Helium Absorption | Grand Partition Function & <N>

In summary, helium absorption is the process of gas molecules being taken in and held by a material, such as activated carbon. The grand partition function for helium is a mathematical expression that describes the statistical behavior of a system of helium atoms, taking into account the number of particles, energy levels, and temperature. It is calculated using the statistical mechanics approach and is crucial in understanding the absorption capacity of helium in materials. The number of helium atoms in a system affects the grand partition function, indicating a higher absorption capacity as the number of atoms increases.
  • #1
Lyons_63
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Homework Statement



The atomic site that is in thermal and diffusive equilibrium with a gas of Helium atoms that is on the surface of a metal can either absorb an atom of Helium or it can be vacant.
(a) What is the Grand Partition function of the system?
(b) Derive the average thermal occupancy <N> of a site

Homework Equations





The Attempt at a Solution


I have no idea where to even begin!
 
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  • #2
The partition function is given by z = Ʃ e^ -β (Ni) (εi-μ)
how do you account for the fact that the surface is either vacant or not
 

FAQ: Helium Absorption | Grand Partition Function & <N>

What is helium absorption?

Helium absorption refers to the process by which helium gas molecules are taken in and held by a material. This is commonly seen in materials such as activated carbon, which have a large surface area and can hold a high amount of helium.

What is the grand partition function for helium?

The grand partition function for helium is a mathematical expression that describes the statistical behavior of a system of helium atoms. It takes into account the number of particles, energy levels, and temperature of the system.

How is the grand partition function calculated?

The grand partition function is calculated using the statistical mechanics approach, which takes into account the energy levels and possible configurations of the particles in the system. This involves solving complex equations and using various mathematical techniques.

What is the significance of the grand partition function in studying helium absorption?

The grand partition function allows us to understand the behavior of helium gas molecules in a material and predict their absorption capacity. This is crucial in various fields such as material science, gas storage, and gas separation processes.

How does the number of helium atoms affect the grand partition function?

The number of helium atoms in a system affects the grand partition function by altering the statistical behavior of the gas molecules. As the number of atoms increases, the grand partition function also increases, indicating a higher absorption capacity for the material.

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