I need a help on thermodynamics physics relating to Metallic Hydrogen

Thread starter Haozi02133
Start date Apr 30, 2020
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Fermi energy Hydrogen Physics Thermodynamic Thermodynamics

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SUMMARY

The discussion focuses on applying the ideal gas law, represented by the equation PV = NK_bT, to problems in thermodynamics related to metallic hydrogen. Participants emphasize the importance of understanding particle density (n) and the relationship between average distance and temperature, with K_b denoting the Boltzmann constant. The conversation highlights the necessity of correctly identifying variables and their interrelations to solve thermodynamic problems effectively.

PREREQUISITES

Understanding of the ideal gas law and its applications
Familiarity with thermodynamic concepts, particularly relating to particle density
Knowledge of the Boltzmann constant (K_b) and its significance in thermodynamics
Basic grasp of temperature and its role in gas laws

NEXT STEPS

Research the implications of the ideal gas law in different states of matter
Explore advanced thermodynamic properties of metallic hydrogen
Learn about the relationship between particle density and average distance in gases
Investigate the role of the Boltzmann constant in statistical mechanics

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This discussion is beneficial for physics students, researchers in thermodynamics, and anyone interested in the properties of metallic hydrogen and gas laws.

Apr 30, 2020

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

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May 1, 2020

dRic2

Gold Member

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 ?