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

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• Yathindra
In summary: This results in a change in the overall energy of the system, even though the external parameters remain unchanged. This concept can be seen in the example of a mechanical interaction where external parameters do change and thus, the energy of the system also changes. The idea of an ensemble refers to a group of systems that are in thermal contact and can exchange energy with each other. This explains why energy transfer may not always take place between two systems in contact, as it depends on the distribution of energy levels within each system. In summary, thermal interaction can lead to a change in the average energy of a system without any change in external parameters, due to the redistribution of energy levels within the ensemble of systems.
Yathindra
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.

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?

1. What is the concept of thermal interaction of systems on page 66 of F. Reif's book?

The concept of thermal interaction of systems on page 66 of F. Reif's book refers to the exchange of heat energy between two or more systems in contact with each other.

2. How does F. Reif explain the process of thermal interaction between systems?

F. Reif explains the process of thermal interaction between systems as the transfer of thermal energy from a higher temperature system to a lower temperature system until thermal equilibrium is reached.

3. What are some examples of thermal interaction of systems mentioned on page 66?

Some examples of thermal interaction of systems mentioned on page 66 may include heat transfer between a hot cup of coffee and the surrounding air, or the exchange of thermal energy between a warm body and a cold object.

4. Why is understanding thermal interaction of systems important in physics?

Understanding thermal interaction of systems is important in physics as it helps explain phenomena such as heat transfer, thermal equilibrium, and temperature changes, which are fundamental concepts in thermodynamics and energy transfer.

5. How can the principles of thermal interaction of systems be applied in real-world scenarios?

The principles of thermal interaction of systems can be applied in real-world scenarios such as designing efficient heating and cooling systems, optimizing energy usage in buildings, and understanding climate change and global warming effects on Earth's temperature regulation.

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