deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 8c5b871..7fe3c6c 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
\end{equation}  We can rewrite  \begin{equation}  \frac{d\rho}{rho} \frac{d\rho}{\rho}  = \frac{1}{\rho} \frac{dP}{RT} - \frac{1}{\rho}\frac{P}{RT^2} dT \end{equation}  so that  \begin{equation}  dQ = \frac{R}\left( 1 + \frac{1}{\gamma-1}\right)dT - \frac{d \rho}{\rho}.  \end{equation}  Let's also introduce the enthalpy $h$ in the limit that the number of particles in the system is constant,