THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

Approximate energy spectra and statistical mechanical functions of some diatomic molecular hydrides

2021 ◽  
pp. 1-6
Author(s):  
A.N. Ikot ◽  
U.S. Okorie ◽  
G.J. Rampho ◽  
Hewa Y. Abdullah
Keyword(s):  
Mechanical Properties ◽  
Partition Function ◽  
Thermodynamic Functions ◽  
Potential Model ◽  
Energy Spectra ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation ◽  
Statistical Mechanical ◽  
Vibrational Partition Function ◽  
Maclaurin Formula

In this study, we have investigated the statistical mechanical properties of the Varshni potential model for some diatomic molecular hydrides via the Euler–Maclaurin formula. This was done using the approximate analytical energy eigenvalues, which were obtained by solving the radial Schrödinger equation with the Greene–Aldrich approximation and suitable coordinate transformation schemes. The effect of high temperatures and upper bound vibration quantum number on the vibrational partition function and other thermodynamic functions of the selected diatomic molecular hydrides were studied. We also show that these effects on the thermodynamic functions considered were similar for all the diatomic molecular hydrides selected.

INTEGRAL REPRESENTATION FOR THE GR AND PARTITION FUNCTION IN QUANTUM STATISTICAL MECHANICS OF EXCLUSION STATISTICS

2000 ◽  
Vol 14 (05) ◽  
pp. 485-506 ◽  
Author(s):  
KAZUMOTO IGUCHI ◽  
KAZUHIKO AOMOTO
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Integral Representation ◽  
Quantum Statistical Mechanics ◽  
Ideal Gas ◽  
Alternative Proof ◽  
Quantum Statistical

We derive an exact integral representation for the gr and partition function for an ideal gas with exclusion statistics. Using this we show how the Wu's equation for the exclusion statistics appears in the problem. This can be an alternative proof for the Wu's equation. We also discuss that singularities are related to the existence of a phase transition of the system.

scholarly journals Statistical Mechanics of Simple Dense Fluids Using Functional Integration

1969 ◽  
Vol 22 (6) ◽  
pp. 747 ◽  
Author(s):  
RG Storer
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Short Range ◽  
Equations Of State ◽  
Functional Integration ◽  
Functional Integral ◽  
Grand Partition Function ◽  
Dense Fluids ◽  
Approximate Equations

The use of functional integration in developing approximate equations of state for simple dense fluids is outlined. The repulsive (short range) and attraotive parts of the potential are treated separately and the grand partition function is expressed in terms of a functional integral which involves knowledge of the thermodynamio properties of the "short.range system". Two separate prooedures are outlined to obtain approximate equations of state for dense fluids from this exact functional integral.

STATISTICS OF A LINEAR PARAMAGNETIC MACROMOLECULE

1951 ◽  
Vol 29 (3) ◽  
pp. 236-244 ◽  
Author(s):  
W. Opechowski ◽  
J. M. Bryan
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Low Temperatures ◽  
Paramagnetic Susceptibility ◽  
Physical Systems ◽  
Asymptotic Expressions ◽  
Paramagnetic Atoms

The partition function of a linear "macromolecule" composed of N paramagnetic atoms subject to the Ising interaction is calculated for an arbitrary N. From the partition function the expressions for the specific heat and the initial paramagnetic susceptibility are obtained. It is shown on the example of the susceptibility that the procedure, customary in statistical mechanics, which consists in using the asymptotic expressions (N→∞) to describe actual physical systems (N very large, but finite) should be used with some caution in the region of very low temperatures.

THERMODYNAMICS AND EXTRA DIMENSIONS

2009 ◽  
Vol 23 (13) ◽  
pp. 1625-1632
Author(s):  
JOSE A. MAGPANTAY
Keyword(s):  
Equation Of State ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Extra Dimensions ◽  
Average Energy ◽  
Constant Volume ◽  
Dimensional Torus ◽  
Ideal Gases ◽  
Bose Einstein

We consider the effects of extra dimensions on the thermodynamics of classical ideal gases, Bose–Einstein gases and Fermi–Dirac gas. Assuming a q-dimensional torus for the extra dimensions, we compute the thermodynamic functions such as the equation of state, the average energy and the specific heat at constant volume for the three systems. We show that the corrections due to the extra dimensions are small, proportional to [Formula: see text].

scholarly journals The Equilibrium Statistical Mechanics of a One-dimensional Self-gravitational System

1979 ◽  
Vol 32 (3) ◽  
pp. 289 ◽  
Author(s):  
Y Fukui ◽  
T Morita
Keyword(s):  
Mechanical Properties ◽  
Statistical Mechanics ◽  
Infinite Number ◽  
Virial Expansion ◽  
Gravitational System ◽  
Equilibrium Statistical Mechanics ◽  
One Dimensional ◽  
Statistical Mechanical ◽  
Number Of Particles

It is shown that the exact statistical mechanical properties of a one-dimensional self-gravitational system in. the limit of an infinite number of particles are easily obtained with the aid of the virial expansion.

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