here we are going to discuss different molecular

speeds for a gas molecules. you know that gas molecules are in random brownian motion.

so for various kind of mathematical analysis. some standard different molecular speeds are

defined. and, there are vast range of speeds so with which gas molecules move. here we

are going to discuss about some specific speeds, the first one is. average velocity. of gas

molecules. it is the velocity with which gas molecules are moving on an average. second

we use which is quite important which is use for various analysis of energy in pressure

this is, root mean square . velocity. of gas molecules. root mean square is abbreviated

as, r m s velocity of gas molecules. will discuss all these one by one in detail. the

third one in sequence is mean speed. of gas molecules. mean speed is just the magnitude

. magnitude of average or average magnitude of speed of gas molecules . with which the

molecules move. between successive collision, that is considered as mean speed of gas molecule.

and the last important , speed which is use for analysis , is most probable. Speed, of

gas molecules. after this section will study about an article where we’ll see. that different

molecules in a gas moves with different speeds. so the speed with which maximum number of

molecules , would be moving or the probability of. a particular speed, carried by a particular

molecule is maximum is termed as most probable speed of gas molecules. lets discuss these

four , analytical molecular speeds, one by one. to analyze the average velocity of a

gas molecules lets consider a container. in which various gas molecules are moving randomly

in different directions like this. i am just drawing random direction in which the gas

molecules can move. and say they are having there independent speeds. v one. with a particular

direction its velocity vector is v one another is with. vector v two , v three and so on.

now in this situation we can simply state the average velocity. of gas molecules can

be written as v average is equal to. v one vector + v two vector + up to v n vector,

if in total there are , n molecules. then this divided by n that will be regarded as

the , average velocity. and we know well that, as the motion is totally random . then corresponding

to each molecules there will be some other molecule which will be moving with the opposite

, direction with the same speed. in opposite direction with same speed so, in all we can

say, the, random summation of all the vectors which are, having the directions distributed,

randomly through out the container. its summation can be taken as zero because corresponding

to each motion , there would be some opposite motion, this can be found. in this random

motion of particles. so we always assume that, average velocity of gas molecules in a container

is equal to zero. next is , root mean square velocity of gas molecules. this root mean

square means , square root of mean of square of all the velocities. to calculate this r-m-s

velocity of gas molecules first we calculate. mean square velocity. that is the mean of

squares. we talk about mean square velocity is for this we first square all the velocities

and we take mean like. square of velocity of first molecule. + square of velocity of

second molecule and so on up to, the velocity of n-eth molecules, and if divided by the

total number of molecules . this is the mean square velocity. and this, r m s velocity

is defined as, v-r m s is equal to, root of this mean of squares. that is root of. v one

square + v two square up to, v n square. divided by n. basically its mathematical expression

is calculated by maxwellian velocity distribution function which will study, in next article,

but this is the analytical, form, by which you can understand how this r m s velocity

is calculated and this velocity is quite important to use mathematically in calculation of energy

of a gas or pressure exerted by a gas. and. using. maxwells. velocity distribution function.

its expression is. the expression which we, get by using this expression maxwellian-velocity

distribution function is, it is given as root of three r t by m, where m is the molar mass

of the gas. and t is the absolute temperature , this quite important to keep in mind that

r m s velocity is directly proportional to square root of. absolute temperature. and

you can also write this , v r-m-s. is used in , energy. and pressure calculation. of

a gas. we can, state that , for calculation of total energy of a gas which is generally

considered as. total ki-netic energy of all the gas molecules. if we just write down total

energy of a gas is half m . v r m s square, you can see this will give us. m is the total

mass of gas and v r-m-s is velocity of one gas molecule. so here we can write if we substitute

v r m s as v one square + v two square plus v n square , you can see this will transform

into half m, when we substitute this v r-m-s here , total mass upon number of molecules

will give us the mass of one molecule . multiplied by v one square + v two square plus up to

, v-n square. you can see that just by using this v r m s . square, in calculation of total

energy of gas it automatically transforms into, the total ki-netic energy of all the

gas molecules. the next speed of gas molecules is mean speed of gas molecules. mean speed

or we can also call it average speed, can be directly calculated. by calculating the

average of magnitude of all velocities. that will be given as v one magnitude + v two magnitude.

+ up to v-n magnitude. divided by n. obviously as we are taking the average of magnitudes

it can never be zero. like the very first speed we have. seen that was the average velocity.

so velocity include the direction also that’s when we calculate it the average of all velocities

it was zero because. due to directions all opposite directions, canceled each other.

in this situation we are just calculating the, average of magnitudes that is the mean

speed. and its final expression, can be obtained , again by maxwellian velocity distribution.

so we can say. by maxwell’s velocity distribution function . its expression. is. this mean,

speed. is given in expressional form as root of, eight r t by, pie, m. the derivation of

this result is out of the scope of. this article so right now you just need to, keep this result

in your mind, as well as the way. how it is calculated if , speed of an individual molecule

is given to us. this mean speed is use to calculate the mean free path that we have

studied. which is the distance travelled by the particle mean distance travelled by the

particle , between two successive collisions denoted by lambda m, which can be given as

v-mean multiplied by , the relaxation time that is time between two successive collisions.

so mean speed is quite useful in calculation of mean free path. for a given gas. the last

speed which we need to study is the most probable speed of gas molecules. about most probable

speed which can be by its name which can be , understood as the probability. a particular

speed for which the probability for a gas molecule to have, is maximum is called most

probable speed. or in another way we can write . this is the speed . which is. common. in.

maximum number of molecules. of a gas. and it is given as. again we want get into the

derivation of the most probable. speed for a gas molecules. we just need to keep the

result in your mind it is root of two r t by m. this is the most probable speed which

we use. and we can also analyze about the, important speed we can see this most probable

speed is the least. and mean speed is more then , this most probable speed and r m s

speed is, further more then the mean speed. this you need to keep in mind in the very

next article will study about the distribution of molecule speed. the basic phenomena related

to , the molecular speed distribution that is maxwellian distribution curve . with which

he’ll be clear with how. the. speed of gas molecules are distributed among all the molecules.

again we’ll not get into the depth of, that maxwellian function. as it is out of the scope

of this lectures.

Sir where are your coachings? I mean which city?

Jaipur

Sir Please Upload video on this year's JEE Advance Physics paper analysis means about concept related each question and its solution.

Great

sir why are there these 3 velocities particularly, why can't we use something else

Sir 8:03 pe formula should be E= 1/2 m×N×( Urms)²

Plzzz correct me sir

With regards,

Thank U sir

Very good teaching

Really very helpful video sir

Are you great teacher in the world ???????☺️☺️☺️☺️☺️☺️☺️

Sir please upload booster classes on your channel also.

sir from where I can access booster classes if I was unable to access them earlier ?

What will happen to avg velocity…if the container is moving at some speed v… Also what will happen to other velocities or speeds…please enlighten☺?

Sir here are we finding mean square speed and RMS speed?

Sir any video lecture suggestions for IIT JAM physics?

Very nice sir thank you bhut bhut achaa vedio hai sir ???

Sir for avg vel. Of gas molecules is it important that there will be another molecule to cancel each molecule