So hopefully when

you were listing down all the types of energy

that you could think of, you thought about kinetic

energy and potential energy. For particles, we’ve

got different types of kinetic energy. So there’s the translational

kinetic energy, which is the normal

1/2 mv squared one associated with movement. And hopefully, you

also remembered about the rotational kinetic

energy, 1/2 i omega squared, associated with the

rotation of the body. Now potential energy

is not actually too important for

particles, because one of the assumptions

of the ideal gas law was that the only forces

that we needed to consider occurred in the collisions

between the particles. So we don’t need to worry

about the gravitational force. That’s because the mass of

the particles is really small, so that gravitational

potential energy is tiny. And we also don’t have

to worry about things like electrostatic fields and

the potential energy associated with that when we are

considering a gas, which obeys those assumptions of

the kinetic theory of gases. There is another type of energy

associated with particles. When you’ve got a molecule with

one or more atoms connected with a bond, we

can actually have vibrational kinetic energy,

where the bonds vibrate. And we have energy

associated with that. So what we’re going to do now is

consider a few different types of particles. Let’s start with the

simplest– a monotonic atom. So this is something

like a helium atom, which is just one atom by itself. Now, this helium atom can store

translational kinetic energy. It can move backwards

and forwards– let’s say that’s the x direction. It can move up and down– let’s call that the y direction. And it can also move

in and out like this, so we can say that’s

in the z direction. So there’s actually

three dimensions in which it can store this

translational kinetic energy. So each of those dimensions

is associated with what we call a degree of freedom. So degree of freedom is a way

in which a molecule or an atom can store energy. So this single monotonic atom

has three translational degrees of freedom. Now this atom can also

rotate, but that’s actually got a negligible amount of

kinetic energy associated with it. The reason for that is

that atoms are very small, and the mass of the atom is

concentrated in the nucleus. The nucleus of the atom

is about the size of 10 to the minus 15

metres, so it’s tiny. The moment of

inertia for a sphere, such as this, if we model

our atom as a sphere, is given by 2/5 mr squared. So you can see that the

rotational kinetic energy, which is 1/2 i

omega squared, it’s going to be absolutely tiny

because of the very tiny mass and the very, very tiny radius. And so any rotational

kinetic energy is negligible, and we don’t have any

degrees of freedom associated with the rotational kinetic

energy for a monotonic particle or atom. Also, there’s no vibrations here

because we don’t have any bonds for it to vibrate against– vibrate about. So this monotonic particle just

has three degrees of freedom, and they’re associated with

that translational movement, so it can move in the

x, y, and z direction. Let’s now consider

a diatomic particle. So H2 is a common example,

you also got N2, O2. So this is two atoms

connected by one bond. Now in this case, it can also

move in the three directions. So it can move backwards

and forwards, up and down, in and out. So it has got three

translational degrees of freedom. Now this particle

can also rotate. When it rotates about–

let’s call this the z-axis– that has got energy

associated with it. It can also move about the

axis this way, so like this. And that has also got

energy associated with it. Now if it rotates

about this axis, like this, there’s

actually very little rotational kinetic

energy stored in that way for the same reasons as before. The mass is concentrated in

the nucleus with a tiny radius, and so we’ve got very little

rotational kinetic energy stored in that way. So this diatomic molecule

has two rotational degrees of freedom. Now the diatomic molecules

can also vibrate. So here’s another model

with a spring in between, so you can see they can

spring in and out like this. Now when we start

it springing, we can set the initial

kinetic energy and the initial potential

energy for that oscillation. You’ll be learning more about

that in the oscillations topic. But because we have

those two choices when starting it to vibrate,

that’s got two degrees of freedom associated with it. Now an important thing

about degrees of freedom is that it does actually

depend on the temperature. At low temperatures,

below 100 kelvins, the particles can

move, so they all have the translational

kinetic energy. But when they collide

with other particles, they don’t actually

have enough energy to start those are the

particles rotating. So low temperatures,

below about 100 Kelvin, these diatomic

molecules only have the translational

kinetic energy. They also do not

have enough energy to start other

particles vibrating. So they’ve just got the

three translational degrees of freedom at low temperatures. In the medium range, between

100 kelvins and 1,000 kelvins, they do have enough energy to

start other particles rotating when they collide. But they do not

have enough energy to start other

particles vibrating. So between 100 kelvins

and 1,000 kelvins, diatomic molecules have

five degrees of freedom– three translational

and two rotational. Above 1,000 kelvins,

they have enough energy to start things vibrating. And so at that point, they’ve

got seven degrees of freedom– three translational,

two rotational, and two vibrational. Now we can have more complex

molecules, such as this methane molecule here. At low temperatures,

this methane molecule can also move in

three dimensions. And so it also has three

translational degrees of freedom associated with it. This one, it can actually rotate

about three different axes, and so it also has three

rotational degrees of freedom. At high temperatures,

it’s also going to have vibrational

degrees of freedom. So for more complex

molecules, below 100 kelvins, they also only

have three degrees of freedom associated

with translation. As the temperature

increases, depending on the geometry of

the molecule, they can have additional

rotational degrees of freedom. And then when we get above

1,000 kelvins as well, they can start

vibrating, and so we’ll have additional degrees

of freedom in that way. But you won’t be

expected to calculate how many vibrational degrees of

freedom complex molecules have, because that gets difficult. But here is one for you to try. What I’ve got here is

a model of a crystal. Now I want you to

consider this particle in the middle of the crystal. So it’s surrounded

by lots of partners, and we can model the crystal

as having bonds between it, and bonds can have vibrations. So they’ve got springs here

representing those vibrations. So what I want you to do

is think about this crystal and try and work out how

many degrees of freedom associated with translation,

rotation, and vibration you think this crystal would have.

Best video on the youtube for this topic. Thank You!!

awesome !! u explained all of dem

How many degrees of freedom does that crystal have? I counted 9.

Such a good explanation compared to other videos!

Very good explanation

ft= 3 fr= 3 and fv = 6 so f= 15. Is it right

Thank you ! It helped me a lot..

Amazing explanation..

Thank you again..

Thank you so much, it helped me alot…

so detailed and clear

This was such an amazing explanation.Thank you so much.Helped me a lot 🙂

Thank you. Clear and concise lecture! 👍🏻

extremely good mam

Very nice explanation

Thank u soo muchh

Much better explanation than any other videos

Best video on this topic!

Then what will be the dof of triatomic linear and nonlinear??

How many no. Of freedom of vibration….In CH4

Fantastic

thanks a lot…

Thank you mam….this really helped!

Bang On.

I'm just learning about Dulong and Petit Law and came across the fact that by adding enough energy to solid, it's atomic vibration will contribute THREE additional degrees of freedom (instead of 2). Can you explain to me how that is? ><'" Thank you

thanks mam so much…..

The best video,thanks a lot

Is it possible in theory to have a context where we'd want to account for the effects of a hydrogen atom's rotation and then would you say it has 4 degrees of freedom? Or is there some fundamental physical law the precludes this from ever being relevant?

Best explanation!!!👌

Thnku mam

you are a legend…wonderfully explained

Plz show such models for mechanics too madam….??

NIce Mom..,,we need more vadios on C.Mechanics

best video on the YouTube to understand this topic…thnkuh 😊

Amazing explained

Finally! Been searching for a clear explanation of this for a while. Thanks.

I don't understand vibrating freedom why it is 2 ?

nice explanation..

Thanks

wow explanation

Thanks for the explanation. Just as a note, I have checked some references and they all mention the degree of freedom for vibrational movement of diatomic gas is 1, not 2.

Mamm pls make playlist of your channel