Exploring System Energy in Statistical Mechanics

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Homework Help Overview

The discussion revolves around the concept of energy in statistical mechanics, particularly focusing on systems with fixed total energy and the implications of multiple energy values presented in examples. Participants are exploring the relationship between microstates and macrostates, as well as the definition of entropy in this context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning how multiple energy values can exist in a system that is described as having a fixed total energy. There is an exploration of the distinction between individual systems and ensembles, and how this affects the understanding of energy and entropy.

Discussion Status

The conversation is ongoing, with participants attempting to clarify the concepts of microstates and macrostates. Some guidance has been offered regarding the interpretation of the examples in the notes, but there is still confusion regarding the implications of energy values presented.

Contextual Notes

There is a noted tension between the description of the system as isolated with fixed energy and the examples that suggest variability in energy values. This discrepancy is central to the discussion.

latentcorpse
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In my notes,

http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM3.pdf

on page 1 we are told we're dealing with systems of fixed total E but in the expilicit example on page 3, do we not find 4 different values for the total energy. how is this possible?
 
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Right. The point is to look at how many different microstates (arrangements of up/down spins) correspond to the same macrostate (total energy). This is used to give us entropy as a function of total energy, S(E).

Notice that total energy is still an input parameter. So once we find the function S(E), we can fix E to be any particular allowed value.
 
yes but this is supposed to be an isolated system hence E is fixed

yet in the table we have E being -3mH, -mH +mH, +3mH which means it's not fixed. i guess i just can't really follow your argument sorry
 
We're not talking about a single system, but an ensemble of many possible systems. Each of those systems has a different energy and entropy. Your notes describe how to find the entropy as a function of energy, S(E).

Once we know S(E), we can then calculate properties of any particular system of some given energy E.
 

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