Talk:PlanetPhysics/Ideal Gas Law

Original TeX Content from PlanetPhysics Archive

%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: ideal gas law %%% Primary Category Code: 51.30.+i %%% Filename: IdealGasLaw.tex %%% Version: 8 %%% Owner: pahio %%% Author(s): pahio, invisiblerhino %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

\setlength{\topmargin}{0.00in} \setlength{\headsep}{0.00in} \setlength{\headheight}{0.00in} \setlength{\evensidemargin}{0.00in} \setlength{\oddsidemargin}{0.00in} \setlength{\textwidth}{6.5in} \setlength{\textheight}{9.00in} \setlength{\voffset}{0.00in} \setlength{\hoffset}{0.00in} \setlength{\marginparwidth}{0.00in} \setlength{\marginparsep}{0.00in} \setlength{\parindent}{0.00in} \setlength{\parskip}{0.15in}

\usepackage{html}

% this is the default PlanetPhysics preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners.

% almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts}

% used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic}

% there are many more packages, add them here as you need them

% define commands here

\begin{document}

The equation that characterizes any amount of a gas is

\[ pV = nRT \] where $p$ is the pressure, $V$ the \htmladdnormallink{volume}{http://planetphysics.us/encyclopedia/Volume.html}, $n$ the number of the gas moles and $T$ the \htmladdnormallink{absolute temperature}{http://planetphysics.us/encyclopedia/ThermodynamicLaws.html} of the gas; $R$ the universal gas constant (approximately 8.314472 $\frac{\mbox{Pa}\cdot\mbox{m}^3}{\mbox{mol}\cdot\mbox{K}}$).

The gas law is accurately valid for an ideal gas, but a good approximation for real gases.

The law contains the following gas laws: \begin{itemize} \item Boyle--Mariotte law ($pV =$\, constant when $n$ and $T$ are constants) \item Gay--Lussac law ($\frac{V}{T} =$\, constant when $n$ and $p$ are constants) \item Avogadro's law (in equal conditions, equal volumes of different gases contain the same number of \htmladdnormallink{molecules}{http://planetphysics.us/encyclopedia/Molecule.html}) \end{itemize}

\subsection{Alternative definition} The ideal gas law can also be defined using \htmladdnormallink{Boltzmann's constant}{http://planetphysics.us/encyclopedia/BoltzmannConstant.html}: \[ pV = NkT \] The symbols are those defined above, with the difference that $N$ is the number of gas molecules, and $k$ is the Boltzmann constant, $k \approx 1.38 \times 10^{-23} \mbox{JK}^{-1}$. This form is often preferred by physicists who consider the number of molecules to be more fundamental than the number of moles.

\end{document}