A Question about F.Reif page 66 (thermal interaction of systems)

AI Thread Summary
Thermal interactions allow for the exchange of heat between systems without altering external parameters, leading to changes in the average energy of each system. The quantum energy levels remain constant, but the distribution of systems across these levels shifts, affecting mean energy values. In contrast, mechanical interactions involve changes in external parameters, which directly alter energy levels and eigenstates. The discussion highlights the distinction between thermal and mechanical interactions in terms of energy distribution and system behavior. Understanding these concepts is crucial for grasping thermodynamic principles.
Yathindra
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It was described that the thermal interaction changes average energy of each system by a different amount and the external parameters do not change at all in a thermal interaction. I do not understand how energy of a system changes without a change in external parameters.
 
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Yathindra said:
It was described that the thermal interaction changes average energy of each system by a different amount and the external parameters do not change at all in a thermal interaction. I do not understand how energy of a system changes without a change in external parameters.
Can you please provide more context or a direct quote regarding this?
 
Sure, the explanation in reif proceeds as follows:
The quantum energy levels of a system Er depend on external parameters like Volume, Magnetic field, etc. Er(x1,x2,x3...) In a purely thermal interaction ( only heat is exchanged and work done is zero), these external parameters are not altered. And yet we see a change in the overall energy of the system. But, this change is due to the relative number of systems of an ensemble being on those energy levels alters. Whereas in a mechanical interaction, external parameters do change and so Er which is a function of those would obviously change.
What confuses me is the idea of an ensemble here. It looks like in some cases even though a hotter and colder system is in contact, energy transfer would not take place.!

PFA. (page 66, chapter 2)
 

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If a hotter and a colder system are brought into contact, the distribution of energy levels within each of them changes as a result of the heat transferred from the hotter system to the colder system.
 
Chestermiller said:
If a hotter and a colder system are brought into contact, the distribution of energy levels within each of them changes as a result of the heat transferred from the hotter system to the colder system.
I'm going through Reif and had the same question. This is how I understand it:

When a system ##A## with mean energy ##\bar{E}=\varepsilon## interacts (only) thermally with a system ##A^{'}## by transfering heat ##\Delta E = \varepsilon / 3##, the proportion of systems ##A## of the ensemble in various energy levels (of system ##A##) changes such that the mean energy of a system ##A## in this ensemble is ##\frac{2}{3}\varepsilon##, but the energy levels themselves are the same. Also there should be a similar shift in the proportions of systems ##A^{'}## over various energy levels (of ##A^{'}##) such that the mean energy of an ##A^{'}## in the ensemble is ##\frac{1}{3}\varepsilon##

On the other hand if these two systems interacted mechanically the energy levels of both systems would change as a result of a change in external paramaters. As I understand it , external parameters are those that appear in the Hamiltonian, which is the reason for the energy levels changing (different Hamiltonian ##=## different quantum system ##\implies## different energy eigenstates ##=## different energy levels. The proportion of systems should also shift accordingly to change the mean energies of the system in line with macroscopic thermodynamics.

Am I correct in understanding it this way?
 
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