Gravity Chapter
4: On the Kinetic Motion of Atoms
Brownian motion
In a 1905 paper on Brownian motion Einstein asserted
‘that Brownian motion, although random obeys a
definite statistical law and is in accordance with statistics used
by Boltzmann and Maxwell to describe the kinetic motion of molecules’.
In 1908 Jean Perrin, who ‘was committed to the
usefulness and the truth of molecular kinetic theory’, subjected Brownian
motion to detailed microscopic analysis over a period of
five years. The results of which work were generally accepted as
confirming firstly the existence of atoms and molecules and secondly
the random kinetic motion of molecules.
In his book ‘Les Atomes’, an English translation of which
(‘Atoms’) was published in 1916, with respect to kinetic
theory he states, that ‘each molecule of the air
we breathe is moving with the velocity of a rifle bullet: travels
in a straight line between two impacts for a distance
of nearly one ten thousandth of a millimetre: is deflected from its
course 5000 million times per second –. There are 30 milliard milliard
(billion billion) molecules in a cubic centimetre of air, under normal
conditions. 3000 million of them placed side-by-side in a straight
line would be required to make up 1 millimetre. 20,000 million must
be gathered together to make up 1000 millionth of a milligram’.
M. Perrin carried out his Brownian motion experiments with
microscopic particles of gamboge that were 0.2 microns
(0.0002mm) in diameter and by his own calculations these
particles would therefore be 600,000 times the diameter
of a molecule.
He also states that, ‘if our theory is correct,
the weight of an air molecule should therefore be one 10,000 millionth
of the weight-of one of the grains.’
Or to put it the other way the mass of one of the microscopic
grains of gamboge would be ten billion times the mass of
an air molecule.
To try to put these incomprehensible numbers into a human
perspective - if we imagine an atom to be 1 millimetre
in diameter, then a grain of gamboge of 0.2 microns would
be in proportion (600,000 x 1mm =) 600 metres in diameter
and which (if we assume this to have the equivalent density
of water) would weigh 750,000 tonnes. 7
To put this in a visual perspective, the arc of a circle
of one tenth of this, i.e. 60 metres in diameter, if drawn
across this page, would appear to the human eye as a perfectly
straight line.
Accordingly the horizontal line in the diagram below represents
such an arc. The small circles represent air molecules
at their relative size (1mm) and distribution at Standard
Temperature and Pressure according to Kinetic Theory and
the smoke particle depicted is 600 metres in diameter.
Figure 9
With respect to kinetic atomic theory Perrin states ‘if
we consider a large number of molecules, taken at random at a given
moment, then the projection of all the molecules speeds on to any
arbitrary axis (in other words, the resultant along that axis) will
have a mean value of zero; no particular direction will be privileged.’
Here he is repeating the basic assumption of the kinetic
atomic theory of gases in that the average velocity of
the atoms or molecules of any volume of a kinetic gas, such as in
any container, is zero, or in other words that, as is observed, the
pressure within a gas and on the internal walls of any container
is consistent. Of course if we reverse this to consider the pressure
of a gas on the exterior of any object the same conditions must apply.
He also subsequently states with respect to Brownian motion
that ‘every granule suspended in a fluid (i.e.
gas or liquid) is being struck continually by the molecules in its
neighbourhood and receives impulses from them that do not in general
exactly counterbalance each other; consequently it is tossed hither
and thither in an irregular fashion.’
This second statement seems to contradict the first by
saying that any object surrounded by gas or liquid is subjected
to impulses from molecules that do not have a mean value
of zero (M.Perrin even suggests that a brick weighing 1
kilo could be affected).
Further M.Perrin says that ‘each molecule would
be able, if stopped, to raise a particle of dust just visible under
the microscope by its own height’ and ‘the
work developed by the stoppage of a molecule would be sufficient to
raise a spherical drop of water 1 micron in diameter to a height
of nearly 1 micron’.
Here he is suggesting that the ‘kinetic’ energy of motion
of a molecule in colliding with a particle 1 micron in
diameter is sufficient to move or raise the particle by
its own height against the force of gravity.
Let us be quite clear that this is suggesting that a molecule
of air has sufficient energy of motion (kinetic energy)
to overcome the inertial mass of a particle over ten billion
times its mass and move it a distance equal to the particle’s
own diameter.
This is tantamount to saying that a rifle bullet fired
into the stern of a battleship will apply sufficient force
to move the battleship its own length.
The suggestion that a molecule can have this effect defies
common sense and is clearly completely unsupportable by
any laws of mechanics and Newton’s second law of motion
of course will apply in these circumstances.
We are considering the motion of Brownian particles suspended
in a ‘kinetic’ gas or liquid and these particles are at
any instant, by definition, being subjected to many thousands
of billions of collisions by the molecules of the gas or
the liquid from every direction and over its entire surface.
In these circumstances it is extremely difficult to imagine
that one infinitesimally irregular or unbalanced collision
on one side, will not almost immediately be counterbalanced
by another on the opposite side of the particle.
It is one thing to say that the assumed random kinetic
motion of atoms and molecules in a gas is similar to that
of the observed Brownian motion, it is quite another thing
however to suggest that the latter is a direct result of
the former.
Kinetic Velocities - Molecular Beam Experiments
After Clerk Maxwell
published his statistical analysis of the velocity distribution
function of an ideal kinetic gas, which enabled the calculation of
the variable properties of a gas, i.e. pressure, temperature and volume,
under certain conditions, a number of experiments have been carried
out in attempts to demonstrate molecular kinetic motion and the assumed
velocities. These experiments can be described as ‘Molecular Beam’
experiments.
An example of the first experiments is where a quantity
of gas was heated to a temperature of 800°C in an oven
that was provided with a tiny aperture. The oven was placed
in a larger container that was evacuated to a very low pressure,
or partial vacuum.
The first experiments, set up on the basis of these assumptions
and carried out to prove the Maxwell-Boltzmann distribution
of velocities, did not do so. A textbook states that the
results were ‘not the Maxwell distribution of
speeds, but a distribution tilted towards larger values of speeds’.
This required an explanation, and the explanation of course
required new assumptions as to the characteristics of kinetic
molecules and atoms.
However it was still suggested that is this experiment
“confirmed” the Maxwell distribution.
Further experiments were carried out in the 1900s, notably
by Stern, using more sophisticated techniques, some of
which did not achieve a satisfactory results and were thus
not published, others however by Stern in 1920, and Stern
with others in 1947 produced results that again were said
to confirm the Maxwell distribution.
The point must be made here however that whatever the atomic
characteristics of a gas are, it is a simple observed phenomenon
that opening the aperture in these circumstances (of a
very high pressure gas into a very low pressure gas) would
produce a high velocity stream of gas.
However, it must be emphasised, that these experiments
do not and cannot measure the actual velocities of atoms,
collectively or individually, additionally these experiments
were all set up based on the assumptions of kinetic atomic
theory, and the results were also analysed based on these
assumptions. Of course the purpose of those carrying out
these experiments was not to disprove the theory, but to
prove the theory. Even so the results of these experiments
did not conform to the predicted values and then an explanation
had to be devised to explain why this was so.
Also the question has to be asked that if prior experiments
confirmed the theory why were subsequent, expensive and
technically difficult experiments necessary?
The point is that, unlike the clear and unequivocal experimental
evidence that led to Dalton’s Laws of Definite Proportions
that matter is ultimately finite or ‘atomic’ there is no
satisfactory experimental proof or confirmation of the
kinetic motion of atoms or molecules.
On the other hand there are a number of instances of natural
phenomena where the assumed characteristics of a kinetic
gas simply cannot provide an explanation for observed reactions.
Convection
This force is of fundamental and critical importance
to life on earth and to our understanding of the movement
of atmospheric gases and the climate of earth, however
there is a notable lack of discussion of the ultimate cause
of this essential thermodynamic force in any textbook or
other publication concerned with the physical sciences,
whether general or statistical, the following brief comments
are two rare examples: -
‘In free convection the heating process produces
a temperature and density gradient in the fluid and fluid motion is
induced by the action of gravity’
‘Temperature gradients induce convection in fluids,
a phenomena that involves the movement of gases or liquids’.
Which is of course simply stating the obvious, but there
is no explanation given of how the actions and interactions
of kinetic atoms produce or induce convective currents.
Even in specialist publications, such as those concerned
with relevant disciplines of fluid dynamics or thermodynamics,
which set out the mathematical means or the formulae by
which the practical effects of convective motion in fluids
and gases in various circumstances can be calculated and
predicted, the atomic origins of convection are not discussed.
Gravity is, as we have discussed, the force that is the
direct or indirect cause of all other forces and is the
fundamental force that affects all matter in the universe,
accordingly it affects each and every atom of all matter
in any state.
Kinetic theory assumes however that atoms in a gas ‘between
collisions are free of forces and move with constant speed’
and ‘any change in velocity arising from gravity is small
compared with the molecular velocity and can be ignored’
(My emphasis)
Convection is a very simple and basic force and is the
transport upward and downward of gases and liquids relative
to the surface of the earth. Simply speaking, hotter fluids
(having a greater energy content) rise away from the surface
in the vicinity of cooler fluids, which (having a lower
energy content) in turn replace these by descending towards
the surface.
In the case of the gases that comprise the atmosphere,
the radiated energy from the sun warms the earth continually
and this heat energy is absorbed by the surface of the
earth both liquid and solid (i.e. by the water of the oceans
and lakes and by the solid landmasses). Part of this heat
energy is subsequently transferred to the air that is in
contact with these surfaces.
This process of absorption of heat energy from the solid
and the liquid matter at the surface of the earth results
in the air involved expanding and thus reducing in density
relative to surrounding air masses and, as a result, rising
away from the surface and then being replaced by the denser,
cooler gases from adjacent areas.
This process is the basis of the cycle of weather patterns
that we experience at the surface of the earth.
Understanding how this natural force works at atomic level
is therefore of fundamental importance to our understanding
of the forces of nature in general.
These questions are not merely of academic interest, as
for example, misconceptions as to the true nature of the
interaction of the earth and its atmosphere with that of
the solar system, when combined with ignorance of the effects
of man’s interference with this structure, could have catastrophic
consequences for the future of life on earth and for the
human species.
Kinetic atomic theory states that: – molecules
that move more rapidly because they are in a region of higher temperature
collide with molecules and a neighbouring region, giving
the adjacent molecules more kinetic energy and consequently
more thermal energy.
In other words molecules of a gas absorb heat energy and
this energy is by some (unexplained) process converted
into an increase in velocity (kinetic energy) relative
to surrounding molecules and by the process of further
collision with other outlying molecules distribute this
kinetic/thermal energy in all directions.
Kinetic theory also states that heat applied to a gas results
in an increase in the velocity of molecules and a corresponding
increase in collisions and a greater average molecular
separation. In other words this means that the volume of
empty space between molecules increases when heat is applied
to a gas.
Clearly this would mean that where this occurs there would
be fewer molecules per unit volume and the total mass and
therefore the density of this would be reduced by comparison
with adjacent cooler unit volumes of the gas, as shown
in the diagram below.
Fig. 10
However if a gas consists of molecules moving independently
of each other in space and the mass of these molecules remains the
same and further, as the theory states, there is no attraction between
molecules, then gravity can only act on individual molecules and
not on the gas as a whole, because if the gas as a whole is 99.9%
empty space, this proportion of a gas has no mass and accordingly
cannot be influenced by gravity.
The diagram above shows this situation graphically, the
hot gas molecules having greater kinetic energy and thus
more surrounding space than the cool gas molecules and it follows
that individual molecules in a larger volume of space have precisely
the same gravitational attraction to earth as another molecule of
the same mass in a smaller volume of space.
Kinetic atomic theory therefore cannot describe how molecules
having a greater average molecular separation rise against
the force of gravity, or in other words how these molecules
acquire a lesser gravitational attraction to the earth than do slower
molecules having a lesser separation.
On the one hand ‘gravity can be ignored’ however in this
case gravitational forces are clearly influencing the gas
as a whole, and ultimately these forces can only be affecting
the individual atoms that make up the gas.
So on the one hand a series of contrived, or artificial
experiments are set up and carried out on the basis of
the assumptions of two hypotheses, the atomic and the kinetic
atomic theories, in order to prove the validity of the
latter in particular, the results of which were analysed
on the same basis, and while none these results conformed to the
Maxwell-Boltzmann distribution expectations they were nonetheless
said to ‘confirm’ kinetic theory.
On the other hand where an easily observed, natural phenomenon
is analysed, again on the basis of the assumptions of these
theories, and the application not only completely fails
but in fact contradicts the theory, this clear evidence
is conveniently ignored while the inconclusive and contrived
experiments are generally accepted as ‘proof’.
This is clearly the reason why no clear explanation of
this force or phenomenon is attempted in textbooks.
Continued >
Back to Gravity Contents >
|
