PX285 - I3 - pressure equation

P V^{γ} = constant

where, $γ = \frac{C_{P}}{C_{V}}$ is the adiabatic index $\approx 5 / 3$

\frac{d}{d t} (P V^{γ}) = 0

\begin{matrix} m^{γ} \frac{d}{d t} (\frac{P}{ρ^{γ}}) = 0 \\ ⟹ \frac{d}{d t} (\frac{P}{ρ^{γ}}) = 0 \end{matrix}