 So please draw this plot. On x axis you have pressure for here you have p to v divided by n. In physics number of moles is taken as mu. Mu is number of moles. In chemistry we take it as small n. But small n in physics means something else. What kind of graph I should take? Straight line. What? It would be like this. This distance should be what? This should be r. This is what ideally should be observed. But what is observed is this. This is at a temperature T1. This is at a temperature of T2 where T1 is more than T2. It is not a straight forward position. Okay? Are you getting it? It does not give you a straight line. But if you increase the temperature, if you increase the temperature this bulge will straighten out. You have higher temperature, you are closer to the attic as less. If you increase the pressure and you of T by mu T will shoot up. Are you getting it? This is the off temperature and lower pressure P v by mu T is almost a constant. At higher temperature and lower pressure P v by mu T is almost a constant. Okay? Now people started to analyze why is that such kind of behavior is observed. Okay? But they came up with various hypothesis. Okay? So one of the scientists said that if you increase lot of pressure the molecules of the atom will come close to each other and they will start attracting or repelling each other. Okay? Then you cannot ignore the interatomic attraction or repulsion. Fine? That is the reason why at higher pressure it is not behaving like an algeas. Are you getting it? And similarly when you at a much lower temperature, atoms are not vibrating very fast. Their velocity is very less. Because of that, even if it is very less or negligible can affect the motion of the atom. It behaves similar to an ideal gas. Fine? Understood the reasoning? So from assumption starts to coming in that people were trying to put a framework of what is the assumption for an ideal gas. So we will start the chapter with all the assumptions that we should make before analyzing any gas. Okay? So do you already know the assumptions? Assumptions for an ideal gas is what? What? Okay, please write down the first are elastic. Not just atoms or any wall or something. What do you think the reason for this could be? If it is not an elastic collision then what will happen? It will go to a, go to surrounding and what is surrounding? According to, it should go to some atom. The energy has to go to some atom only. Go from ground state to the first accepted state. If the loss energy is not sufficient to go from ground to excited state, it reject that loss energy. Are you getting? So the collision does not generate so much energy so that the ground state electron goes to the first accepted state. That is why it rejects the loss energy and hence all the atomic collisions are treated as elastic and it is a very accurate assumption. Okay? It is not a false assumption. Fine? But of course if atom is coming with huge amount of velocity then there is a chance that the collision are not elastic. The energy loss may be sufficient to make sure the electron transition happens from ground state to the first accepted state. Okay? But for all practical purpose whenever we analyze a gas we do not deal with such high atomic speeds. All the collisions are elastic. A fairly good assumption. What is the next assumption? What do you think? The intermolecular or interatomic forces. We write down no interatomic or molecular forces. What does it mean? If there is no interatomic or molecular force, can there be potential energy of an atom? How do we define potential energy? The work done by some force and I am saying force in ideal gas. So all the energies are kinetic energy. The entire is kinetic energy. This is what this assumption means. We write down in bracket the entire energy, the ideal gas will be kinetic energy. There is no potential energy. What do you think is the third assumption? This is very important. They move in, their motion is random. Okay? We write down motion of items of gas is random. Now when I say item even if it is hydrogen molecule I mean to say that also. Okay? Now what does it mean? Random means what? Does random means unpredictable? They move in a? Okay? But when they collide we will be able to move in a same state line. A molecule, an atom comes from here, hits this atom and then goes in that direction. Okay? So randomly means what? Okay? What else can I say? Any direction or there is no preferred direction in which it will move? There is no preferred direction. Forget it. Now mathematically what does it mean? What can you say about the velocity? Mathematically how will I say that? Anyone? Okay? Here is what mathematically it means. If I take a snapshot of the atom's motion and then if I take the velocity of all the atoms the velocity will be what? If 2 meter per second this way and the atom should be, again the velocity of the atoms will be 0. No, it is as good as me saying that all atoms are, it doesn't take away the squares and then take the square. That is root mean square. So basically I am taking the mean of the squares. What I am saying is take square of this, 4, square of that, again 4, take the average which is 4 and then take the square root. It comes out to be 2. So count it will come out to be 0. Okay? So the average velocity if I say that this is the average in x direction velocity plus average in y direction velocity square plus average in z direction velocity square. I can write like this p y square and p z square. What can I say? They are equal or not? They are equal because it is random. There is no preferred direction. So v x square average will be equal to v y square will be equal to v z square. This is the outcome of this assumption. Okay? Any doubt? Now tell me other assumptions. Say there are any other assumptions on the left side. The volume of the atoms and the intensity of the molecules. Exactly. So right term, the volume of the atoms or molecules in the molecule is negligible. Okay? So volume of the atoms and molecules is negligible. Compared to what? Compared to the atoms, all the atoms or molecules is negligible compared to the amount of volume the entire gas is. Okay? What else? What are these? No, that is obvious. I mean that is true for any gas. I will talk about specific to ideal gas. What are the assumptions specific to ideal gas? Please write down ideal gas will occupy, it will occupy our level. Which if I put two moles of the gas, I need to say that property is same as property of gas like the gas one of the gas. So it get uniformly, yes you mean that. Right? By having these assumptions. Okay? And there are some questions that are and they test your common sense. There is no formula make you think. Okay? So let's take some questions which test your understanding of the atomic model itself. Okay? Please write down. All right. So density is 0.6 kg per micro cube. The density of the cells is that of atomic fashion. But volume of the molecules divided by volume of the water vector is one mole of gas. Suppose there is one mole of gas, you need to find out volume of, how much volume that one mole of gas a question. No. These molecules individually add it up. So what these molecules are, what are the questions? We can. This is not right. You, come here. Yes, it's going. It's still going. Yes, it's still a bit. Little bit count is how much? Eight or nine percent. Eight or nine percent? Eight or nine percent. My hemoglobin is eight or nine percent. Oh, it has to be around twelve, right? No, the plainly count is what is the. I'm not sure. Okay, so you feel rightly at the test base. And who else? You. When? As you can see, you can assume mass to be whatever. The ratio doesn't depend. Can't be more than one. Okay, no one. Six into 10 square. Correct. Six into 10 square minus four. Assume one kg of water. Assume one kg of water. All right. One kg of water or volume of one kg of water molecules. Fine. So how much it is? One kg of water. One volume, one divided by. Now same one kg now become water vapor. So what do you mean by the volume? This is the volume of one kg of water. This is the volume occupied by the vapor of one kg. Fine. So this will be six into 10 raise to power minus four. Okay, no physics common sense is used here. Now tell me volume of one molecule of water. I'm not sure. Understood, right? So the next one. Find the volume of one molecule of water. Next two molecules have what volume? No. Should I do it? Three into 10 is power. The answer is three into 10 is minus 29. How many you got it? Only two. Should I do it now? Three. If you want the volume find the radius. Okay, this one here. One kg is the volume. One kg has that. This many moles can into stationery transport 23. These many molecules have this much volume. So one molecule will have that derivative. The answer will be three into 10 raise to power minus 29 meter 3. They are asking it out. Is it here?