According to the
specialized treatises^{1}36,
the power released on the area unit, by a black body^{1}37,
which have the temperature T, within an elementary interval of
wavelengths
is:

(X.24.8.1.1)

whereis given by the following relation:

(X.24.8.1.2)

*h*
is the Plank’s constant, *k*
is the Boltzmann’s constant, and *c*,
the light speed. The relation X.24.8.1.2 is the well-known *Plank
distribution* of the thermal photons
released by a black body which have the temperature *T*,
the support of this distribution being the infinite interval of the
photonic wave lengths.

The above-mentioned relations, converted for the frequency domain may become:

(X.24.8.1.3)

and the frequency (spectral) density of the released power is:

(X.24.8.1.4)

It is worth reminding that in terms of
the abstract object type, the Plank distribution, with its frequency
attribute support (or wave length) represents a *spectrum*. The
graphical plotting of this spectrum, in which both the support
frequency attribute and the distributed attribute are substituted
(represented) by the spatial position attribute, becomes however a *2D
form* of the spectrum.

We may recognize the term
used in the relation X.24.8.1.4 as the energy contained in a photon
with the frequency
,
and the term *kT *(from the ideal gas equation) also means
energy, the thermal energy mentioned into the equation X.24.7.1. For
the time being, we know that this energy *kT *has an invariant
value if the temperature of the black body is invariant, and
according to this value, the form of Plank distribution is invariant
as well. As a result of these explanations, we may notice that the
exponent of *e* from the above mentioned relation is a
dimensionless amount (a number, the ratio of two energy types) which
is noted with *x* and which has a variation domain also by
.
Once with this variable change, the relation X.24.8.1.4 becomes:

(X.24.8.1.5)

where
is an unique relation for all the Plank distributions. According to
this paper, the relation X.24.8.1.5 is named *normalized
Plank distribution*. The function *f(x)*
which is integrated on its support domain
has
a finite value, equal to
.
This means that the total power which is radiated on the area unit by
a black body at the temperature T is:

(X.24.8.1.6)

power which means the intensity of the radiated thermal energy flux, that is an energy contained in the thermal photons released by that particular body. The relation X.24.8.1.6 written as:

(X.24.8.1.7)

where *e* is a coefficient called
emissivity^{1}38
of
the body surface (that is equal to one as regards the black body),
and *
*
a constant named the Stefan’s constant, becomes
Stefan-Boltzmann relation. In this relation, the reader may note
that, in terms specific to the objectual philosophy, this emissivity
coefficient *e*
is nothing else but the RBS permeability of the radiating body to the
inner influx of thermal photons.

But, let us return
to the function *f(x)*
whose illustration is given in the figure X.24.8.1.1, where we may
also find the graphical plotting of the derivative*
f‘(x)*, for making much visible
the position of the peak value of this function.

As it may be observed from the figure,
the crossing through zero of the derivative (which is related to the
peak value *f(x)*)
occurs for a value *x*_{R}
which is the solution of the equation resulted from the null of the
derivative *f’(x)*
:

(X.24.8.1.8)

By means of
numerical methods, as regards the non-trivial solution (the trivial
one is *x=0*) we have a value
.
Therefore, the normalized Plank distribution has a peak value which
corresponds to this unique value for any distribution of this kind.
As we have seen in the chapters focused on distributions and objects,
this distribution is also an abstract object which must be
differentiated from other abstract objects from the same class, which
has an internal reference, reference which represents the object
within its external relations. Since the position of the maximum
value specific to all the normalized Plank distributions is always
the same, according to the value:

, (X.24.8.1.8)

*Fig. X.24.8.1.1*

resulting that the
only attribute type which makes the difference between two Plank
distribution is the value of this maximum (density’s amplitude)
which corresponds to the support value *x*_{R}
(according to the specific terms of this paper, it is the value of
the attribute distributed on the singular value *x*_{R}).
However, we saw that a value which is invariant for a class of
objects, against which the objects attributes may be determined,
represents itself a reference. Therefore, *x*_{R}
is an internal reference, also because its value is not imposed by an
IPS, but it is auto-settled as a result of the interactions between
the elements of the atomic medium and the ones of the medium of the
interstitial thermal photons, which means that *x*_{R}
is a *natural reference*.

136
**P. W. Atkins**
– *Tratat de chimie fizică*,
Editura Tehnică, 1996, **B. H. Bransden,
C.J. Joachain** – *Fizica
atomului și a moleculei*, Editura
Tehnică, 1998

137
By using the specific terms of this paper, the notion of *black
body* is translated as a hypothetical
material system whose bounding surface shows an unitary permeability
to the photon fluxes. However, we have seen that by definition, the
material systems own a RBS and they always have a sub-unitary
permeability in relation to the real fluxes. This means that this
black body is an abstract object, that is only a theoretical model.

138
This *e*
must not be mistaken with the basis of the natural logarithms *e*
from* f(x)*.

Copyright © 2006-2011 Aurel Rusu. All rights reserved.