The observed nonlinear space-time fluctuations of microscopic objects such as atoms and molecules in an ideal gas are now (since 1980s) identified as

The important new contributions of the general systems theory applied to model ideal gases are as follows: (1)

The general systems theory concepts used in the derivation of the fundamental equations for the kinetic theory of gases have been applied earlier by the author for the simulation and prediction of both microscopic and macro-scale dynamical systems (Selvam, 1990; Selvam, 1993; Selvam, and Fadnavis, 1998; Selvam and Suvarna Fadnavis, 1999a; Selvam, and Suvarna Fadnavis, 1999b; Selvam, 2001).

In the following, Sections 2, 3 and 4 deal respectively with application of the model concepts to derive the following three classical relationships for an ideal gas: (1) pressure exerted by an ideal gas (2) the

The

(1)

In Equation (1) Chaotic fluctuations such as those executed by molecules in a gas are now identified as

Mary Selvam (1990) has developed a general systems theory (Capra, 1996) for the observed space-time

(2)

The above equation represents
the growth of an eddy continuum with formation of a hierarchy of successively
larger eddies from enclosed smaller scale eddies. The square of the eddy
amplitude, i.e., By analogy with quantum mechanics the square of the eddy amplitude

The macro-scale eddy continuum represented by Equation (2) obeys quantum-like mechanical laws, a manifestation of quantum-like chaos. The apparent paradox of wave-particle duality exhibited by microscopic scale quantum systems such as an electron or photon is however physically consistent in the context of real world macro-scale dynamical systems as explained in the following. The bi-directional energy flow intrinsic to eddy circulations is associated with bimodal, i.e., formation and dissipation respectively of phenomenological form for manifestation of energy such as the formation of clouds in updrafts and dissipation of clouds in adjacent downdrafts resulting in the observed discrete cellular geometry to cloud structure. The commonplace occurrence of clouds in a row is a manifestation of wave-particle duality in macro-scale atmospheric flows. By analogy, the molecules (atoms) of an ideal gas may be visualised as the manifestation of matter during a half-cycle of an eddy circulation (Mary Selvam, 1990; Selvam and Fadnavis, 1999a). The primary perturbation of r.m.s circulation speed

The length scale ratio

Considering two large eddy circulations of respective radii

(3)

Introducing the factor
representing eddy volumes on both sides of the above equation we have
(4)

Therefore
(5)

Substituting for (6)

The length scale ratio
(7)

In
the above equation the large eddy circulation speed (8)

The r.m.s eddy circulation
speed (9)

Equation (9) is almost
the same as Equation (1), the fundamental equation of the kinetic theory
of ideal gases, namely,
.
The important differences in the physical concepts underlying the derivation of the

(10)

(11)

The r.m.s circulation
speed (12)

In Equation (12) the variable
(13)

Incidentally, Equation
(12) represents the observed logarithmic spiral air flow structure in the
planetary atmospheric boundary layer and the constant From Equations (11) and (13) it is seen that, for successive large eddy growth steps generating the quasiperiodic

(14)

(15)

The ratio (16)

From Equations (15) and
(16)
(17)

The square of r.m.s circulation
speed (18)

Representing the larger
scale eddy energy as (19)

The length scale ratio
(20)

The above Equation (20)
is the same as the The derivation of

(21)

where r(22)

A graph of (23)

In Equation (23) (24)

A graph of Figure 1