deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 3328cb4..6cc7c37 100644  --- a/untitled.tex  +++ b/untitled.tex 
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For an ideal gas  \begin{align}  d\epsilon &= \frac{R}{\gamma -1}dT \\  PdV &= -\left(\gamma -1\right)\epsilon \frac{d \rho}{\rho} = RT -RT\frac{d \rho}{\rho}  \end{align}  Then  \begin{equation} 
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\end{equation}  so that  \begin{align}  dQ &= R\left( 1 + \frac{1}{\gamma-1}\right)dT - \frac{d \rho}{\rho} P}{\rho}  \\ &= \frac{\gamma R}{\gamma-1}dT - \frac{d P}{\rho}  \end{align}