Thermal physics. Entropy's functional dependecy

In summary, the author of Kittel&kroemer's Thermal Physics assumes the functional dependency of entropy without providing any explanation and derives some equalities. This can be seen on pages 66-67 and 43 of the 2nd edition. On page 66, the author states that the number of states and therefore the entropy only depend on U and V, for a fixed number of particles. However, it is unclear why the number of states depend on these variables. In chapter 2, it is mentioned that the multiplicity and thus entropy are functions of U and N. On page 43, the author also mentions that the entropy may depend on additional independent variables, but it is not clear in what circumstances this would occur
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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?
 
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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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Related to Thermal physics. Entropy's functional dependecy

1. What is thermal physics?

Thermal physics is the branch of physics that studies the behavior of matter at the microscopic level, specifically related to temperature and heat. It involves understanding the properties and interactions of particles and energy in thermal systems.

2. What is entropy in thermal physics?

Entropy is a measure of the disorder or randomness of a system. In thermal physics, it is a measure of the distribution of energy among the particles in a system. As a system's entropy increases, its energy becomes more spread out and less useful.

3. How is entropy related to functional dependency?

In thermal physics, entropy is a function of the state of a system, meaning it depends on the values of the system's properties such as temperature, volume, and pressure. Entropy's functional dependency refers to the relationship between these properties and the resulting value of entropy in a given system.

4. What is the second law of thermodynamics and how does it relate to entropy?

The second law of thermodynamics states that the total entropy of a closed system will always increase over time, or at the very least remain constant. This means that in any natural process, there will be a net increase in the disorder of the system, or an increase in entropy. Entropy is therefore used as a measure of the irreversibility of a process.

5. How is entropy used in practical applications?

Entropy is a crucial concept in many areas of science and engineering, including thermodynamics, chemistry, and information theory. It is used to predict the behavior and efficiency of systems, such as in the design of engines and refrigerators. In information theory, it is used to measure the amount of uncertainty or randomness in a system.

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