%
% Chapter 1  The Governing Equations
%            1-4 EQUATION OF STATE
%
% 2002/05/17 ���� ����   ����
% 2002/07/04 ���� ����   �������R�˴ؤ���Appendix���ɲ�
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%         title and date setting         %%%%%%%%
\markboth{2-4 ����������}{2-4 ����������}
%\markright{1-4 ����������}
%\Ddate{2002/07/04}
%\Dfile{hw-01-04.tex}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%        page and section setting        %%%%%%%%
\setcounter{chapter}{2}
\setcounter{section}{3}
\setcounter{equation}{7}
%\setcounter{page}{1}
%\setcounter{figure}{0}
\setcounter{footnote}{0}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%              text start                %%%%%%%%

\section{����������}

3�Ĥ�Ǯ�ϳ��ѿ� $p$ [N/m$^2$], $\alpha$ [m$^3$/kg],
������$T$ [K]����Ω�Τ�ΤǤʤ����Ȥ�
Boyle��Charles�ˤ�ä��᤯�����������Ƥ���.
���Ƥ�ʪ���ˤϰʲ��Τ褦�ʾ����������Ȥ����Τ���ط���¸�ߤ���.
%
\begin{eqnarray*}
 f(p, \alpha, T)=0.
\end{eqnarray*}
%
�ºݤ�ʪ���ǤϤ��δط�������ʣ���ʤΤ�,
ñ��˲���Ū��ɽ���ϤǤ��ʤ�.
������, �ѿ��θ����ϰϤ�����������Ū�ʼ���¸�ߤ���.
���ΰ���Ū�ʼ���, �������۲����줿���֤��ꤹ�뤳�Ȥ�Ƴ�����.
�㤨��, Boyle��ˡ§��Charles��ˡ§�˸�̩�˽���{\bf ���۵���}
������������, �ʲ��Τ褦�ʷ��ξ������������ưפ�����Ω��.
%
\begin{eqnarray}
 \Deqlab{����������}
 p \alpha = RT.
\end{eqnarray}
%
���������۵��Τ�¸�ߤ��ʤ���, \Deqref{����������}��¿���ξ��̤�
������줿�ºߵ��Τ����Ѥ���, 
¿���η�̤�Ф��Ƥ���.
�絤�ϼºݤˤ�¿���ε��Τκ���ʪ�ʤΤ���,
�絤��������ġ��ε��Τε��������ʿ�Ѥ������줿
�������$R$ [J$\cdot$kg$^{-1}\cdot$K$^{-1}$]��Ϳ���뤳�Ȥ�, 
\Deqref{����������}������Ω��
\footnote{
�������$R$�˴ؤ��Ƥ�{\bf 2-4-A}����.
}.




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%             �ʲ���Appendix             %%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%           ���ֹ�Υ������饤��         %%%%%%%% 
\setcounter{equation}{0}
\def\theequation{2-4-A-\arabic{equation}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\begin{center}
% {\bf 
% --------------------------------------
% ��ʸ�����ޤ�
% --------------------------------------
% } 
%\end{center}

\subsection*{2-4-A \qquad �������$R$�ˤĤ���}

��ʸ�Ǥ�$R$�˴ؤ��Ƥϡص�������Ǥ���٤Ȥ������Ȥ������Ҥ��Ƥ��ʤ�
�Τ�, �����Ǿ�����������ˤĤ��ƿ����.

�������$R$�Ϥ����絤��ʬ���̤˰�¸�����̤Ǥ���.
���ε������$R$��{\bf ���̵������}({\it universal gas constant\/})
$R^*$
\footnote{
$R^* = 8.3143$ [J mol$^{-1}$ K$^{-1}$] �Ǥ���.
}
�������.
���̵���������Ѥ��ƾ�����������񤯤Ȱʲ��Τ褦�ˤʤ�.
%
\begin{eqnarray}
 \Deqlab{����������1}
 pV = nR^{*}T.
\end{eqnarray}
%
������$n$ [mol]�ϥ���, $V$ [m$^3$]�ϵ��Τ����ѤǤ���.
����, $M$ [kg]���絤�μ��̤Ȥ����, ����$\alpha$��
$\alpha = V/M$�Ȥʤ�, \Deqref{����������1}��
%
\begin{eqnarray*}
 p \alpha = \frac{n R^* T}{M}.
\end{eqnarray*}
%
�Ȥʤ�. (2-8)����Ӥ����,
%
\begin{eqnarray*}
 R = \frac{n}{M} R^*
\end{eqnarray*}
%
�Ȥ����ط�������Ω�Ĥ��Ȥ��狼�������.
������ʬ����$W = M / n$ [kg/mol]�����������
%
\begin{eqnarray*}
 R = \frac{R^*}{W}
\end{eqnarray*}
%
�Ȥʤ�, �絤�ε������$R$�ϰ��̵������$R^*$���ͤ�
�絤��ʬ����$W$�ˤ�äƷ�ޤ뤳�Ȥ��狼�������.




%\subsection*{Appendix \qquad }

%\subsubsection*{}

%%%%%%%%          ���ֹ�Υ������Х饤��        %%%%%%%% 
\setcounter{equation}{8}
\def\theequation{\arabic{chapter}-\arabic{equation}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%              text end                  %%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
