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2.3.1 Basic thermodynamic equations

Differential relations:
{\rm d} e = T {\rm d} s + \frac{p}{\rho^2} {\rm d} \rho
\end{displaymath} (20)

where $e$ is the internal energy .
{\rm d} h = T {\rm d} s + \frac{1}{\rho} {\rm d} p
\end{displaymath} (21)

where the specific enthalpy , $h$, is defined as
h = e + p/\rho
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This implies:
\left(\frac{\partial e}{\partial s}\right)_{\rho} = T
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\left(\frac{\partial e}{\partial \rho}\right)_{s} = \frac{p}{\rho^2}
\end{displaymath} (24)

\left(\frac{\partial h}{\partial s}\right)_{p} = T
\end{displaymath} (25)

\left(\frac{\partial h}{\partial p}\right)_{s} = \frac{1}{\rho}
\end{displaymath} (26)