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I've been given the following equation for a perfect gas:

\begin{equation} p = k \rho^\gamma \end{equation}

Where $k$ and $\gamma$ are constants. I'm trying to find out where this comes from or a source for it but I've had no luck. I've looked up different definitions of ideal gases & perfect gases but I can't seem to derive this. Any ideas?

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For an adiabatic process and an ideal gas, then it can be shown that (see Why is $PV^\gamma$ constant in an adiabatic process? ) $$ pV^{\gamma} = {\rm constant},$$ where $\gamma$ is the ratio of specific heats $c_p/c_v$.

If we consider a fixed mass of gas, then $V \propto \rho^{-1}$ and so $$ p = k \rho^{\gamma}$$

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