Gravity Chapter
4 continued
Thermal Conductivity and Diffusion
There are number of other instances
where the assumed high velocities of ‘kinetic’ atoms in
gases cannot rationally explain the atomic interactions resulting in
other simple natural, observable phenomena, and examples are the thermal
conductivity (heat transport) in gases and the diffusion (or mixing)
of different gases. The following two, unusually frank, quotations
are from a Russian textbook on molecular physics.
‘It should seem to follow from the fact that the velocities
of molecules are very great that the temperature should
level out very rapidly. Experiments show, however, that
the thermal conductivity of gases is low. A considerable time elapses
before the temperature of a gas levels out if one part of it is heated
more than another.’
‘Since this transport is also ensured by motion
of the molecules, and the velocity of the molecules are high,
diffusion should seem to occur rapidly with the concentrations
levelling out almost instantaneously. Experiments show,
however, that at atmospheric pressure diffusion is a very slow process,
and mixing in any absence of motion of the gases as a whole may
last several days.’8 (My emphasis)
There follow long and convoluted arguments in an attempt
to explain why these thermal and physical transport phenomena
do not conform to the predictions of the theory. Essentially
this is explained by saying that as the molecules have
frequent chaotic, collisions with one another they tend to stay in
the same area and not move in any great linear distance.
Diffusion (Helium/Nitrogen Admixture)
Helium is a very good
medium for the testing for leaks in gas piping and pressurised
equipment, as it escapes through the smallest of apertures and simple
equipment is available to detect the gas. It is however relatively
expensive and a mixture of 5% helium and 95% nitrogen serves
the purpose equally well. Companies producing medical and
industrial gases are able to supply this mixture. However
simply introducing both gases into a cylinder, in any order,
does not achieve a homogenous mixture suitable for practical
use unless it is left for many days.9
Mixing is therefore accelerated by placing such a cylinder
horizontally on rollers and rotating (or ‘rumbling’) it
for some time, which process clearly creates an internal
friction between the internal walls of the rotating cylinder
and the gas in contact with it.
The simple diagrams below show a hypothetical cylinder
1 m high and 200 mm in diameter and an example where a
mixture consisting of 5 percent of helium is required.
The numbers of atoms indicated are clearly incorrect and
are simply included to show the principle; the pressure
inside this cylinder is set at one atmosphere.
The average velocity of nitrogen molecules in air according
to kinetic theory is around 500 metres per second; the
velocity of helium atoms is 1300 metres per second. The
relative mass of a nitrogen molecule is 14, and that of
helium. 4.
Figure 11
At these velocities it would be possible for the slower, but significantly
more massive, nitrogen molecules that are in the vicinity of the helium
atoms at the top of the cylinder, if uninhibited by collisions, to
travel to the top of the cylinder and back 5,000 times in one second,
300,000 times in one minute. Extending the time to one hour would enable
each nitrogen molecule to travel this distance 18 million times, a
total distance of 900 kilometres.
With respect to each of the helium atoms they could each
travel in the other direction to the bottom of the cylinder
and back around 680 times in a second, 41,000 times in a minute and
in one hour 2,460,000 times, a total distance of 4680 kilometres,
and in one day they would travel a total distance of 112,320 kilometres.
Let us consider this situation and apply M.Perrins’ assumptions
of kinetic molecular agitation to it.
He states that nitrogen molecules have a velocity of 500
metres per second, travel 0.00001mm between collisions
(e.g. ‘mean free path’) and undergo 5 billion collisions per second.
If we consider a hypothetical situation where we have a
sheet of rigid matter placed horizontally between these
two gases, we can say that according to kinetic theory, all molecules
within one or two molecular diameters of the sheet of matter on both
sides of it are either moving in a direction towards the sheet or
away from the sheet (ignoring the small number of molecules that
are travelling in a perfectly parallel direction to the plane of
the sheet). Thus on either side of the sheet about 50% of the molecules
are travelling in general direction away from the sheet after having
collided with it, and about 50% are travelling towards the sheet
and will collide with it, (or rather with the atoms of which it is
comprised).
If we now remove the sheet of matter, the molecules that
we are discussing of course will be moving in precisely
the same directions and the 50% of the molecules from each side of
our now hypothetical plane of division between the two gases that
are travelling towards it, will instead of colliding with the molecules
of the rigid matter of the sheet will collide with the molecules
of the opposing gas.
If we now consider the 50% of these molecules that are
in moving in one direction away from the plane of division
and accept that their motion from this point is completely chaotic
and random as a result of the subsequent multiple collisions with
other molecules, we can assume that there are two extremes of overall
motion of these molecules. On the one hand a molecule proceeds in
such a random manner that it ends up after a period of time back
at the plane of division between the two gases, represented by molecule
A in the diagrams below, and the other extreme would be a molecule
whose path, while again completely random, did not encounter any
collision that could reverse its motion away from the plane of division
(molecule B below). (It could be argued that a third extreme could
occur as represented by molecule C, which after a single collision
continues to travel indefinitely in the opposite direction, however
such instances will be cancelled out by the statistical probability
that of the 50% of molecules moving downwards away from the plane,
a similar number would achieve a similar overall motion upwards).
Of course if all molecules followed one or the other of
these patterns then the situation could not be described
as ‘random’.
Figure 12
Thus we can suggest that 50% of these molecules at the
plane of intersection will either remain in the vicinity
of the plane of intersection or will move at varying overall velocities
away from it in one general direction i.e. either upwards or downwards.
Of those moving in an upwards direction let us take one
of the molecules that will continue to rise away from the
plane of intersection, and assume that its actual motion
away from the plane in a period of time is 1/20th of the actual total
‘random walk’ motion. The diagram below represents such a motion,
and in this case the molecule has encountered 20 separate collisions
that have caused 11 upwards trajectories and 9 downwards, the final
result being that the actual movement away from the plane of intersection
is equal to the mean free path of 1/10,000th of a millimetre as deduced
by M. Perrin.
Fig.13
As a molecule undergoes 5 billion collisions per second and, if we
assume that this particular molecule continues progressively upwards
at the same rate, then the rate of rise would be 5 billion divided
by 20 multiplied by 1/10,000ths of a millimetre every second.
Thus 
This would mean that this molecule would, by an extremely convoluted,
‘random walk’ path, travel to the top of the cylinder in (50mm/25000mm)
= 1/500th of a second.
Let us now suppose that an intermediary sample (i.e. a
sample from somewhere between the two above extremes) of
just one percent of the nitrogen molecules that are at the plane
of intersection of the two gases achieves this modest overall velocity
upwards and let us further suppose that just one percent per second
of the nitrogen molecules achieves this feat, (This is of course
underestimating the number of molecules that are propelled in this
direction in one second by a factor of billions) it is clear that,
if kinetic theory is valid, then a mixture would result at the very
least within minutes. As it is an observed fact that a homogenous
mixture does not occur for days, this is clear, unequivocal proof
that the kinetic motion of atomic matter does not exist.
To seal the argument let us take this further, to a statistically
quite ridiculous extent in favour of kinetic theory, and
let us suppose that our one percent of the nitrogen molecules take
one hour to reach the top of the cylinder.
The number of collisions encountered by these molecules
in one hour is (5 x 109 X 3600 =) 1.8 x 1013, the distance
of 50mm is (50 x 1/10000 =) 5,000,000 times the mean free path, thus
after one hour the collisions encountered by these molecules have
resulted in 5 million effective upwards movements and 1.8 x 1013
collisions, a ratio of one upward effective movement to 3.6 million
collisions, or to put it another way 1,300,001 upwards movements
to 1,300,000 downwards movements. (E.g. they travel 900 km (900 million
mm) for an overall motion of 50mm).
Even this rate of mixing would result in a homogenous mixture
of these gases well within a day.
But such a situation could not by any means be described
as completely random, i.e. meaning ‘chaotic’ or ‘unpredictable’,
it is far, far closer to a state of order or equilibrium and would
certainly not conform to the observed chaotic Brownian motion paths
as described in Perrin’s book.
Even allowing for the incomprehensible number of collisions
between atoms and molecules in these circumstances, and
the most convoluted, multidirectional, ‘random walk’ paths taken
as a result of these collisions it is clear that, given the assumptions
of kinetic atomic theory, it is conceptually, practically and statistically
(i.e. mathematically) impossible for this not to happen within a
short period of time.
Human Respiration
In this context of diffusion of gases let us now
consider how the process of human (and other mammalian)
respiration functions in a kinetic atmosphere.
If observed phenomena are combined with kinetic theory
assumptions we can make the following statements: –
Observed Phenomena and Characteristics
1) The atmosphere is made up of 78 percent nitrogen and
21% oxygen.
2) The time between inhalation and exhalation for humans
is from one second up to four seconds. (This is dependent
on age and on the degree of physical exertion at the time.)
3) Between 25 and 30% of the oxygen content of the gases
that are inhaled, is absorbed by the lungs, and the remainder
is exhaled.
Kinetic Theory Assumptions
1) Given that 99.9% of the volume of atmospheric gas is
empty space then this means that matter, in the form of atoms or
molecules, take up 0.1% of the volume of the gas, which means that
oxygen molecules take up 0.02% of the volume of the air that we inhale.
2) The average velocities of both oxygen and nitrogen molecules
are in the region of 4-500 metres per second.
3) The molecules of oxygen and nitrogen are travelling
at these velocities and colliding with each other and with the tissue
matter (i.e. molecules) that comprise the internal surfaces of the
lungs and in doing so maintain an atmospheric level of pressure on
these surfaces.
The simple diagram below shows atmospheric kinetic gases in the close
proximity of lung tissue.
 Figure 14
On this basis the first question is that, in view of the
low volumetric concentration of oxygen molecules and the proven slow
diffusion of gases; how can the lungs absorb about 25% of the oxygen
available in the space of, in some cases, less than one second?
With the conditions as outlined above this does not seem
possible. However let us for the moment ignore the issue
of the slow diffusion of gases, and assume that somehow oxygen molecules
in sufficient quantities collide with the inner walls of the lungs
(or rather with its constituent molecules) and consider the second
question.
This is that, as the relative atomic masses of oxygen and
nitrogen molecules are very similar at about 16 and 14
respectively and their average velocities are also similar, which
means that in many instances their velocities would be identical.
Accordingly as these molecules cannot therefore be identified by
any difference in velocity; how is it possible that the lung tissue
is capable of identifying the different characteristics of these
gases in the period of the collisions they have with it, so that
the nitrogen molecules presumably rebound from the molecules of the
lung tissue while the oxygen molecules are absorbed?
Thus a perfectly elastic collision is allowed between the
molecules of the lung and the nitrogen molecules so that
they rebound (and in doing so create the observed force of atmospheric
pressure on the internal surfaces of the lungs), while the collisions
of oxygen, of a similar mass and often identical velocities, are
not elastic and these molecules are accordingly by some means absorbed.
The human body is a wonderful instrument, with the period
between sensory stimulation and physical reaction occurring
within thousandths of a second, but as to how the lung tissue is
able to differentiate between ‘kinetic’ molecules of oxygen and those
of nitrogen during the period, less than a billionth of a second,
of a kinetic molecular collision is beyond imagination.
Phase Changes from Solid to Liquid to Gas
It is acknowledged that kinetic
atomic theory cannot be quantitatively applied to liquids
and solids, (i.e. statistically as in the Maxwell Boltzmann distributions)
‘The development of a quantitative microscopic
theory for liquids similar to the kinetic theory for gases has not
been successful’10.
It is observed that the phase changes from a solid via
the liquid to the gaseous state are induced by the application
of a consistent supply of heat energy and that a considerable quantity
of heat energy is needed.
When the temperature of a solid reaches a certain level,
and while heat is still being applied continuously, no
further change either in temperature or volume occurs until a large
quantity of heat has been absorbed.
This heat energy imparted with no apparent change in property
is described as ‘latent’ heat and one reason for this description
is that there is no rational explanation for this phenomenon. The
same progression occurs in the change from liquid to gas, the difference
being that a much larger quantity of ‘latent’ heat energy
is needed to induce the change of state.
For most elements and compounds the expansion in volume
from the solid to the liquid phase is not large, typically
between 10 and 20 percent. However the expansion from the liquid
to the gas state is extraordinary by comparison and can be by a factor
of over a 1000 times the volume of the liquid.
Water is an extreme example and in the expansion to the
gaseous state (water vapour or steam) the volume increases
by a factor of nearly 1700 times that of the liquid state,
or to put this into a practical perspective one litre of liquid produces
1.7 cubic metres of gas.
This phenomenon is difficult to explain in kinetic theory
terms and accordingly any discussion or explanation of
it is generally avoided in most advanced textbooks. The following
is one commendable attempt (refer to Figure 15 below): –
“Because molecules are more strongly held in
the solid phase and in the liquid phase, heat is required to bring
about the solid-liquid phrase transition. Looking at
the heating curve (as shown below) we see that when the solid is heated,
its temperature increases gradually until point A is reached. At this
point, the solid begins to melt. During the melting period
(A-B), the first flat portion of the curve in the figure, heat is being
absorbed by the system, yet its temperature remains constant.
The heat helps the molecules to overcome the attractive forces in
the solid. Once the sample has melted completely (point B),
the heat absorbed increases the average kinetic energy of the liquid
molecules, and the liquid temperature rises (B-C). The vaporisation
process (C-D) can be explained similarly. The temperature remains constant
during the period when the increased kinetic energy is
used to overcome the cohesive forces in the liquid. When
all molecules are in the gas phase, the temperature rises again.”11
This is similar to the attempts to explain the aberrations
in gas behaviour that led to the Van der Waals Equations
of State, where the assumed neutrality of molecules was changed to
attractive and repulsive at certain molecular separations to suit
the observed results. In the above case the underlined statements
are clearly an attempt to adapt the theory to observed results by
means of further vague and unsubstantiated assumptions of fluctuating
forces of attraction and repulsion between molecules.
Kinetic theory clearly states that heat energy applied
to matter results in an increase in the average velocities
of the atoms and a resultant increase in separation, and during the
period when this latent heat energy is being applied it is observed
that there is no significant expansion or ‘increase in molecular
separation’ that is in proportion to the energy input and, one must
assume, accordingly that there is little or no increase in kinetic
velocity.
Thus the modified theory states that the atoms of both
a solid and a liquid somehow absorb an enormous amount
of heat without any increase in kinetic velocity and then
at a particular point this absorbed energy is somehow, instantaneously
converted into kinetic energy with a resultant extraordinary increase
in molecular velocity and separation.
Let us be quite clear that, according to the theory, in
the change of state from liquid to gas the molecules themselves
have not expanded, it is just the ‘empty space’ in which
they are moving that has expanded, by a factor of over
1000 times.
It is important to note that this means that it is only
the vacuum, or the void, in which they are moving that
increases by this amount, and this component of the gas can, by definition,
have no characteristic that can inhibit the expansion of the gas
as a whole.
Atmospheric Gases
As previously discussed the observed phenomenon of
very slow diffusion of two gases contradicts kinetic atomic
theory, but the other characteristic of diffusion noted, in that different
gases when introduced ultimately form an homogeneous mixture,
also causes problems for the theory.
It could be argued that the completely random kinetic motion
of the atoms of any two undisturbed gases would ultimately
result in a thorough mixture, but the ‘kinetic’ explanation for slow
diffusion would tend to contradict this and would lead to a suggestion
that the different gases could occur in different concentrations
within the mixture.
There is however one phenomenon that needs examination
in this respect and that is the mixture of nitrogen and
oxygen in atmospheric gases.
The proportions of these gases in air is consistent both
vertically, from the deepest mines to 300 kilometres altitude
from the surface of the earth, and horizontally, at sea level, in
the middle of the oceans, on the coasts, in the middle of deserts,
in the middle of cities and in the deepest rainforests.
With very slight variations these percentages are 78% and
21%, (the remaining 1% being mostly the inert gas argon)
and if we are to accept both the observed fact of the slow diffusion
of gases and the assumed kinetic atomic motion, it would be apparent
that in the places where oxygen is generated, the rainforests, there
should be a significantly greater concentration of this gas.
On the other hand, in places where this gas is consumed
in large proportions, such as in the cities, by cars and
other forms of power generated by internal and other combustion engines,
as well as, to a far lesser extent, human respiration, the concentrations
should be much less than the norm.
Also as the mass of oxygen is 12 percent greater than that
of nitrogen, it should be assumed that, oxygen atoms being
heavier than nitrogen atoms in an ‘empty space’, should tend to oxygen
existing in greater concentrations nearer the earth’s surface.
As this does not occur, there is clearly a characteristic
of atmospheric gases, and therefore of all admixtures of
gases, that is not explained by kinetic atomic theory.
Conclusion
We have seen that the ‘confirmations’ of the Maxwell-Boltzmann
distributions are questionable and that the kinetic theory
of gases has been modified and adjusted on a number of
occasions and still fails completely to describe simple basic phenomena
such as diffusion, respiration and convection, and also that it cannot
be applied to solids and liquids.
Further it has been noted that on the one hand an insignificant,
and unimportant phenomenon, i.e. Brownian motion is examined
in great detail and this analysis is accepted as demonstrating the
validity of this theory, while on the other hand a fundamentally
important force of nature, convection, which cannot be explained
by kinetic atomic energy and tends to disprove this concept, is completely
ignored.
If kinetic theory cannot in a simple and logical manner
describe the atomic interactions that lead to these natural
phenomena, then it’s explanations for other phenomena must come into
question, particularly if these are often approximate and require
complex mathematical ‘adjustments’.
The examples given of convection, respiration and diffusion
are clear, unequivocal evidence that atoms in gases are
not constantly moving at high velocities.
It now remains to have an objective look at the development
of the concept of the existence of a vacuum and the relevance
of this today in the light of current knowledge.
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