Abstract
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the entropy is not extensive. The inextensivity leads to the so-called Gibbs paradox in which the mixing entropy of two identical classical gases increases. Lots of literature from different points of view were created to resolve the paradox. In this paper, starting from the Boltzmann entropy, we present the thermodynamics of the system of distinguishable particles. A straightforward way to get the corrected Boltzmann counting is shown. The corrected Boltzmann counting factor can be justified in classical statistical mechanics.
Highlights
The concepts of distinguishable and indistinguishable particles is important in Statistical Mechanics as their corresponding entropies are different
The entropy in statistical mechanics is defined in terms of the logarithm of the number of the accessible microstates in the phase space
We present the thermodynamics of the system of distinguishable particles, starting from the definition of entropy for the distinguishable particles
Summary
The concepts of distinguishable and indistinguishable particles is important in Statistical Mechanics as their corresponding entropies are different. The entropy in statistical mechanics is defined in terms of the logarithm of the number of the accessible microstates in the phase space. The microstates numbers for distinguishable and indistinguishable particles are certainly different and their corresponding The essence of the paradox is that the entropy of the distinguishable particles is not extensive.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
