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Maxwell–Boltzmann statistics of the quantum ideal gas in the canonical ensemble

Journal Article · · Journal of Statistical Mechanics
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Abstract

The Maxwell–Boltzmann statistics of the quantum ideal gas is studied through the canonical partition function by exactly counting discrete quantum states without the continuum approximation. Analytic expressions for energy, pressure, entropy, and heat capacity are expressed in terms of Jacobi theta functions and complete elliptic integrals. The results show typical effects of discrete energy levels in the low temperature limit while they reproduce thermodynamics of the classical ideal gas in the high temperature limit.

Research Organization:
Utah State Univ., Logan, UT (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
FG02-04ER54746
OSTI ID:
1849567
Journal Information:
Journal of Statistical Mechanics, Journal Name: Journal of Statistical Mechanics Journal Issue: 10 Vol. 2020; ISSN 1742-5468
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English

References (9)

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conference January 2002
Numerical computation for teaching quantum statistics journal November 2013
An alternative expression to the Sackur-Tetrode entropy formula for an ideal gas journal March 2018
Diffusion-driven fluid dynamics in ideal gases and plasmas journal June 2018
The nearly perfect Fermi gas journal May 2010
A Note on the Partition Function for Systems of Independent Particles journal February 1971
Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases journal February 2018
Time asymmetry in a dynamical model of the one-dimensional ideal gas journal November 2008
New Approach to Statistical Mechanics journal August 1967

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Related Subjects

Mechanics
Physics