Thermal physics. Entropy's functional dependecy

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SUMMARY

The discussion centers on understanding the functional dependency of entropy as presented in Kittel & Kroemer's "Thermal Physics." The author highlights specific pages (66-67, 43) where the text assumes entropy's dependency on energy (U) and volume (V) for a fixed number of particles (N). Key points include the assertion that the number of states, and thus entropy, is a function of U and V, while also acknowledging that entropy may depend on additional independent variables under certain conditions. The author expresses confusion regarding the derivation of these relationships and the assumption of constant entropy during interdependent changes in U and V.

PREREQUISITES
  • Understanding of thermodynamic concepts such as entropy and multiplicity.
  • Familiarity with the definitions of energy (U), volume (V), and the number of particles (N).
  • Knowledge of fundamental temperature (τ) in thermodynamics.
  • Basic grasp of the principles outlined in Kittel & Kroemer's "Thermal Physics."
NEXT STEPS
  • Study the derivation of entropy in relation to energy and volume in thermodynamics.
  • Examine the concept of multiplicity and its relation to entropy in statistical mechanics.
  • Research the conditions under which entropy may depend on additional independent variables.
  • Review the implications of constant entropy in thermodynamic processes.
USEFUL FOR

This discussion is beneficial for students of thermodynamics, particularly those studying Kittel & Kroemer's "Thermal Physics," as well as educators and researchers seeking clarity on entropy's functional dependencies.

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Homework Statement


I'm reading Kittel&kroemer's Thermal physics. How can I know Entropy's functional dependency?
Author assume entropy's functional dependecy without explanations and derive some equaltities. So I can't follow it.

N the number of particles. U Energy of the system. V. volume of the system [itex]\tau[/itex] fundamental temperature
[itex]\sigma(N,U)[/itex], [itex]\sigma(\tau,V) etc...[/itex]

Homework Equations


The Attempt at a Solution

 
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On what page(s) does this occur?
 
2nd edition p66~p67, p43. "" is what author says.
p66 "The number of states and thus the entropy depend only on U and on V, for fixed number of particles," I don't know why the number of states depend on on U and V.
In chapter2 multiplicity thus entropy is function of U and N. p43 "The entropy may depend on additional independent variables" I don't know in what circumstance the entropy depend on what variables.
p67 "If we denote these interdependent values of dU and dV by [itex](\delta U)_{\sigma}[/itex] and [itex](\delta V)_{\sigma}[/itex], the entropy change will be zero." I don't know why it's possible to assume constant entropy and make U and V be interdependent.
 
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