The application of closed Bragg-Williams equation to elementary particles

Abstract

The Bragg-Williams equation is actually a form of van der Waal’s equation of gases presented in the form of an infinite Maclaurin’s series. The problem with such expressions is that discrepancies tend to arise during computations of an infinite series. To make computation easier and in addition obtain more accurate results, a closed form of Bragg-Williams equation was obtained using geometric progressions. The comparison of the closed and open Bragg-Williams equations shows that the point at which the two equations agree increases with increase in the power of θ in the open expression. The increase in the dimensionless quantity, Pb/kT, with increase in powers of θ suggests that the pressure of the gas is increased since kT is constant at a given temperature. Increase in pressure means that the interaction energy of the gas represented by Pb is increased. By relating the number of particles to bosons and fermions, it is seen that this energy is less for bosons and more for fermions. Thus, interaction energy between the fermions particles will be expected to be more than for the bosons in a given matter. Increase in pressure can guarantee increase in other thermodynamic quantities.