Perfect Gas

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Low Temperature ◽  
Black Body ◽  
Black Body Radiation ◽  
Einstein Condensation ◽  
Quantum Gas ◽  
Perfect Gas ◽  
Special Cases ◽  
Planck Distribution ◽  
Bose Einstein ◽  
Boltzmann Law

The perfect gas is perhaps the most prominent application of statistical mechanics and for this reason merits a chapter of its own. This chapter briefly reviews the quantum theory of many identical particles, in particular the distinction between bosons and fermions, and then develops the general theory of the perfect quantum gas. It considers a number of limits and special cases: the classical limit; the Fermi gas at low temperature; the Bose gas at low temperature which undergoes Bose–Einstein condensation; as well as black-body radiation. For the latter we derive the Stefan–Boltzmann law, the Planck distribution, and Wien’s displacement law. This chapter also discusses the effects of a possible internal dynamics of the constituent molecules on the thermodynamic properties of a gas. Finally, it extends the theory of the perfect gas to dilute solutions.

Thermodynamics

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Chemical Potential ◽  
Black Body ◽  
Black Body Radiation ◽  
Spin Systems ◽  
Atomic Scale ◽  
Einstein Condensation ◽  
Maxwell Distribution ◽  
Bose Einstein Condensation ◽  
Thermodynamic Variables ◽  
Bose Einstein

This chapter is about thermodynamics, or statistical mechanics, which explains macroscopic features of the world in terms of the motion of vast numbers of particles on the atomic scale. It discusses how macroscopic variables such as temperature and entropy were originally introduced, before presenting modern definitions of temperatures and entropy and the Laws of Thermodynamics. Alternative thermodynamic variables, including enthalpy and the Gibbs free energy, are defined and the Gibbs distribution is explained. The Maxwell distribution is derived. The chemical potential is introduced and the pressure and heat capacity of an electron gas is calculated, The Fermi–Dirac and Bose–Einstein functions are derived. Bose–Einstein condensation is explained. Black body radiation is discussed and the Planck formula is derived. Lasers are explained. Spin systems are used to model magnetization. Phase transitions are briefly discussed. Hawking radiation and the thermodynamics of black holes is explained.

On the Bose-Éinstein condensation of a perfect gas

Physica ◽  
1949 ◽  
Vol 15 (7) ◽  
pp. 671-672 ◽  
Author(s):  
S.R. De Groot ◽  
C.A. Ten Seldam
Keyword(s):  
Einstein Condensation ◽  
Perfect Gas ◽  
Bose Einstein Condensation ◽  
Bose Einstein

scholarly journals The Bose-Einstein statistics: Remarks on Debye, Natanson, and Ehrenfest contributions and the emergence of indistinguishability principle for quantum particles

2020 ◽  
Vol 19 ◽  
pp. 423-441
Author(s):  
Józef Spałek
Keyword(s):  
Black Body ◽  
Black Body Radiation ◽  
Quantum Particles ◽  
Particle Wave Function ◽  
Planck’S Law ◽  
The Many ◽  
Bose Einstein ◽  
Grand Canonical ◽  
Fundamental Physical

The principal mathematical idea behind the statistical properties of black-body radiation (photons) was introduced already by L. Boltzmann (1877/2015) and used by M. Planck (1900; 1906) to derive the frequency distribution of radiation (Planck’s law) when its discrete (quantum) structure was additionally added to the reasoning. The fundamental physical idea – the principle of indistinguishability of the quanta (photons) – had been somewhat hidden behind the formalism and evolved slowly. Here the role of P. Debye (1910), H. Kamerlingh Onnes and P. Ehrenfest (1914) is briefly elaborated and the crucial role of W. Natanson (1911a; 1911b; 1913) is emphasized. The reintroduction of this Natanson’s statistics by S. N. Bose (1924/2009) for light quanta (called photons since the late 1920s), and its subsequent generalization to material particles by A. Einstein (1924; 1925) is regarded as the most direct and transparent, but involves the concept of grand canonical ensemble of J. W. Gibbs (1902/1981), which in a way obscures the indistinguishability of the particles involved. It was ingeniously reintroduced by P. A. M. Dirac (1926) via postulating (imposing) the transposition symmetry onto the many-particle wave function. The above statements are discussed in this paper, including the recent idea of the author (Spałek 2020) of transformation (transmutation) – under specific conditions – of the indistinguishable particles into the corresponding to them distinguishable quantum particles. The last remark may serve as a form of the author’s post scriptum to the indistinguishability principle.

scholarly journals Modified Bose-Einstein condensation in an optical quantum gas

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mario Vretenar ◽  
Chris Toebes ◽  
Jan Klaers
Keyword(s):  
Radiative Decay ◽  
Open Quantum Systems ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Destructive Interference ◽  
Quantum Gas ◽  
Bose Einstein Condensation ◽  
Open Quantum ◽  
Physical Mechanisms ◽  
Bose Einstein

AbstractOpen quantum systems can be systematically controlled by making changes to their environment. A well-known example is the spontaneous radiative decay of an electronically excited emitter, such as an atom or a molecule, which is significantly influenced by the feedback from the emitter’s environment, for example, by the presence of reflecting surfaces. A prerequisite for a deliberate control of an open quantum system is to reveal the physical mechanisms that determine its state. Here, we investigate the Bose-Einstein condensation of a photonic Bose gas in an environment with controlled dissipation and feedback. Our measurements offer a highly systematic picture of Bose-Einstein condensation under non-equilibrium conditions. We show that by adjusting their frequency Bose-Einstein condensates naturally try to avoid particle loss and destructive interference in their environment. In this way our experiments reveal physical mechanisms involved in the formation of a Bose-Einstein condensate, which typically remain hidden when the system is close to thermal equilibrium.

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