Internal energy and hydrostatic pressure of a quantum relativistic ideal gas

Vincenzo Molinari, Domiziano Mostacci, Francesco Pizzio, Barry D Ganapol

Research output: Contribution to journalArticle

Abstract

In the classical case, the hydrostatic pressure of an ideal gas is defined as being two-thirds of the specific kinetic energy of the gas: p = 2/3n < U k >, where < U k > is the average kinetic energy of the particles. However, this is no longer the case when relativistic cases are considered. Further concerns may be raised by quantum considerations. In the present paper, both pressure and kinetic energy are calculated taking the appropriate averages weighted with the equilibrium distribution function of the gas. For the purpose of this work the quantum relativistic Fermi–Dirac and Bose–Einstein distribution functions, will be considered for the cases of bosons and weakly degenerate fermions. Integration yields results in a closed form containing modified Bessel functions. A large-argument approximation is then taken, leading to an equation of state composed of the classic part plus correction terms.

Original languageEnglish (US)
Pages (from-to)140-147
Number of pages8
JournalRadiation Effects and Defects in Solids
Volume174
Issue number1-2
DOIs
StatePublished - Feb 1 2019

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ideal gas
Hydrostatic pressure
internal energy
Kinetic energy
hydrostatic pressure
Gases
kinetic energy
Distribution functions
distribution functions
Bosons
Bessel functions
Fermions
Equations of state
gases
equations of state
bosons
fermions
approximation
energy

Keywords

  • average kinetic energy
  • Equation of state
  • pressure
  • quantum relativistic

ASJC Scopus subject areas

  • Radiation
  • Nuclear and High Energy Physics
  • Materials Science(all)
  • Condensed Matter Physics

Cite this

Internal energy and hydrostatic pressure of a quantum relativistic ideal gas. / Molinari, Vincenzo; Mostacci, Domiziano; Pizzio, Francesco; Ganapol, Barry D.

In: Radiation Effects and Defects in Solids, Vol. 174, No. 1-2, 01.02.2019, p. 140-147.

Research output: Contribution to journalArticle

Molinari, Vincenzo ; Mostacci, Domiziano ; Pizzio, Francesco ; Ganapol, Barry D. / Internal energy and hydrostatic pressure of a quantum relativistic ideal gas. In: Radiation Effects and Defects in Solids. 2019 ; Vol. 174, No. 1-2. pp. 140-147.
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