The document discusses key concepts from kinetic theory of gases and thermodynamics. It defines kinetic theory of gases as describing gas as particles in random motion that collide with each other and container walls. This explains macroscopic gas properties like pressure. It then outlines Maxwell-Boltzmann distribution and related equations that describe the distribution of molecular speeds at a given temperature. The document also summarizes the four laws of thermodynamics, including definitions of entropy, Carnot cycle efficiency, and applications of thermodynamic concepts.

1. THERMODYNAMICS AND KINETIC
THEORY OF GASES
MADE BY:-
Naman Jain
Roll No- A-36

2. KINETIC THEORY OF GASES
The kinetic theory of gases describes a gas as a large number of small
particles (atoms or molecules), all of which are in constant, random
motion. The rapidly moving particles constantly collide with each other
and with the walls of the container. Kinetic theory explains 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 is due to the impacts, on
the walls of a container, of molecules or atoms moving at different
velocities.

3. ASSUMPTIONS OF KINETIC THEORY OF
GASES
• Molecules are moving randomely in all directions.
• Molecules exert no appreciable force on one another or on the walls
of the container expect during collision.
• All collisions between the molecules or with walls of the container are
perfectly elastic.
• The duration of a collision is negligible in comparison to the time
spent between collision.
• The average kinetic energy of the gas particles depends only on the
absolute temperature of the system. The kinetic theory has its own
definition of temperature, not identical with the thermodynamic
definition.
• The volume occupied by the gas molecules is negligible as
compared to the total volume of a gas.

4. MAXWELL BOLTZMANN DISTRIBUTION
• Maxwell Boltzmann showed that as a result of collision, some
molecules are speeded up and some others are slowed down and
hence the fraction of molecules possessing a particular speed
remains constant . Therefore, the Maxwell-Boltzmann distribution is
used to determine how many molecules are moving between
velocities v and v + dv. Assuming that the one-dimensional
distributions are independent of one another, that the velocity in the
y and z directions does not affect the x velocity, for example, the
Maxwell-Boltzmann distribution is given by-
𝑑𝑁
𝑁
= (𝑚/2Π𝑘𝑇)1/2
𝑒−𝑚𝑣2/2𝐾𝑇
dV. Where-
• dN/N is the fraction of molecules moving at velocity v to v + dv,
• m is the mass of the molecule,
• kb is the Boltzmann constant, and
• T is the absolute temperature.

5. MAXWELL BOLTZMANN DISTRIBUTION GRAPH

6. RELATED SPEED EXPRESSIONS.
• From the Maxwell-Boltzmann distribution, three speed expressions can be
derived: the most probable speed, the average speed, and the root-
mean-square speed. The most probable speed is the maximum value on
the distribution plot. The average speed is the sum of the speeds of all the
molecules divided by the number of molecules. The root-mean-square
speed is square root of the average speed-squared.
• V(mp)= 2𝑅𝑇/√𝑀
• V(avg)= 8𝑅𝑇/√𝜋𝑀
• V(rms)= 3𝑅𝑇/√𝑀
Where-
• R is the gas constant,
• T is the absolute temperature and
• M is the molar mass of the gas.
• It always follows that for gases that follow the Maxwell-Boltzmann
distribution
Vmp<Vavg<Vrms

7. EQUIPARTITION THEORAM
• The name "equipartition" means "equal division," as derived
from the Latin equi from the antecedent, æquus ("equal or
even"), and partition from the antecedent, partitionem
("division, portion"). The original concept of equipartition was
that the total kinetic energy of a system is shared equally
among all of its independent parts, on the average, once the
system has reached thermal equilibrium. Equipartition also
makes quantitative predictions for these energies. For
example, it predicts that every atom of a noble gas, in thermal
equilibrium at temperature T, has an average translational
kinetic energy of (3/2)kBT, where kB is the Boltzmann constant.
As a consequence, since kinetic energy is equal to
1/2(mass)(velocity)2, the heavier atoms of xenon have a lower
average speed than do the lighter atoms of helium at the
same temperature.
U=I/2kT ( Where K is the Boltzmann constant).

8. THERMODYNAMICS
• Thermodynamics is a branch of physics concerned with heat and
temperature and their relation to energy and work. It defines macroscopic
variables, such as internal energy, entropy, and pressure, that partly
describe a body of matter or radiation. It states that the behaviour of those
variables is subject to general constraints, that are common to all materials,
not the peculiar properties of particular materials. These general constraints
are expressed in the four laws of thermodynamics. Thermodynamics
describes the bulk behaviour of the body, not the microscopic behaviours of
the very large numbers of its microscopic constituents, such as molecules.
Its laws are explained by statistical mechanics, in terms of the microscopic
constituents.

9. ZEROTH LAW
• If two thermodynamic systems are each in thermal equilibrium with a
third, then they are in thermal equilibrium with each other.
• When two systems are put in contact with each other, there will
be a net exchange of energy between them unless or until they
are in thermal equilibrium. That is the state of having equal
temperature. Although this concept of thermodynamics is
fundamental, the need to state it explicitly was not widely
perceived until the first third of the 20th century, long after the first
three principles were already widely in use. Hence it was
numbered zero -- before the subsequent three.

11. FIRST LAW
Energy can neither be created nor destroyed. It can only change
forms.
• In any process in an isolated system, the total energy remains the same.
• A definate amount of mechanical work is needed to produce definate
amount of heat and vive versa.
W/H= j. where j is called joules constant.

12. For a closed system, in any process, the change in the internal energy is
considered due to a combination of heat added to the system and work done by
the system. Taking as a change in internal energy, one writes-
∆ U= Q – W ( sign convention of clausius)
Where Q and W are quantities of heat supplied to the system by its surroundings
and of work done by the system on its surroundings, respectively. This sign
convention is implicit in Clausius' statement .
In modern style of teaching science, however, it is conventional to use the IUPAC
convention by which the first law is formulated in terms of the work done on the
system. With this alternate sign convention for work, the first law for a closed
system may be written:
U= Q + W ( sign convention of IUPAC).
This convention follows physicists such as Max Planck, and considers all net energy
transfers to the system as positive and all net energy transfers from the system as
negative, irrespective of any use for the system as an engine or other device.
When a system expands in a fictive quasistatic process, the work done by the
system on the environment is the product, P dV, of pressure, P, and volume
change, dV, whereas the work done on the system is -P dV. Using either sign
convention for work, the change in internal energy of the system is:
dU=dQ – PdV.

13. LIMITATIONS OF FIRST LAW OF
THERMODYNAMICS.
• No restriction on the direction of the flow of heat: the first law
establishes definite relationship between the heat absorbed and the
work performed by a system. The first law does not indicate whether
heat can flow from a cold end to a hot end or not.
• Does not specify the feasibility of the reaction: first law does not
specify that process is feasible or not.
• Practically it is not possible to convert the heat energy into an
equivalent amount of work.
• To overcome this limitations, another law is needed which is known as
second law of thermodynamics.

14. SECOND LAW OF THERMODYNAMICS
• In thermodynamics, entropy (usual symbol S) is a measure of the number of specific ways in
which a thermodynamic system may be arranged, commonly understood as a measure of
disorder. According to the second law of thermodynamics the entropy of an isolated system
never decreases; such a system will spontaneously evolve toward thermodynamic equilibrium,
the configuration with maximum entropy. Systems that are not isolated may decrease in entropy,
provided they increase the entropy of their environment by at least that same amount. Since
entropy is a state function, the change in the entropy of a system is the same for any process that
goes from a given initial state to a given final state, whether the process is reversible or
irreversible. However irreversible processes increase the combined entropy of the system and its
environment.
• The change in entropy of a system was originally defined for a thermodynamically reversible
process as-
∆𝑆 =
𝑑𝑄 𝑟𝑒𝑣
𝑇
.
Where T is an absolute temperature of a system.

15. CARNOT CYCLE
• The Carnot cycle is a theoretical thermodynamic cycle
proposed by Nicolas Léonard Sadi Carnot in 1824 and
expanded by others in the 1830s and 1840s. It can be shown
that it is the most efficient cycle for converting a given
amount of thermal energy into work, or conversely, creating a
temperature difference (e.g. refrigeration) by doing a given
amount of work.
• Every single thermodynamic system exists in a particular state.
When a system is taken through a series of different states and
finally returned to its initial state, a thermodynamic cycle is
said to have occurred. In the process of going through this
cycle, the system may perform work on its surroundings,
thereby acting as a heat engine. A system undergoing a
Carnot cycle is called a Carnot heat engine, although such a
"perfect" engine is only a theoretical limit and cannot be built
in practice.

16. EFFICIENCY OF CARNOT CYCLE
W= 𝑃𝑑𝑣 = (𝑇 𝐻 - 𝑇𝑐)( 𝑆 𝐵- 𝑆𝐴 )
The total amount of thermal energy transferred from the hot reservoir to the
system will be- 𝑄 𝐻 = 𝑇 𝐻 (𝑆 𝐵 - 𝑆𝐴 )
and the total amount of thermal energy transferred from the system to the cold
reservoir will be- 𝑄 𝑐 = 𝑇𝑐 (𝑆 𝐵 - 𝑆𝐴 )
The efficiency is defined to be:
n=
𝑊
𝑄 𝐻
= 1-
𝑇𝑐
𝑇 𝐻
.

17. APPLICATIONS OF THERMODYNAMOCS
• All types of vehicles that we use, cars, motorcycles, trucks, ships, aeroplanes, and
many other types work on the basis of second law of thermodynamics and Carnot
Cycle. They may be using petrol engine or diesel engine, but the law remains the
same.
• All the refrigerators, deep freezers, industrial refrigeration systems, all types of air-
conditioning systems, heat pumps, etc work on the basis of the second law of
thermodynamics.
• All types of air and gas compressors, blowers, fans, run on various thermodynamic
cycles.
• One of the important fields of thermodynamics is heat transfer, which relates to
transfer of heat between two media. There are three modes of heat transfer:
conduction, convection and radiation. The concept of heat transfer is used in wide
range of devices like heat exchangers, evaporators, condensers, radiators, coolers,
heaters, etc.
• Thermodynamics also involves study of various types of power plants like thermal
power plants, nuclear power plants, hydroelectric power plants, power plants
based on renewable energy sources like solar, wind, geothermal, tides, water
waves etc.,
• Renewable energy is an important subject area of thermodynamics that involves
studying the feasibility of using different types of renewable energy sources for
domestic and commercial use.

18. THANK
YOU