Easy entropy problem, what is the permitted entropy?

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In summary, during the conversation, it was mentioned that there are five physically possible entropy to exist and five entropy which cannot be real. The question was raised about the possibility of a fifth entropy, to which the response was that only four were found. The conversation then shifted to discussing a problem from Callen's textbook regarding violations of Callen's Postulate IV. The speaker considered this postulate and its relation to temperature and discussed the difficulty in dealing with this equation. The conversation then moved on to considering states where the partial derivative of U with respect to S is equal to zero and whether these states satisfy S=0. The conversation ended with a realization and a thank you for clarifying the confusion.
  • #1
LCSphysicist
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Homework Statement
All below
Relevant Equations
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There is five physically possible entropy to exist, and five entropy which can't be real, find it all.

I could found just four entropy, what is the another?

B, H and J:
S(λU,λV,λN) ≠ λS(U,V,N)
D:
∂S/∂U < 0

what is the another?
(another or other??)
 
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  • #2
This is a problem from Callen's textbook. Did you consider violations of Callen's Postulate IV?

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  • #3
TSny said:
This is a problem from Callen's textbook. Did you consider violations of Callen's Postulate IV?

View attachment 267814
Actually i thought about it, since was the only postulate i not mentioned, however, i don't know how could i deal with this, since i don't have an equation in the options which leave me direct to the temperature.
I don't think we can say U = NfkT/2 as generally do for some cases.
 
  • #4
From the functional form of each relation between S and U, you can consider if there are any states where $$\left( \frac{\partial U}{\partial S} \right)_{V, N} = 0$$
If there are such states, do these states satisfy ##S = 0##?
 
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  • #5
TSny said:
From the functional form of each relation between S and U, you can consider if there are any states where $$\left( \frac{\partial U}{\partial S} \right)_{V, N} = 0$$
If there are such states, do these states satisfy ##S = 0##?
Oh, i was making a confusing zzz thx
 

1. What is entropy?

Entropy is a measure of the disorder or randomness in a system. It is commonly used in thermodynamics to describe the amount of energy that is unavailable for work in a system. In simpler terms, it can be thought of as a measure of the level of chaos or unpredictability in a system.

2. How is entropy related to the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system will always increase over time. This means that as energy is converted from one form to another, some of it will inevitably be lost as unusable energy, increasing the overall entropy of the system.

3. What is the difference between easy entropy and regular entropy?

Easy entropy is a simplified version of entropy that is often used in introductory physics courses. It is based on the idea that a system can only have two possible states - ordered or disordered - and therefore the amount of entropy in a system can only be either 0 or 1. Regular entropy, on the other hand, takes into account the degrees of freedom and possible states of a system, resulting in a more accurate measure of entropy.

4. How is entropy calculated?

The exact calculation of entropy depends on the specific system being studied. In general, it involves determining the number of possible microstates (individual arrangements of particles or energy) that correspond to a given macrostate (overall state of the system). The entropy is then calculated using the formula S = k ln W, where k is the Boltzmann constant and W is the number of microstates.

5. What is the permitted entropy?

The permitted entropy refers to the maximum possible entropy that a system can have. This is determined by the number of possible microstates in a system and can vary depending on the specific conditions and constraints of the system. In general, the permitted entropy will increase as the system becomes more disordered or chaotic.

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