 Now write down next heading, candidate theory of an ideal gas. The chapter name is we are learning candidate, then we will be learning, then we will be learning candidate theory of solids. Write down your gas, please write down molecules. For example pressure, I am going to define in terms of its velocity, okay. I am going to define its energy in terms of the velocity in terms of the kinetic energy, fine. So these things, all right, so small small balls that are moving in the air. So what do you think the pressure exerted by the molecules will be because of pressure? The pressure is there, if more or more will be higher? Simple, okay. So let us try to find out how much will be the value of pressure in terms of the velocity of the molecules of the atoms, okay. So I am going to take a very simplistic scenario, let us take a cubical room sort of thing like this. Are you ready for me to tell? I am going to place coordinate set over here, y and z, which plane direction for molecule. What I am trying to say is suppose this is y z plane, this, so a molecule keep on going like this, so only two collides with this volume of change will happen around the y and z axis for this volume, okay. So please write down, the pressure will be due to the decrement of change, right. So whatever collection of molecules, multiple molecules will hit. So I don't, I can't. So suppose small n denotes number of finite volume, I distributed uniformly across, you need to tell me how many number of collisions will happen in delta t. vx, you can assume that all the molecules on an average have the same velocity along x axis. So how many number of collisions will happen? Yes, given as k, that is also. In delta t time, how many collisions will happen? For one collision, this much commons have transferred, so that's too much. As I tell you, can it reach the wall, which is two meter away in less than one second? No. A molecule can, if a molecule is away from this distance, will it be able to, so if a number into a into delta t, now there is something around here, tell me what it is. No, that is taken care of. No, they will collide at different moment, that is fine. One will collide in one second, other will collide in two seconds, that is fine. Fundamentally, no, actually it is fine. Assumption is not valid when you write like this. What? Not all will. No, that is taken care of. What do you mean? Exactly, so half of it, because it is random, half of it is x direction. So total number is not able to move this way only. Half of it goes this way, half of it goes that way. That is why I am taking half. What? Why half? Statistically, it is based on the Herodotum chapter mathematical probability. Herodotum probability and voice, isn't it? So it is equal chance that molecule is taking half. Any other doubt? In one collision, in this many collisions, total change is 2.21. So delta P total is equal to m n m v x square A into delta T. Now take delta T on the left hand side. So delta P T divided by delta T, this will give me force. This is the force because of the collision. This is the force. Pressure will be what? There is force divided by area. So we have successfully the velocity of the molecule. But this is not the total. It is very difficult. Can you do that yourself first? Can you write down this expression of pressure in terms of total? So we have already found out that v x square is equal to v y square is equal to v z square on an average. And total velocity square is sum of these. This can be written as 3 times v x square. From here v x square will be v square by 3 on an average. And hence has one third n m v square. Now instead of v, I will use u because I am going to use v for volume. So we have got the value of pressure. What is small m? Small m is what? Mass of volume. Mass of a single molecule. Small m is mass of single volume. What is small n? It is huge. So small n will be a big number. And small n will be a very small number. Big number multiplied by smaller number will be like small. Not temperature. In terms of temperature. If you do it yourself. Cut it. The hint is you have to. Number of moles I can write in terms of number. Number of molecules. This will be r into t. And it will be u square also. v and v gone. So one third u square is equal to r. So half m u square which is the kinetic energy is equal to 3 by 2 times constant. Gas constant. Many doubts. So we have defined pressure as a function of the velocity. And we have in a way function of the kinetic energy. If you say y is equal to x, x is also equal to y. Of one molecule is 3 by 2. Equal to kinetic energy plus potential energy which is k only. For one mole. One mole of gas. If the change in temperature is delta t. If temperature changes delta t. Then how will you alternate? It is same. As if the fundamental conservation. So one atom have total changes in energy. So for one mole it will be very important gas coming. Is this change in energy is also change in internal energy. Is this change in energy also change in internal energy. Of the atoms and molecules and this is what it is. So this is also equal to change in internal energy and what is change. So this will be equal to cv into delta t. So cv is how much? 3 by 2 r. So we have kinetic area of gas. So cv is the cp between 5 by 2 r. What is the assumption? The assumption if I come to a single sphere. It is a single sphere or mono atomic gas. That is why half mv square is kinetic energy. Otherwise ignore the rotation assumption here. I am assuming it is a mono atomic gas. A single atom can rotate. A sphere can rotate like this. Then why I am ignoring that? Because it is very small. Negligible size. That was the assumption. Point. Point cannot rotate. If it is a base it can rotate about it axis. Like horizontal rotates. Fine.