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\Drireki{93/03/18 �¸��ء��ݺ�����}
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\section{������ήĴ��}

������ήĴ���, 
Ϣ³����2�ĤΥ�٥�δ֤��ؤˤ�����
����2�Ĥξ�郎���������Ȥ���,
\begin{itemize}
\item ���ؤ������԰���, ���ʤ�����ٸ�Ψ��������Ǯ��Ψ�����礭��
\item ˰�¤ޤ��ϲ�˰�¾��֤ˤ���
\end{itemize}
���礦��˰�¤����Ĳ��ٸ�Ψ��������Ǯ��Ψ�Ǥ���褦��
2�ĤΥ�٥�β��٤��漾��ִ�Ū��Ĵ�᤹��.
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�����������ƤΥ�٥�ˤĤ��ƹԤʤ����Ȥ�,
��«����ޤǷ����֤�.

��$(k-1,k)$�������԰���Ǥ������,
%
\begin{equation}
{\cal S}_{k-1/2}
\equiv \hat{T}_{k-1} - \hat{T}_{k} + \frac{L}{C_p} 
                  \left( q^*(\hat{T}_{k-1},p_{k-1}) 
                       - q^*(\hat{T}_{k},  p_{k}  )  \right)
- \frac{R}{C_p} \frac{ \Delta p_{k-1/2} }{ p_{k-1/2} }
                \frac{ \hat{T}_{k-1} + \hat{T}_{k} }{2}
> 0
\end{equation}
%
��ɽ�����.
���ΤȤ�, �����,
%
\begin{equation}
\hat{q}_{k-1} > q^*(\hat{T}_{k-1},p_{k-1}) , \,\,\,\,
\hat{q}_{k}   > q^*(\hat{T}_{k},  p_{k}  )
\end{equation}
%
��������������Ĵ�᤬������.

Ĵ��η�� $(T_k,q_k)$ ��,
%
\begin{equation}
q_{k-1} = q^*(T_{k-1},p_{k-1}) , \,\,\,\,
q_{k}   = q^*(T_{k},  p_{k}  )
\end{equation}
%
\begin{equation}
     T_{k-1} - T_{k} + \frac{L}{C_p} 
                  \left( q^*(T_{k-1},p_{k-1}) 
                       - q^*(T_{k},  p_{k}  )  \right)
 - \frac{R}{C_p} \frac{ \Delta p_{k-1/2} }{ p_{k-1/2} }
                 \frac{ T_{k-1} + T_{k}  }{2}
= 0
\end{equation}
%
\begin{equation}
    \sum_{l=k-1}^{k} ( C_p T_l       + L q_l       ) \Delta p_l
=   \sum_{l=k-1}^{k} ( C_p \hat{T}_l + L \hat{q}_l ) \Delta p_l
\end{equation}
%
�Ȥʤ�褦�˷���.

���,
%
\begin{eqnarray}
T_{k-1} & = & \hat{T}_{k-1} + \Delta T_{k-1}  \\
T_k     & = & \hat{T}_k + \Delta T_k  \\
q_{k-1} & = & q^*(\hat{T}_{k-1},p_{k-1}) 
              + \left. \DP{q^*}{T} \right|_{k-1} \Delta T_{k-1} \\
q_{k}   & = & q^*(\hat{T}_{k}  ,p_{k}  ) 
              + \left. \DP{q^*}{T} \right|_{k}   \Delta T_{k}  
\end{eqnarray}
%
\begin{equation}
\Delta T_k
    = \frac{ \displaystyle
             (1+\gamma_{k-1})\Delta p_{k-1} {\cal S}_{k-1/2} 
             + \left[ 1 + \gamma_{k-1} 
                     - \kappa \frac{\Delta p_{k-1/2}}{p_{k-1/2}}
               \right] \frac{L}{C_p} \Delta \hat{Q}                        }
           { \displaystyle
             (1+\gamma_{k-1})(1+\gamma_{k}) 
             (\Delta p_{k-1} + \Delta p_{k})
             + \kappa \frac{\Delta p_{k-1/2}}{p_{k-1/2}}
               \left[ (1+\gamma_{k-1})\Delta p_{k-1} 
                    - (1+\gamma_{k}  )\Delta p_{k}
               \right]                                                     }
\end{equation}
%
\begin{equation}
\Delta T_{k-1} = - \frac{(1+\gamma_{k}  )\Delta p_{k}  }
                        {(1+\gamma_{k-1})\Delta p_{k-1}}
                   \Delta T_k
                 + \frac{1}    
                        {(1+\gamma_{k-1})\Delta p_{k-1}}
                        \frac{L}{C_p} \Delta \hat{Q} .
\end{equation}
%
������,
%
\begin{equation}
\gamma_{k} = \frac{L}{C_p} \left. \DP{q^*}{T} \right|_{k} , \,\,\,
\gamma_{k-1} = \frac{L}{C_p} \left. \DP{q^*}{T} \right|_{k-1} ,
\end{equation}
