FUNDAMENTAL
ASSUMPTIONS IN THE KINETIC THEORY
The kinetic theory of gases is based upon the
following simplifying fundamental assumptions or postulates, first stated by
Clausius in 1860:
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| Clausius |
(i)
The kinetic
theory assumes that a gas consists of an exceedingly large number of minute
particles (the molecules of the atomic theory), all having the same mass and
obeying Newton’s
laws of motion.
(ii)
The molecules
are supposed to be perfectly elastic spheres or mass points. The volume
occupied by the molecules may be neglected in comparison with the volume of the
container of the gas. These molecules can experience elastic collision with one
another and with the walls of their container. (At this level there no
frictional or other non-conservative forces.)
(iii)
The molecules
are continuously moving at random with high velocities colliding with each
other and against the walls of the container. The pressure exerted by a gas is
due to the continuous bombardment of the molecules with the walls of the
container.
(iv)
Between two
successive collisions the molecules move in a straight line with uniform
velocity. This is because; they obey Newton’s
laws of motion.
(v)
The molecules of
the gas are sufficiently far apart most of the time so that they do not exert
any force of attraction or repulsion between them. Therefore, they cannot have
any potential energy (other than gravitational, which is so small that we can
neglect it), but have only kinetic energy.
(vi)
The dimension of
a molecule may be neglected in comparison with the distance traversed by it
between two successive collisions, called its free path. The perfect gas theory treats the molecules as mere mass
points.
(vii)
The time during
which a collision lasts is negligible compared with the time required to
traverse the free path.
(viii)
The distribution
of velocities among the gas molecules at equilibrium does not change with time.
The same number of molecules always has a particular velocity, although the
specific molecules having this velocity may be different at different time.
On account of the frequent
collisions between the molecules the velocities of different molecules as well
as the lengths of the path traversed by a molecule between two successive
encounters called the free path vary
considerably and so to investigate the physical properties of a gas in terms of
the motions of the molecules, we are to consider ‘mean velocity’ and ‘mean free
path’ of all the molecules under the same conditions of temperature and
pressure.
Note:
Gravitational attraction always acts between the molecules. But the force is
exceedingly small and is generally neglected.
THE MEAN FREE PATH OF GAS MOLECULES
 |
| FREE PATH OF GAS MOLECULES |
In deriving the expression
for the pressure exerted by a gas, the molecules were treated as geometrical
points which could fly freely from one wall of a container to another without
colliding with other molecules. One of the objections raised in the early days
of the development of the theory was that if molecules acted in this way a
small amount of gas, say ammonia, released in a large room would spread
throughout the room practically instantaneously. But we know that if the
stopper is removed from a bottle of perfume a considerable time elapses before
the odor can be detected even at a point only a few away. It was soon realized
that this relatively slow diffusion of one gas in another resulted from
molecular collisions, which cause a molecule to move in an irregular zigzag
path.
Really speaking the
molecules are of finite size and because of these finite sizes they constantly
collide with each other in course of motion. These collisions alter both the
magnitudes and the directions of their velocities. A collision between two
molecules is considered to take place whenever one molecule makes contact with
another. The length of the (approximately straight) segment of the path of a
molecule traversed between two successive collisions is called the free path.
But when a molecule undergoes a number of collisions, this path will be
different in length and direction between successive collisions.
Distinction
between a gas and a vapor
 |
| vapor |
We are now in a position to understand the scientific
difference between a gas and a vapor. When a substance is below its critical
temperature, we refer to the substance as ‘vapor’, thereby implying that the
liquid from is easily obtainable. When the substance is above its critical
temperature, however, we refer it to a ‘gas’ since it can not be liquefied. The
critical temperatures of hydrogen and nitrogen are -241°C and -147°C and hence
these substances are normally well above their critical temperatures. Hydrogen
and nitrogen are consequently known as permanent
gases. It can now be seen that the terms ‘vapor’ and ‘gas’ are artificial
distinctions; above the critical temperature the substance is termed a ‘gas’,
but below the critical temperature it is termed a ‘vapor’.
State of
matter near the critical point
 |
| critical point |
The most important properties of a substance which
are actually observed near its critical point are the following:
(a)
The surface of
demarcation between the liquid and its vapor vanishes at the critical
temperature. This indicates a fall of surface tension. Rapid inter-diffusion of
molecules between the liquid and the gaseous mass takes place and at the
critical temperature the process becomes complete and so the surface just
disappears.
(b)
Vapor at the
critical point attains a very high compressibility.
(c)
The whole mass
presents a very flickering appearance which suggests a fluctuation of density
inside the mass.
(d)
The densities of
the liquid and the vapor gradually approach each other till they become equal
at the critical point.
But the experiments of
Callendar appear to throw fresh light on the state of matter near the critical
point. Taking very pure water freed from all traces of dissolved air, Callendar
found that the densities of liquid and vapor did not become equal at 374°C, the
critical temperature at which the meniscus disappeared, but that a difference
of density was perceptible even beyond the critical point which under favorable
conditions could be traced upto 380°C. This suggests the existence of a
critical region rather than a critical point. More research is needed to arrive
at a final decision in this matter.
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