INVESTIGATORY PROJECT ON UNIFORM CIRCULAR MOTION

This investigatory project is for class 11 of cbse board

1. DAV PUBLIC SCHOOL
INVESTIGATORY PROJECT
UNIFORM CIRCULAR MOTION
Submitted in partial fulfillment of the requirements for the AISSCE CBSE Board
examination
IN
PHYSICS
For the Academic year
2023-24
To be carried out by
NAME: Amrit Mohanty
REG NO.:
Under the guidance of
Mr.Ashutosh Lenka
Vice Head
Department of Physics
MCL JA DERA

2. Certified that the project work entitled Kinetic Theory of GasesCertified that the project work entitled Kinetic Theory of Gases carried out by Kumarcarried out by Kumar
Harekrishna Das, Roll No: 41 , ofHarekrishna Das, Roll No: 41 , of
class XI ‘B’ is a bonafide work in partial fulfilment of AISSCE in theclass XI ‘B’ is a bonafide work in partial fulfilment of AISSCE in the
subject Physics prescribed by the Central Board ofsubject Physics prescribed by the Central Board of
Secondary Education, during the year 2023-2024. It is certified that allSecondary Education, during the year 2023-2024. It is certified that all
corrections/suggestions indicated for Internal Assessment have beencorrections/suggestions indicated for Internal Assessment have been
incorporated in the Report deposited in the departmental library. Theincorporated in the Report deposited in the departmental library. The
project report has been approved as it satisfies the academicproject report has been approved as it satisfies the academic
requirements in respect of the Project work prescribed for the saidrequirements in respect of the Project work prescribed for the said
examination.examination.
DAV PUBLIC SCHOOLDAV PUBLIC SCHOOL
MCL, JA, DERA.MCL, JA, DERA.
Department of PhysicsDepartment of Physics
CERTIFICATECERTIFICATE
Name and Signature of the StudentName and Signature of the Student
Name and Signature of the GuideName and Signature of the Guide
Signature of the PrincipalSignature of the Principal

3. ACKNOWLEDGEMENT
We would also like to express our thanks to Mr. AshutoshWe would also like to express our thanks to Mr. Ashutosh
LenkaLenka, the vice head of physics department of DAVPS JA,DERA who, the vice head of physics department of DAVPS JA,DERA who
gave us this opportunity to learn the subject with a practicalgave us this opportunity to learn the subject with a practical
approach, guided us and gave us valuable suggestions regardingapproach, guided us and gave us valuable suggestions regarding
the project.the project.

4. Sl.no.
1
2
3
4
5
introduction
theory
photos
Graph charts
Precautions
1
2 to 7
8 to 13
14
15
content Page no.
INDEX
6 bibilography 15

5. INTRODUCTION
KINETIC THEORY OF GASES
The kinetic theory of gases describes a gas as a
group of large number of small sub microscopic
particles (atoms or molecules), all of which are in
constant, rapid, random motion. The randomness
arises from the particles' many collisions with each
other and with the walls of the container
The kinetic theory was developed in the nineteenth
century by Maxwell, Boltzmann and others. It
explains the behaviour of gases based on the idea
that the gas consists of rapidly moving atoms or
molecules.
This theory of gases explains various types of
macroscopic properties of gases, such as pressure,
temperature, viscosity, thermal conductivity, and
volume, by considering their molecular composition
and motion. The theory posits that gas pressure
results from particles' collisions with the walls of a
container at different velocities.

6. The theory for ideal gases makes the following
assumptions:
 The gas consists of very small particles known as
molecules. This smallness of their size is such that the
total volume of the individual gas molecules added up
is negligible compared to the volume of the smallest
open ball containing all the molecules. This is
equivalent to stating that the average distance
separating the gas particles is large compared to
their size.
 These particles have the same mass.
The number of molecules is so large that statistical
treatment can be applied.
There are negligible gravitational force on molecules.
The rapidly moving particles constantly collide among
themselves and with the walls of the container. All
these collisions are perfectly elastic. This means the
molecules are considered to be perfectly spherical in
shape and elastic in nature.
Except during collisions, the interactions among
molecules are negligible.

7. IDEAL GAS :
An ideal gas or a perfect gas is that gas
which strictly obeys gas
laws such as Boyle’s law, Charle’s law,
Gay Lussac’s law etc.
An ideal gas has following characteristics-
(I) Molecule of an ideal gas is a point mass
with no geometrical
dimensions.
(II) There is no force of attraction or
repulsion amongst the
molecules of the gas.
Kinetic Theory and Gas Pressure
The pressure of a gas is the result of continuous bombardment
of the gas molecules against the walls of the container.
According to the kinetic theory, the pressure P exerted by an
ideal gas is given by,
According to this law, the volume (V) of a fixed mass of a gas is
inversely proportional to the pressure (P) of the gas, provided
temperature of the gas is kept constant.
Boyle's law
P=
where P is the pressure of the molecules on the container, V is
the volume of the container, and k is a constant.
The value of k always stays the same so that P and V vary
appropriately. For example, if pressure increases, k must remain
constant and thus volume will decrease. This is consistent with
the predictions of Boyle's law.

8. CHARLE'S LAW
According to this law, the volume
(V) of a given mass of a gas is
directly proportional to the
temperature of the gas, provided
pressure of the gas remains
constant.
where V is the volume of the container, T is the temperature of
the system in Kelvin, and k is the constant.
According to Charles' law, gases will expand when heated. The
temperature of a gas is really a measure of the average kinetic
energy of the particles. As the kinetic energy increases, the
particles will move faster and want to make more collisions
with the container. However, remember that in order for the
law to apply, the pressure must remain constant. The only way
to do this is by increasing the volume.
GAY LUSSAC'S LAW
According to this law, the pressure (P) of a given mass of a gas
is directly proportional to its absolute temperature (T),
provided the volume (V) of the gas remains constant.
where P is the pressure of the particles on the container, T is the
temperature in Kelvin, and k is a constant. At constant volume,
this results in more collisions and thereby greater pressure the
container. Because the value of k is the same for differing values
of pressure and temperature, the pressure law can be written as

9. Avogadro's law
Avogadro’s law states that the volume of a gas is directly
related to the number of moles of atoms contained in the gas.
The equation for Avogadro's law is
where V is the volume of the container, n is the amount of gas
as measured by the moles of atoms, and k is a constant. Say you
have a given amount of particles in a box. If you want to add
more particles, but you do not want to increase the pressure,
you must make the container larger.
Graham's law of diffusion of gases
It states that rate of diffusion of a gas is inversely proportional
to the square root of the density of the gas.
Dalton's law of partial pressure
In gaseous mixture, each component in the gas phase can be
treated separately. Each component of the mixture shares the
same temperature and volume. (Remember that gases expand to fill the volume of their container; gases in a mixture
continue to
do that as well.) However, each gas has its own pressure.
The partial pressure of a gas, Pi, is the pressure that an
individual gas in a mixture has.
According to this law, the resultant pressure exerted by a
mixture of non-interacting gases is equal to the sum of their
individual pressures
Your paragraph text

10. Equation of state of ideal gas
Consider a further extension of the combined gas law to include n. By analogy to Avogadro’s law, n is positioned in the
PV/nT= constantt
Because pressure, volume,
temperature, and amount are the
only four independent physical
properties of a gas, the constant
in the above equation is truly a
constant; indeed, because we do
not need to specify the identity of
a gas to apply the gas laws,
this constant is the same for all
gases. We define this constant
with the symbol R, so the
previous equation is written as
PV/nT= R
PV = nRT
This equation is
called the ideal
gas law. It relates
the four
independent
properties of a
gas at any time.
The constant R is
called the ideal
gas law constant.
Its value depends
on the units
used to express
pressure and
volume.
The ideal gas law relates the four independent physical
properties of a gas at any time.
The ideal gas law can be used in stoichiometry problems
whose chemical reactions involve gases.
Standard temperature and pressure (STP) are a useful set
of benchmark conditions to compare other properties of
gases.
At STP, gases have a volume of 22.4 L per mole.
The ideal gas law can be used to determine densities of
gases
Your paragraph text

11. Degrees of Freedom
The total number of independent
co-ordinates required to
specify the position of a molecule
or the number of independent
modes of motion possible with
any molecule is called degree of
freedom
Mono-, di-, and polyatomic (N)
molecules have 3, 5 or (3 N-K)
number of degrees of freedom
where K is the number of
constraints [restrictions
associated with the structure].

12. Law of eqipartition of energy
For a dynamic system in thermal equilibrium, the energy of the
system is equally distributed amongst the various degrees of
freedom and the energy associated with each degree of freedom
per molecule given by
Kinetic Energy of a single molecule: KE = 1/2 mv²
. A gas in
thermal equilibrium at temperature T, the average Energy is
where K = Boltzmann’s constant. In case of a monoatomic
molecule, since there is only translational motion, the
energy
allotted to each motion is 1/2KT. This is calculated by
dividing
total energy by the degrees of freedom:
3/2 KT ÷ 3 = 1/2 KT
According to the Law of Equipartition of Energy, in thermal
equilibrium, the total energy is distributed equally among all
energy modes. While the translational and rotational motion
contributes ½ KT to the total energy, vibrational motion
contributes 2 x 1/2KT = KT since it has both kinetic and potential
energy modes.

13. Boyle's
law

14. Gay LUSSAC'S LAW

15. Charle's law

16. – @reallygreatsite
Avogadro's
law

17. Graham's law
of diffusion

18. Dalton's law of
partial pressure

19. Precautions
1. All instruments must work properly without any leal
2. We must wear gloves and mask before dealing
with hot gaseous substance.
3. Experiments should be conducted under teacher's guidance
4. Handle equipment and materials with care to prevent damage and ensure the
accuracy of the experimental setup.
Bibliography
1.Guidance from Teacher
2. NCERT Class 12 Physics Book
3. Comprehensive Physics Practical Book
4. www.cooljunk.in/physics-project-kit
5. www.google.com