Finite size effect on classical ideal gas revisited

Abstract

Finite size effects on classical ideal gas are revisited. The micro-canonical partition function for a collection of ideal particles confined in a box is evaluated using Euler-Maclaurin's as well as Poissonʼs summation formula. In Poissonʼs summation formula there are some exponential terms which are absent in Euler-Maclaurin's formula. In the thermodynamic limit the exponential correction is negligibly small but in the macro/nano dimensions and at low temperatures they may have a great significance. The consequences of finite size effects have been illustrated by redoing the calculations in one and three dimensions keeping the exponential corrections. Global and local thermodynamic properties, diffusion driven by the finite size effect, and effect on speed of sound have been discussed. Thermo-size effects, similar to thermoelectric effects, have been described in detail and may be a theoretical basis with which to design nano-scaled devices. This paper can also be very helpful for undergraduate and graduate students in physics and chemistry as an instructive exercise for a good course in statistical mechanics.

Multiplicity and pseudorapidity distributions of charged particles in asymmetric and deformed nuclear collisions in the wounded quark model

“…We see that in Cu − Cu system c 2 s is more than in Au − Au systems at some energies and at some energies c 2 s have almost same value as in the case of Au − Au collisions. The medium created in smaller colliding system like Cu − Cu, the finite size effects have important role which causes fluctuation in the mean value of c 2 s [75] which makes speed of sound a bit random.…”

Comment on ‘Thermodynamics of a particle in square well potential’

“…In order to obtain a suitable approximate expression for Z, Bhattacharyya and Mitra [1] resorted to an impractical version of the Euler-MacLaurin summation formula and, consequently, they had to carry out the Taylor expansion of some integrals that cannot be solved analytically. This fact is surprising because the same result was derived several years earlier in a clearer, cleaner and more straightforward way by Ghosh et al [2] (whom they already cited). More precisely, Ghosh…”

“…The improved expression for the canonical partition function proposed by Bhattacharyya and Mitra [1] was already derived earlier by other authors in a more efficient way [2][3][4]. Bhattacharyya and Mitra's calculation of the thermodynamic functions for the particle in a finite box is incorrect because the authors omitted the contribution of the continuous spectrum.…”

“…It is worth mentioning that all the terms of higher order in the Euler-MacLaurin summation formula vanish identically [2][3][4] which does not mean that app is exact. The reason is revealed by the Poisson summation formula that Ghosh et al [2] wrote as…”

Thermodynamics of regular Kerr-Sen black hole

“…Inspired by Bardeen [6], regular (nonsingular) black hole have been considered that has a spherically symmetric, static, asymptotically flat spacetime, and regular at the center. In 2015, Ghosh employ Newman-Janis trick to static regular black hole into rotating version [7]. These solution characterized by the same parameter as Kerr, but with the free parameter, k, which determinde the regularity of the black hole.…”