# Perfect gas relationship between pressure and density

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

$$$$p = k \rho^\gamma$$$$

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?

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 $$p = k \rho^{\gamma}$$