I need a help on thermodynamics physics relating to Metallic Hydrogen

In summary, metallic hydrogen is a state of hydrogen that exhibits metal-like properties under extreme pressure and temperature. It is important in thermodynamics physics due to its potential as a room-temperature superconductor and its ability to provide insight into extreme conditions. This state can be created in a laboratory by subjecting hydrogen gas to high pressures and temperatures, and some potential applications include creating superconductors and energy storage devices. However, there are challenges in studying metallic hydrogen, such as creating the necessary conditions and accurately measuring its properties.
  • #1
Haozi02133
1
0
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
question 2.png
 
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  • #2
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 ?
 

1. What is Metallic Hydrogen?

Metallic Hydrogen is a form of hydrogen that has been compressed to extreme pressures, causing it to take on metallic properties. It is believed to exist in the cores of gas giant planets, such as Jupiter, and has the potential to be used as a powerful rocket fuel.

2. How is Metallic Hydrogen created?

Metallic Hydrogen is created by subjecting hydrogen gas to extremely high pressures, typically over 4 million times the atmospheric pressure on Earth. This can be achieved using a diamond anvil cell or by using powerful lasers to compress the gas.

3. What are the properties of Metallic Hydrogen?

Metallic Hydrogen is highly conductive, meaning it can efficiently transfer heat and electricity. It is also reflective, making it appear shiny and metallic. Additionally, it is predicted to be a superconductor at room temperature, meaning it could conduct electricity with zero resistance.

4. What are the applications of Metallic Hydrogen?

One potential application of Metallic Hydrogen is as a new, more efficient rocket fuel. It has also been theorized that it could be used in high-speed computing and energy storage devices. However, more research is needed to fully understand its properties and potential uses.

5. What is the current state of research on Metallic Hydrogen?

Research on Metallic Hydrogen is ongoing and has been met with some controversy. While some experiments have shown evidence of its existence, others have not been able to replicate these results. Further research and advancements in technology will be needed to fully understand and utilize this unique form of hydrogen.

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