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annaphys
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Gibbs introduced the N! to then make S extensive. He then attributed the N! to the particles being indistinguishable. How does the N! signify the indistinguishability?
Lost is only spurious information that is physically nonexistent anyway.annaphys said:Are we losing any information of the system by doing this? Of course in quantum mechanics particles are indistinguishable but it'd be interesting to know if any information is lost.
The N value in the Gibbs Paradox represents the number of particles in a system. In this context, it signifies the indistinguishability of particles because it assumes that all particles in the system are identical and cannot be differentiated from one another.
Indistinguishability is important in the Gibbs Paradox because it is a fundamental concept in statistical mechanics. It allows us to treat particles as identical entities and simplifies the mathematical calculations involved in understanding the behavior of a system with a large number of particles.
The N value affects the entropy in the Gibbs Paradox because it is directly related to the number of microstates that a system can have. As the number of particles increases, the number of possible microstates also increases, leading to a higher entropy value.
The Gibbs Paradox is significant in thermodynamics because it highlights the limitations of classical thermodynamics in dealing with systems with a large number of particles. It also led to the development of statistical mechanics, which provides a more accurate description of the behavior of such systems.
The Gibbs Paradox is closely related to the concept of entropy because it deals with the increase in entropy when two identical systems are combined. It also highlights the importance of considering indistinguishability when calculating entropy, as it can significantly affect the results.