### 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 language | English (US) |
---|---|

Pages (from-to) | 140-147 |

Number of pages | 8 |

Journal | Radiation Effects and Defects in Solids |

Volume | 174 |

Issue number | 1-2 |

DOIs | |

State | Published - Feb 1 2019 |

### Fingerprint

### 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

*Radiation Effects and Defects in Solids*,

*174*(1-2), 140-147. https://doi.org/10.1080/10420150.2019.1577851

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

Research output: Contribution to journal › Article

*Radiation Effects and Defects in Solids*, vol. 174, no. 1-2, pp. 140-147. https://doi.org/10.1080/10420150.2019.1577851

}

TY - JOUR

T1 - Internal energy and hydrostatic pressure of a quantum relativistic ideal gas

AU - Molinari, Vincenzo

AU - Mostacci, Domiziano

AU - Pizzio, Francesco

AU - Ganapol, Barry D

PY - 2019/2/1

Y1 - 2019/2/1

N2 - 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.

AB - 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.

KW - average kinetic energy

KW - Equation of state

KW - pressure

KW - quantum relativistic

UR - http://www.scopus.com/inward/record.url?scp=85063859772&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063859772&partnerID=8YFLogxK

U2 - 10.1080/10420150.2019.1577851

DO - 10.1080/10420150.2019.1577851

M3 - Article

VL - 174

SP - 140

EP - 147

JO - Radiation Effects and Defects in Solids

JF - Radiation Effects and Defects in Solids

SN - 1042-0150

IS - 1-2

ER -