Can we consider this system as an Einstein model of a Solid?

In summary, the conversation discusses the concept of an isolated Einstein Solid (ES) with a fixed amount of energy and a decreasing number of oscillators. As oscillators leave the system, the total energy and entropy decrease. The question arises whether this system can still be considered as a single isolated ES and if the entropy continues to decrease, moving further away from equilibrium. A related article is mentioned, which aims to extend the model of an ES to a finite number of oscillators and explore its thermodynamic behavior. The main question remains about the fate of the oscillators as the number of particles in the solid decreases or increases, and whether an interaction between two ES systems should be considered.
  • #1
Ted Ali
12
1
Hello Everyone!
I am interested in examining the case of an isolated Einstein Solid (ES) with a decreasing number of oscillators. The total amount of energy of the ES is considered fixed. Whenever an oscillator abandons our model, it "leaves behind" the amount of energy it contained, so that the total amount of energy of the ES remains constant. As a result, the multiplicity and entropy of this ES decreases.
Can this system be considered as one (1) isolated ES?
Can we say that the entropy decreases and that our ES system gets further and further away from equilibrium?
Thank you for your time and answers,
Ted.
 
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  • #2
When I started this thread, I thought that the topic and answers, would be trivial! I now think it is not.
I found the following/attached article through a Google search. In the second paragraph of the Introduction we read:

"The aim of this work is to extend the model proposed by Einstein for the case of finite
number of harmonic oscillators. To this end, mathematical functions describing analogous
thermodynamic properties for finite solids such as the specific heat and the chemical potential
were deduced. Although exhibiting, for N → ∞ , the thermodynamic behavior well-known from
textbooks [6], such analogous functions have the advantage of being defined for any N, which
allows one to explore how close to the thermodynamic behavior the properties of solids with low
numbers of particles can be. In other words, the introduction of analogous thermodynamic
functions extends the range of applications of thermodynamic, statistical and quantum mechanics,
from macroscopic to microscopic scales."

However my main question remains quite the same: What happens to the oscillators that abandon/enter the solid as N decreases/increases? Where do they go/come from? Should we consider an interaction between two (2) ES systems?
 

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1. What is an Einstein model of a Solid?

The Einstein model of a Solid is a theoretical model proposed by Albert Einstein to describe the behavior of atoms in a solid material. It assumes that the atoms are arranged in a regular lattice and vibrate around their equilibrium positions with a fixed frequency.

2. How does the Einstein model differ from other models of solids?

The main difference between the Einstein model and other models, such as the Debye model, is that it takes into account the quantization of energy levels for the atoms in a solid. This allows for a more accurate description of the heat capacity of solids at low temperatures.

3. Can we consider any solid material as an Einstein model?

No, the Einstein model is only applicable to solids that have a regular lattice structure and where the atoms vibrate around their equilibrium positions with a fixed frequency. Real-world solids may deviate from this idealized model.

4. What are the limitations of the Einstein model?

The Einstein model does not take into account the interactions between atoms, which can affect the behavior of solids at high temperatures. It also does not consider the anharmonicity of atomic vibrations, which can lead to deviations from the predicted heat capacity at low temperatures.

5. How is the Einstein model used in scientific research?

The Einstein model is often used as a starting point for more complex models of solids. It provides a good approximation for the heat capacity of solids at low temperatures and can be used to compare with experimental data. It also helps in understanding the fundamental principles of solid state physics.

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