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].

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.

scholarly journals The Thermal Expansion of Solids

1959 ◽  
Vol 12 (3) ◽  
pp. 237 ◽  
Author(s):  
GC Fletcher
Keyword(s):  
Thermal Expansion ◽  
Sodium Chloride ◽  
Equation Of State ◽  
Specific Heat ◽  
High Temperatures ◽  
Isothermal Compressibility ◽  
Constant Volume ◽  
Normal Vibrations ◽  
Ionic Solid ◽  
Theory And Experiment

From the theory of normal vibrations of a lattice, a practical means of obtaining the equation of state of an ionic solid is developed from which the thermal expansion can be derived. Using previous work by Kellermann, application is made to the case of sodium chloride and the results compared with experiment. Possible reasons for the discrepancy between theory and experiment, which is very large at 'high temperatures, are discussed. The variation with temperature of the specific heat at constant volume and the isothermal compressibility are also investigated.

The thermodynamic properties of fluid helium

1960 ◽  
Vol 252 (1013) ◽  
pp. 357-395 ◽  
Keyword(s):  
Thermodynamic Properties ◽  
Specific Heat ◽  
Internal Energy ◽  
Thermodynamic Functions ◽  
Single Phase ◽  
Constant Pressure ◽  
Pressure Coefficient ◽  
Differential Method ◽  
Constant Volume ◽  
Gibbs Function

Measurements have been made from which all the thermodynamic properties of fluid helium can be calculated in the temperature range from 3 to 20 °K and up to 100 atm pressure. The quantities measured were: (i) the specific heat at constant volume as a function of temperature and density, (ii) the pressure coefficient at constant volume ( also as a function of temperature and density, (iii) the pressure as a function of temperature at constant volume (isochores) for a range of densities. A particular feature of the experiments is that the important derivative ( )v, from which the changes of entropy and internal energy with volume at constant temperature are calculated, was measured directly by a differential method. Starting from the known entropy and internal energy of the liquid near its normal boiling point, these two quantities were calculated for all single phase states within the experimental range. From these, and using the equation of state data, the enthalpy, free energy, Gibbs function, and the specific heat at constant pressure have been deduced. The thermodynamic functions, together with some useful state properties, are tabulated as functions of temperature and either volume or pressure as relevant. The choice of the measured quantities was such that all the thermodynamic functions except the specific heat at constant pressure were obtained by integration of the experimental data; these functions therefore have the same accuracy as the measured quantities, about 1 %.

A Study of Fluid Argon via the Constant Volume Specific Heat, the Isothermal Compressibility, and the Speed of Sound and their Extremum Properties along Isotherms

1975 ◽  
Vol 53 (14) ◽  
pp. 1367-1384 ◽  
Author(s):  
John Stephenson
Keyword(s):  
Equation Of State ◽  
Specific Heat ◽  
Speed Of Sound ◽  
Isothermal Compressibility ◽  
Constant Volume ◽  
Liquid Region ◽  
Fluid Argon ◽  
Unified Description ◽  
Dense Liquid ◽  
Sound Data

The properties of fluid argon are investigated via the maxima and minima along isotherms of selected thermodynamic functions, the isothermal compressibility, χT, the constant volume specific heat, CV, and the speed of sound, W. Calculations are based on an equation of state due to Gosman, McCarty, and Hust and on speed of sound data compiled by Thoen, Vangeel, and Van Dael. The calculation of CV in the dense liquid region, from the equation of state and from the speed of sound, is discussed in detail. Also, the linear dependence of W on the density in the liquid region is reconciled with the behaviour of W at temperatures above critical to obtain a unified description of the variation of W along isotherms.

A Rational Equation of State for Water and Water Vapor in the Critical Region

1964 ◽  
Vol 86 (3) ◽  
pp. 320-326 ◽  
Author(s):  
E. S. Nowak
Keyword(s):  
Water Vapor ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Critical Point ◽  
Critical Region ◽  
Constant Pressure ◽  
Parametric Equation ◽  
Enthalpy And Entropy ◽  
Specific Volumes

A parametric equation of state was derived for water and water vapor in the critical region from experimental P-V-T data. It is valid in that part of the critical region encompassed by pressures from 3000 to 4000 psia, specific volumes from 0.0400 to 0.1100 ft3/lb, and temperatures from 698 to 752 deg F. The equation of state satisfies all of the known conditions at the critical point. It also satisfies the conditions along certain of the boundaries which probably separate “supercritical liquid” from “supercritical vapor.” The equation of state, though quite simple in form, is probably superior to any equation heretofore derived for water and water vapor in the critical region. Specifically, the deviations between the measured and computed values of pressure in the large majority of the cases were within three parts in one thousand. This coincides approximately with the overall uncertainty in P-V-T measurements. In view of these factors, the author recommends that the equation be used to derive values for such thermodynamic properties as specific heat at constant pressure, enthalpy, and entropy in the critical region.

Specific heat of ordered and isotopically disordered lattices

1978 ◽  
Vol 56 (10) ◽  
pp. 1390-1394
Author(s):  
K. P. Srivastava
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Volume ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Appreciable Difference ◽  
Substantial Change ◽  
Neighbour Interaction

An extensive numerical study on specific heat at constant volume (Cv) for ordered and isotopically disordered lattices has been made. Cv at various temperatures for ordered and disordered linear and two-dimensional lattices have been compared and no appreciable difference in Cv between these two structures has been observed. Effect of concentration of light atoms on Cv for three-dimensional isotopically disordered lattices has also been shown.In spite of taking next-nearest-neighbour interaction into account, no substantial change in Cv between the ordered and isotopically disordered linear lattices has been found. It is shown that the low lying modes contribute substantially at low temperatures.

BOSE–EINSTEIN STATISTICS IN A DISCRETE SPECTRUM TRAP

2004 ◽  
Vol 18 (04n05) ◽  
pp. 555-563 ◽  
Author(s):  
ENRICO CELEGHINI ◽  
MARIO RASETTI
Keyword(s):  
Critical Temperature ◽  
Low Temperature ◽  
Specific Heat ◽  
Discrete Spectrum ◽  
Harmonic Trap ◽  
Statistical Properties ◽  
Bose Einstein ◽  
The Continuum

A detailed description of the statistical properties of a system of bosons in a harmonic trap at low temperature, which is expected to bear on the process of BE condensation, is given resorting only to the basic postulates of Gibbs and Bose, without assuming equipartition nor continuum statistics. Below Tc such discrete spectrum theory predicts for the thermo-dynamical variables a behavior different from the continuum case. In particular a new critical temperature Td emerges where the specific heat exhibits a λ-like spike.

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