}% boltzmann constant
 \def\temperature{298}% room temperature
 \def\Beta{1/(\kB*\temperature)}
 \def\amu{1.660538921e-27}% atomar mass unit in kg
 \def\HMass{2*\amu}% Hydrogen
 \def\HeMass{4*\amu}% Helium
 \def\OMass{32*\amu}% Oxygen
 % plot:
 \begin{axis}[
    domain  = 0:5000 ,
    xlabel  = $v$ in \si{\metre\per\second} ,
    ylabel  = $P(v)$ ,
    title   =
      Maxwell-Boltzmann distribution of different gases at room temperature
  ]
  \addplot[color=red]
    {sqrt(2/pi)*(\HMass*\Beta)^(3/2)*x^2*exp(-.5*\HMass*\Beta*x^2)} ;
  \addplot[color=yellow]
    {sqrt(2/pi)*(\HeMass*\Beta)^(3/2)*x^2*exp(-.5*\HeMass*\Beta*x^2)} ;
  \addplot[color=blue]
    {sqrt(2/pi)*(\OMass*\Beta)^(3/2)*x^2*exp(-.5*\OMass*\Beta*x^2)} ;
  \legend{\ch{H2},\ch{He},\ch{O2}}
 \end{axis}
\end{tikzpicture}

\begin{tikzpicture}
 % parameter:
 \def\kB{1.3806488e-23}% boltzmann constant
 \def\hundredK{100}% 100 K
 \def\rt{300}% ~ room temperature
 \def\thousandK{1000}% 100 K
 \def\Beta#1{1/(\kB*#1)}
 \def\amu{1.660538921e-27}% atomar mass unit in kg
 \def\HMass{2*\amu}% Hydrogen
 % plot:
 \begin{axis}[
    domain  = 0:8000 ,
    xlabel  = $v$ in \si{\metre\per\second} ,
    ylabel  = $P(v)$ ,
    title   =
      Maxwell-Boltzmann distribution for Hydrogen at different temperatures
  ]
  \addplot[color=red]
    {sqrt(2/pi)*(\HMass*\Beta{\hundredK})^(3/2)*x^2*exp(-.5*\HMass*\Beta{\hundredK}*x^2)} ;
  \addplot[color=yellow]
    {sqrt(2/pi)*(\HMass*\Beta{\rt})^(3/2)*x^2*exp(-.5*\HMass*\Beta{\rt}*x^2)} ;
  \addplot[color=blue]
    {sqrt(2/pi)*(\HMass*\Beta{\thousandK})^(3/2)*x^2*exp(-.5*\HMass*\Beta{\thousandK}*x^2)} ;
  \legend{\SI{100}{\kelvin},\SI{300}{\kelvin},\SI{1000}{\kelvin}}
 \end{axis}
\end{tikzpicture}

\end{document}

mbd.png (33.88 KiB) Viewed 11514 times

Regards

[ghostanime2001]

what is /def ? I am not familiar at all with tex sadly Also the x-axis is in velocity (m/s) but I wanted kinetic energy so shouldn't the equation used to compute the graph be different as well ?

[svend_tveskaeg]

I am not familiar at all with tex sadly

Then I suggest you start be reading some introduction manuals before going on to plotting functions. The following are excellent starting points IMHO:

• LaTeX for Complete Novices by Nicola Talbot;
• Math mode by Herbert Voß.

[cgnieder]

what is /def ? I am not familiar at all with tex sadly Also the x-axis is in velocity (m/s) but I wanted kinetic energy so shouldn't the equation used to compute the graph be different as well ?

\def is a TeX's low level command for LaTeX's \newcommand*. It can be replaced by the latter in every case except \def#1{<foo bar>} which needs to be replaced with \newcommand*\foo[1]{<foo bar>}.

Code: Select all

\def\foo{bar} = \newcommand*\foo{bar}
\long\def\ff{bar} = \newcommand\foo{bar}
\def\foo#1{bar: #1} = \newcommand\foo[1]{bar: #1}
\def\foo#1#2{bar: #1 and #2} = \newcommand\foo[2]{bar: #1 and #2}

There are more differences (\newcommand doesn't overwrite existing commands for instance but \def does) but that's it basically.

About the question of energy versus velocity distribution: that's really up to you which function to plot. I wanted to show you an example of how plotting a function could be done. If you want to plot a different function just do so. All the settings I used you can find in pgfplots documentation so you at least have the chance to get started.

You can always ask follow up question if you're struggling with the details.

Regards

[ghostanime2001]

What I don't like about latex and these packages (pst-plot, pgfplots etc..) is that when you try to plot a function, it draws corners at curves of functions. Is there a way to draw functions which has smooth points indefinitely so that when you try to zoom on a portion of that function, the points are not zig-zagged (for example with sin function)? Please see attached example. Maybe there's a software that allows me to customize latex parameters just like if I was drawing a function with latex only ?

By the way, what is RPN notation ? Also, in pst-plot the pi x-axis ticks are a bit offset to the right, does the package automatically do this ? or can it be perfectly center aligned with the x-axis tick mark ?

here is the code I compiled to get the attached PDF:

Code: Select all

\documentclass{article}
\usepackage{etex}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot[red] {sin(deg(x))};
\end{axis}
\end{tikzpicture}
\end{document}

[cgnieder]

[...] it draws corners at curves of functions. Is there a way to draw functions which has smooth points indefinitely ...

Not indefinitely but increasing the samples (i.e. the resolution at with the curve points are calculated) helps:

Code: Select all

\documentclass{article}
\usepackage{etex}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot[red,samples=100] {sin(deg(x))};
\end{axis}
\end{tikzpicture}
\end{document}

By the way, what is RPN notation ?

I've never heard of it before but my favorite search engine tells me Reverse Polish Notation.

Regards

[ghostanime2001]

I asked about RPN because another member said this.

If you are not familiar with RPN notation, you can use the algebraic option for the plot command.