Electron degeneracy pressure scales with density as:
eq.1.1: $p \approx \rho^{5/3}$
By dividing electron degeneracy pressures of 1 mole of electrons at two different densities we obtain:
eq.1.2 $p_1/p_2 = (\rho_1/\rho_2)^{5/3}$
Pressure for adiabatic process with ideal gas scales as:
eq.2.1: $p V^\gamma = const.$
respectively:
eq.2.2: $p_1 / p_2 = (V_2/V_1)^\gamma $
for fixed number of particles $\rho \approx 1/V$ and we can see that
Ratio of electron degeneracy pressures (eq.1.2) formally resembles ratio of pressures in adiabatic process (eq.2.2) with heat capacity ratio $\gamma = 5/3 = 1.666$ which correspond to monoatomic gas (point particles).
=> It seems like a hint that microscopic origin of electron degeneracy pressure can be seen as a result of some internal thermal motion, which cannot be ever cooled (that is $\delta Q=0$, which means it is always adiabatic)
Question
- Does it make some sense?
- Is this just a coincidence?
- Did somebody examined this line of thinking?
- Is this something obvious?