THERMODYNAMICS AND KINETIC

THEORY OF GASES

MADE BY:-

Naman Jain

Roll No- A-36

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.

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.

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)1/2𝑒−𝑚𝑣2/2𝐾𝑇dV. 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.

MAXWELL BOLTZMANN DISTRIBUTION GRAPH

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/√𝑀Where-

• 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

distributionVmp<Vavg<Vrms

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).

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.

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.

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.

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.

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.

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 = 𝑑𝑄𝑟𝑒𝑣

𝑇.

Where T is an absolute temperature of a system.

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.

EFFICIENCY OF CARNOT CYCLE

W= 𝑃𝑑𝑣 = (𝑇𝐻 - 𝑇𝑐)( 𝑆𝐵- 𝑆𝐴 )

The total amount of thermal energy transferred from the hot reservoir to the

system will be- 𝑄𝐻 = 𝑇𝐻 (𝑆𝐵 - 𝑆𝐴 )

and the total amount of thermal energy transferred from the system to the cold

reservoir will be- 𝑄𝑐 = 𝑇𝑐 (𝑆𝐵 - 𝑆𝐴 )

The efficiency is defined to be:

n= 𝑊

𝑄𝐻= 1-

𝑇𝑐

𝑇𝐻.

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.

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