I need a help on thermodynamics physics relating to Metallic Hydrogen

[Haozi02133]

Homework Statement

If we compress H2 gas to the point at which the average inter-molecular distance is equal to the
distance between H atoms within an H2 molecule (that is,<r> = R0 ), then electrons will begin forminga distinct Fermi gas – a metal-like electron “sea” - surrounding H atoms. Find the pressure at whichthis condition occurs.
The calculated n =N/V= 2.71*10^25m^-3
<r> = 3.33nm
T=300K

I am currently stuck on part c

Relevant Equations

n = N/V = pNa/M
<r> = n^(-1/3)
R0 = 0.074nm

 

[dRic2]

The problem says to assume an ideal gas law "throughout" the problem, so my suggestion is to use it: $PV = NK_bT$ or equivalently $P = nK_bT$. The average distance is given (and you correctly identified the way to relate this quantity to the particle density $n$), the temperature is also given and $K_b$ is the Boltzmann constant... Where is your problem in particular ?