Kinetic Theory Class 11th Notes - Free NCERT Class 11 Physics Chapter 13 Notes - Download PDF

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# Kinetic Theory Class 11th Notes - Free NCERT Class 11 Physics Chapter 13 Notes - Download PDF

Edited By Safeer PP | Updated on Mar 16, 2022 06:11 PM IST

The Class 11 Physics chapter 13 notes (Kinetic theory) are notes of the NCERT chapter Kinetic theory. NCERT Class 11 Physics chapter 13 notes provide an overview of the chapter on Kinetic theories.

The main topics covered in Kinetic theory Class 11 notes are

• Molecular nature of matter

• Behavior of gases

• Kinetic theory of ideal gases

• Law of equipartition of energy

• Specific heat capacity

• Mean Free Path

In Class 11 Kinetic theory notes all these topics are important from the perspective of the CBSE exam and can be noted, all of these topics are relevant to the CBSE exam and can be obtained by downloading from Class 11 Physics chapter 13 notes pdf download. Kinetic theory Class 11 notes cover the summary of the chapter. The CBSE Class 11 Physics chapter 13 notes do not include the necessary derivations. The NCERT notes for Class 11 Physics chapter 13 or notes for class 11 physics chapter 13 are extremely beneficial for revision.

## NCERT Class 11 Physics Chapter 13 Notes

Some properties of gases

• Gases can be compressed easily.

• Gases have neither a definite volume nor a definite shape.

• When a substance is in the gaseous state, its density is very small in comparison to the density in its solid or liquid state.

Boyle’s Law: At constant temperature, the volume V of a given mass of a gas is inversely proportional to its pressure P, according to this law.

If P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume for a given mass of a gas at constant temperature, then

A graph is drawn between P and V for a gas at different constant temperatures T₁, T₂, and T₃ (T₁> T₂>T₃).

The gases do not obey Boyle’s law strictly under all conditions of pressure and temperature, gas only obey Boyle’s law only at low pressures and high temperatures.

Charles’ Law:- At constant pressure the volume of the given mass of a gas increases by part of its volume at 0℃ for 1℃ rise in temperature is called Charles's law.

Charles’ Law in terms of absolute temperature:- Let at constant pressure, the volume of a given mass of a gas at 0℃, t₁℃ and t₂℃ are V₀, V₁ and V₂ respectively. T₁ and T₂ are the absolute temperatures corresponding to t₁℃ and t₂ ℃. By Charles' Law

Therefore at constant pressure, the volume of a given mass of a gas is directly proportional to its absolute temperature. This is Charles’ Law in terms of absolute temperature.

A graph is drawn between T and V for a gas at three different constant pressures P₁, P₂, and P₃ ( P₁> P₂>P₃).

Perfect Gas ( or ideal gas):- A gas whose properties are similar to the properties of a real gas at infinitely low pressure such an imaginary gas is called perfect gas or ideal gas. There are following properties of perfect gas:

• It strictly obeys Boyle's Law, Charles’ Law and the law of pressure under all conditions of temperature and pressure.

• Its pressure coefficient and volume coefficient are exactly equal to each other.

• Its molecules are infinitesimally small.

• There is no force attraction between its molecules.

## Equation of State for an Ideal Gas

Let initially pressure, volume, and temperature of a gas are P₁, V₁, and T₁respectively and finally change to P₂ V₂, and T₂ respectively. Now,

i. Let the temperature of the gas kept constant at T₁ and the pressure is changed from P₁ to P₂. If in this process the volume changes from V₁ to V’ then by Boyle’s law,

ii. Let the pressure of the gas is kept constant at P₂ and its absolute temperature is changed from T₁ to T₂. If in this process the volume of the gas changes from V’ to V₂ then by Charles’ law,

From eqn (i) and (ii), we have

Hence for a gas, the volume of PV/T remains constant. Let this constant be equal to K, then

We can write K = nk, k is the same for all gases. It is called Boltzmann constant.

If P, V, and T are the same, then n is also the same for all gase.

If we take 1 gram-molecule (1 mole) of a gas-constant it will be the same for all gases. Then it is called the universal gas constant and it is represented by R. Then,

Where R = Nk, where N = avogadro’s number and k = Boltzmann constant.

It is called the ideal gas equation or perfect gas equation.

The gas equation for μ moles of gas will be

Unit of R:- Unit of R is Jmol⁻¹K⁻¹

Dimension of R:- [ML²T⁻²?⁻¹].

Numerical value of R:- The value of R is 8.31Jmol⁻¹K⁻¹.

## Kinetic Theory of Gases

Following are the fundamental assumptions of kinetic theory of gases:

• A gas is composed of a large number of tiny invisible, perfectly elastic particles, called the molecules.

• The molecules are always in a state of continuous motion with varying velocities in all possible directions.

• The molecules traverse the straight path between any two collisions.

• The size of the molecules is infinitely small compared to the average distance traversed by a molecule between any two consecutive collisions . The distance between any two consecutive collisions is called the free path and the average distance between any two consecutive collisions is called the mean free path.

• The time of collisions is negligible as compared with the time taken to traverse the free path.

• The collisions between molecules and with the walls are perfectly elastic so that there is no loss of kinetic energy in the collisions.

• The molecules exert no force on each other except when they collide and the whole of the molecules energy is kinetic.

• The volume of the molecules is negligible as compared to the volume of a vessel containing gas.

• The inter molecular distances in a gas is much larger than that of a solid or liquid and the molecules of a gas are free to move in the entire space available to them.

## Pressure Exerted by an Ideal Gas

When a certain mass of a perfect gas is confined with a vessel the molecule frequently collides with the walls of the vessel and is reflected from the walls.During the collision with the walls each molecule suffers a change in momentum .

According to Newton ‘s second law of motion the rate of momentum is equal to the force exerted .Thus,it exerts a pressure on the walls . This pressure may be calculated on the basis of postulates of kinetic theory of gases

Let us consider a perfect gas contained in a cubical vessel of side (l) and perfectly elastic walls. Let n be the total total number of molecules of a gas in the vessel and m is the mass of the molecule. Let the sides of the cube represent mutually perpendicular X, Y, and Z-axes.

Consider a molecule molecule P moving in a random direction with velocity v1. Let v1x, v1y, and v1z be the components of the velocity along three mutually perpendicular X, Y, and Z axes , respectively.

Then

The component of velocity with which the molecule P will strike the face DEFA is v1x and the momentum of the molecule X- direction before collisions

As the molecule and the wall are perfectly elastic, during collision speed of the molecule does not change and only the direction of velocity is changed.

Therefore, The momentum along X- axis after collisions

The change in the momentum during one collision along X-axis

The molecule suffering reflection at face DEFA traverses a distance l and strikes the faceCGBO. It is equal to the force exerted on it. Hence, the force exerted by the molecule on the wall A will be mvx2/l Since there are n molecules, the total force exerted on the wall A is given by

Where vxn is the x-component of velocity of the molecule 1, vx2 of molecule 2,.... And so on. Since the area of the wall is l2, the pressure on the wall A is given by

But l3= V

Now, is the average value of vx2 for all the n molecules. This can be written as

.

Therefore,

We know that for any molecule, we have

Because this equation is true for every molecule, this will also be true for the mean value of all the molecules.

Therefore from eqn (ii), we have

or

This is the equation for the pressure of the gas.

is called the mean- square velocity of the molecules. Since, mn is the mass of the whole gas and V is the volume so, mn/V is the density ⍴ of the gas therefore, the above expression can be written as

Again,

Where is the transnational kinetic energy of the gas per unit volume. Thus, the pressure is equal to two-thirds of its transnational kinetic energy per unit volume.

## Law of Equipartition of Energy

It states that the total kinetic energy of a dynamical system consisting of a large number of particles in thermal equilibrium is equally distributed among all degrees of freedom 0.5KT, and the energy associated with each degree of freedom is where k is the Boltzmann constant and T is the absolute temperature of the system.

Thus, the average kinetic energy of a molecule per degree of freedom is 0.5KT which is the law of equipartition of energy.

Root mean-Square (rms) Speed of gas molecule

The speeds of the individual molecules of a gas vary over a wide range. Let v₁, v₂, and v₃…...vₙ. Be the speed of molecules of a gas. Then, the root-mean-square speed of the molecules is defined as the square root of the mean of the squares of the speeds of the all gas molecules, and it is denoted by rms. Thus,

We know that the pressure of a gas is given by

Interpretation of temperature on the basis of Kinetic theory

Let us consider 1 gram molecule of a gas at absolute temperature, T, occupying a volume V. According to Kinetic theory, the pressure of the gas

mN = M

Comparing eqn (ii) and (iii)

Thus, the root mean square speed of the molecules of a gas is directly proportional to the square root of the absolute temperature of the gas.

Relation between temperature and molecular kinetic energy:-

Average kinetic energy of one molecule =

R/N = k (Boltzmann constant)

It means different gase at the same temperature have the same average kinetic energy per molecule and this energy is directly proportional to the absolute temperature of the gas.

## Explanation of Gas Laws from Kinetic Theory

Boyle’s Law

We know

According to kinetic theory, the average kinetic energy of translation of molecules of gas is directly proportional to its absolute temperature,

i.e., at a given temperature, average kinetic energy of a gas is constant and N is also constant, so eqn (i)

= constant at a given temperature

This is Boyle's Law.

Charles’s law:-

From eqn(i)

Also the average K.E. of a molecule,

for constant value P.

Thus at a given pressure for a given mass of a gas, the volume is directly proportional to the absolute temperature. This is Charles' law.

Mean free Path:-The average distance traversed by a molecule between two successive collisions is defined as the mean free path.

Thus, if λ₁, λ₂, λ₃, ….λₙ are the successive free paths traversed in the total time t, then,

If N is the total no. of collisions suffered, then

## Expression for Mean Free Path

We know that,

But by experiment Maxwell found that

The mean free path is inversely proportional to the number of molecules per unit volume (n) which is proportional to the density of the gas.

For N molecule of an ideal gas, we have

This is the mean free path of the molecules of a gas is directly proportional to its absolute temperature and inversely proportional to the pressure of the gas.

Avagadro’s Number: The Avagadro’s number is the number of molecules in 1 mole of a substance. It is denoted by N and its value is 6.0221 X 10 ²³.

Significance of NCERT Class 11 Physics Chapter 13 Notes

Kinetic theory Class 11 notes can be used to review the chapter and get a better understanding of the big topics can be used to go over the chapter again and get a better understanding of the major points covered. Also, these NCERT Class 11 Physics chapter 13 notes are useful for the Class 11 CBSE Physics Syllabus and competitive exams such as VITEEE, BITSAT, JEE Main, NEET, etc. Download all these notes from Class 11 Physics chapter 13 notes pdf download or Kinetic theory Class 11 notes pdf download

## NCERT Class 12 Notes Chapter-Wise

 NCERT Class 11 Physics Chapter 1 Notes NCERT Class 11 Physics Chapter 2 Notes NCERT Class 11 Physics Chapter 3 Notes NCERT Class 11 Physics Chapter 4 Notes NCERT Class 11 Physics Chapter 5 Notes NCERT Class 11 Physics Chapter 6 Notes NCERT Class 11 Physics Chapter 7 Notes NCERT Class 11 Physics Chapter 8 Notes NCERT Class 11 Physics Chapter 9 Notes NCERT Class 11 Physics Chapter 10 Notes NCERT Class 11 Physics Chapter 11 Notes NCERT Class 11 Physics Chapter 12 Notes NCERT Class 11 Physics Chapter 13 Notes NCERT Class 11 Physics Chapter 14 Notes NCERT Class 11 Physics Chapter 15 Notes

### Subject Wise NCERT Solutions

 NCERT Books for Class 11 NCERT Syllabus for Class 11

1. What is the law of equipartition of energy?

It states that the total kinetic energy  of a dynamical system consisting of a large number of particles in thermal equilibrium is equally divided among all its degrees of freedom, and the energy contained with each degree of freedom is kT/2 where k signifies the Boltzmann constant and T signifies the system's absolute temperature

2. What is the significance of this chapter for the CBSE Board Exam?

From the CBSE Class 11 Physics chapter 13 notes, Students can expect 2 to 4 marks question.

3. Write the Kinetic theory assumption of gases from Class 11 Physics chapter 2 notes and Class 11 Physics chapter 13 notes, Kinetic theory Class 11 notes.

Following are the fundamental assumptions of kinetic theory of gases:

• A gas is composed of a large number of tiny invisible, perfectly elastic particles, called the molecules.

• The molecules are always in a state of continuous motion with varying velocities in all possible directions.

• The molecules traverse the straight path between any two collisions.

• The size of the molecules is infinitely small compared to the average distance traversed by a molecule between any two consecutive collisions . The distance between any two consecutive collisions is called the free path and the average distance between any two consecutive collisions is called the mean free path.

• The time of collisions is negligible as compared with the time taken to traverse the free path.

• The collisions between molecules and with the walls are perfectly elastic so that there is no loss of kinetic energy in the collisions.

• The molecules exert no force on each other except when they collide and the whole of the molecules energy is kinetic.

• The volume of the molecules is negligible as compared to the volume of a vessel containing gas.

• The inter molecular distances in a gas is much larger than that of a solid or liquid and the molecules of a gas are free to move in the entire space available to them.

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##### Talent Agent

The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

3 Jobs Available

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
##### Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
##### Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
##### Talent Director

Individuals who opt for a career as a talent director are professionals who work in the entertainment industry. He or she is responsible for finding out the right talent through auditions for films, theatre productions, or shows. A talented director possesses strong knowledge of computer software used in filmmaking, CGI and animation. A talent acquisition director keeps himself or herself updated on various technical aspects such as lighting, camera angles and shots.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. Ever since internet cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.

3 Jobs Available
##### Travel Journalist

The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.

2 Jobs Available
##### Videographer

Careers in videography are art that can be defined as a creative and interpretive process that culminates in the authorship of an original work of art rather than a simple recording of a simple event. It would be wrong to portrait it as a subcategory of photography, rather photography is one of the crafts used in videographer jobs in addition to technical skills like organization, management, interpretation, and image-manipulation techniques. Students pursue Visual Media, Film, Television, Digital Video Production to opt for a videographer career path. The visual impacts of a film are driven by the creative decisions taken in videography jobs. Individuals who opt for a career as a videographer are involved in the entire lifecycle of a film and production.

2 Jobs Available
##### SEO Analyst

An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.

2 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
##### Production Manager

Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers.

3 Jobs Available

A Team Leader is a professional responsible for guiding, monitoring and leading the entire group. He or she is responsible for motivating team members by providing a pleasant work environment to them and inspiring positive communication. A Team Leader contributes to the achievement of the organisation’s goals. He or she improves the confidence, product knowledge and communication skills of the team members and empowers them.

2 Jobs Available
##### Quality Systems Manager

A Quality Systems Manager is a professional responsible for developing strategies, processes, policies, standards and systems concerning the company as well as operations of its supply chain. It includes auditing to ensure compliance. It could also be carried out by a third party.

2 Jobs Available
##### Merchandiser

A career as a merchandiser requires one to promote specific products and services of one or different brands, to increase the in-house sales of the store. Merchandising job focuses on enticing the customers to enter the store and hence increasing their chances of buying a product. Although the buyer is the one who selects the lines, it all depends on the merchandiser on how much money a buyer will spend, how many lines will be purchased, and what will be the quantity of those lines. In a career as merchandiser, one is required to closely work with the display staff in order to decide in what way a product would be displayed so that sales can be maximised. In small brands or local retail stores, a merchandiser is responsible for both merchandising and buying.

2 Jobs Available
##### Procurement Manager

The procurement Manager is also known as  Purchasing Manager. The role of the Procurement Manager is to source products and services for a company. A Procurement Manager is involved in developing a purchasing strategy, including the company's budget and the supplies as well as the vendors who can provide goods and services to the company. His or her ultimate goal is to bring the right products or services at the right time with cost-effectiveness.

2 Jobs Available
##### Production Planner

Individuals who opt for a career as a production planner are professionals who are responsible for ensuring goods manufactured by the employing company are cost-effective and meets quality specifications including ensuring the availability of ready to distribute stock in a timely fashion manner.

2 Jobs Available
##### ITSM Manager

ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.

3 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### IT Consultant

An IT Consultant is a professional who is also known as a technology consultant. He or she is required to provide consultation to industrial and commercial clients to resolve business and IT problems and acquire optimum growth. An IT consultant can find work by signing up with an IT consultancy firm, or he or she can work on their own as independent contractors and select the projects he or she wants to work on.

2 Jobs Available
##### Data Architect

A Data Architect role involves formulating the organisational data strategy. It involves data quality, flow of data within the organisation and security of data. The vision of Data Architect provides support to convert business requirements into technical requirements.

2 Jobs Available
##### Security Engineer

The Security Engineer is responsible for overseeing and controlling the various aspects of a company's computer security. Individuals in the security engineer jobs include developing and implementing policies and procedures to protect the data and information of the organisation. In this article, we will discuss the security engineer job description, security engineer skills, security engineer course, and security engineer career path.

2 Jobs Available
##### UX Architect

A UX Architect is someone who influences the design processes and its outcomes. He or she possesses a solid understanding of user research, information architecture, interaction design and content strategy.

2 Jobs Available