PHYSICS INVESTIGATORY PROJECT

PHYSICS INVESTIGATORY PROJECT
KINETIC THEORY OF GASES

Kinetic Theory of Gases is a theoretical model which helps us understand
the behavior of gases and their constituent particles. This theory suggests
that gas is made up of a larger number of tiny particles which collide with
each other and their surroundings and exchange kinetic energy between
them. The kinetic theory of gases has various applications throughout
physics, chemistry, and engineering and it is essential to understand
many phenomena like diffusion, effusion, and Brownian motion.
What is Kinetic Theory of Gases?

The kinetic theory of gases was introduced to explain the structure and
composition of molecules with respect to submicroscopic particles which
make up the gaseous matter around us. This theory talks about the
increase in pressure due to the constant movement and collision of the
submicroscopic particles. It also discusses other properties of a gas such
as temperature, pressure, volume, viscosity, diffusion, thermal
conductivity, etc. The theory develops a relationship between the
microscopic particles and the macroscopic properties. The molecule of
gas is always in constant motion and keeps colliding with each other and
the walls of the container, in such a case, it is difficult as well important to
learn the dynamics of the gases.
Kinetic Theory of Gases Assumptions

There are several assumptions that were taken into account in order to
develop the kinetic theory of gas which are stated as follows:
 Every gas consists of molecules that are microscopic particles.
 There are uncountably large numbers of particles making up any Gas.
 The size of the molecule also known as the molecular size is negligible
as compared to the molecular distance between two molecules (which
is approximately 10-9 m).
 The speed of the molecules of a gas is very high generally and it can
lie anywhere between 0 and infinity.
 The molecule shape of gas is spherical, rigid, and elastic masses.
 The mean free path is known as the mean of all free paths. The free
path is defined as the distance covered by the molecules between their
two successive collisions.
 The number of collisions per unit volume always remains the same in
gas and is a constant.
 There is no force of attraction or repulsion acting between the gas
molecules.
 The force of gravitation is also negligible due to the fact that the
molecules have a very very small mass and they travel at a very high
speed.
Postulates of Kinetic Theory of Gases

Based on the assumptions, the following Postulates of the Kinetic Theory
of Gases are given:
 All the molecules of a single gas are the same and identical but are
different from the other gas molecules which have different properties
as well.
 Every gas consists of molecules that are microscopic particles such
that the volume of all the molecules combined is negligible when
compared with the total volume of the container i.e., in other words, the
size of the molecule is negligible as compared to the molecular
distance between two molecules (which is approximately 10 -9 m).
 The time in which particles collide with the container’s wall is negligible
compared to the time taken by molecules in two successive collisions.
 The number of particles in the system is a very large number, so we
can use statistics instead of considering individual particles. This
assumption is known as the Thermodynamic limit.
 The collision between two particles of gases is perfectly elastic i.e.,
molecules of a gas are hard round spheres.
 There is no exchange of energy between gas particles except the
collision.
Kinetic Theory and Gas Pressure

The continuous bombardment of the gas molecules against the walls of
the container results in an increase in gas pressure. According to the
Kinetic theory of gases, the pressure at that point exerted by a gas
molecule can be represented as,
P = 1/3ρ×c-2
where
 c is Mean Square Speed of a Gas Molecules
 ρ is Density of Gas
Suppose the container has n number of molecules of gas, with each of
mass m, then the pressure can be represented as,
P = 1/3(nm/v)×c-2
where,
 V is Volume of Gas
Gas Laws for Ideal Gas
If the gases are assumed to be ideal in nature, the following gas laws are
applicable to them. The laws are defined to understand the ideal gases
and their parameters like volume, pressure, etc. Let’s take a look at the
laws,
Boyle’s Law
According to Boyle’s law, the volume of a given gas is inversely
proportional to its pressure at a constant temperature. As this law is given
V ∝ 1/P
by Robert A. Boyle in 1662, hence the name Boyle’s Law.
PV = Constant
For a given ideal gas,
P1V1 = P 2V2
Charles’s Law
Charles’s law (named after Jacques Charles) states that at constant
pressure, the volume of a gas is directly proportional to the absolute
V∝T
temperature of the gas.
V/T = Constant
Thus, for any given ideal gas,
V1T2 = V 2T1
Pressure Law (Gay-Lussac’s Law)
Pressure Law or Gay-Lussac’s laws state that at constant volume, the
pressure of a given gas is directly proportional to its absolute temperature.
This law is named after Joseph-Louis Gay-Lussac who published this law
P∝T
in 1809.
P/T = Constant
For any ideal gas,
P1T2 = P 2T1
Avogadro’s Law
Avogadro’s Law or Avogadro-Ampere’s hypothesis states that an equal
amount of volume of all gases under S.T.P. (Standard temperature and
pressure) contain the same number of molecules i.e., one mole of any
V∝ n
ideal gas at STP always has a volume of 22.4 liters.
V/n = Constant
For any ideal gas,
V1n2 = V 2n1
Graham’s Law of Diffusion of Gases

According to Graham’s law of diffusion of gases , the rate of diffusion of a
gas is inversely proportional to the square root of the density of the gas.
Therefore, the more the density of the gases slower will be its rate of
r ∝ √(1/p)
diffusion.
Dalton’s Law of Partial Gases

According to this law, the net pressure applied by a mix of non-interacting
gas is equivalent to the sum of the individual pressures.
P = P1 + P2 + P3 +… Pn
The arithmetic mean of the speed of gas molecules is known as the
average speed of molecules or the mean speed of the gas molecules. If
there are and are given by
Mean speed = vmean = (v1 + v2 + v3 +… vn)/n
Formula for mean speed, vmean =

Similarly, there is another term known as the root mean square speed of
gas molecules, it is defined as the root mean of the squares of speeds of
gas molecules. The formula for the root mean speed is given as follows:
vrms = √(3RT/M)
Similarly, there is a term known as the most probable speed of a gas
molecule, which is defined as the speed obtained by the maximum
number of gas molecules, and formula for the most probable speed is
given as follows:
vmp = √(2RT/M)
Kinetic Interpretation of Temperature

The overall average energy present in the molecules is directly
proportional to the temperature. Therefore, average kinetic energy is
formed by the measure of the average temperature of the gas. According
to this, the average energy of the molecules is 0 when the temperature is
0. Therefore, the motion of the molecules stops at absolute 0. The formula
for the average energy of the molecules is given as,
U = 3/2 RT
Non-Ideal Gas Behavior

Under low pressure and high temperature, it is presumed that all gases
obey the ideal gas behavior and hence the gas laws. For the real gases,
or during the study of real gases, the deviation from the ideal gas behavior
is mostly pointed out. It involves talking about the wrong postulates
defined for ideal gases that do not follow up in real gas behavior. Let’s
take a look at them,
 Gas particles are point charges and have no volume. In such a case, it
was possible for the particles to get compressed to 0 volume, but is it
true? No. Gases cannot be compressed to 0 volume, not practically,
hence, they do have volume and that cannot be neglected.
 Particles do not interact with each other and are independent. This
postulate is false as the particles do interact with each other depending
upon nature. It also affects some of the terms like the pressure of gas
molecules.
 The collision of the particles is not elastic in nature. Again, the
statement is false. The collision of the particles is indeed elastic in
nature and they do exchange energy upon colliding. Hence, the
distribution of energy is defined.

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PHYSICS INVESTIGATORY PROJECT

KINETIC THEORY OF GASES

What is Kinetic Theory of Gases?

Kinetic Theory of Gases Assumptions

Postulates of Kinetic Theory of Gases

Kinetic Theory and Gas Pressure

Graham’s Law of Diffusion of Gases

Dalton’s Law of Partial Gases

Formula for mean speed, vmean =

Kinetic Interpretation of Temperature

Non-Ideal Gas Behavior

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