In case of an adiabatic process the correct relation in terms of pressure $p$ and density $\rho $ of a gas is
Medium
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Note that $p V^{\gamma}=$ constant and that $\rho$ is inversely
proportional to $V.$
Adiabatic process
$\mathrm{pV}^{\gamma}=$ constant
$\mathrm{p}\left(\frac{\mathrm{M}}{\rho}\right)^{\gamma}=\mathrm{constant}$
$\mathrm{p} \cdot \mathrm{M}^{\gamma} \cdot \rho^{-\gamma}=$ constant $\quad\left(\mathrm{M}^{\gamma} \text { is constant }\right)$
$\mathrm{p} \cdot \rho^{-\gamma}=$ constant
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