 The first point to write down, it is based upon, based upon the law of probability. Based upon the law of probability. Second point. It is a graph between, a fraction of molecules. It is just based on the probability, there is no exact thing of it. Like what should be the value of the speed of a given fraction of molecules based on that. So just a guess, it is not very exact. Graph between the fraction of, fraction of molecules and the speed of the molecules. Fraction of molecules and speed. Third point. The fraction of molecules, of molecules having zero speed or very low also you can write. Zero or very low speed. The fraction of molecules, very high speed, very high speed is negligible, is negligible. The fourth point. The maximum fraction of molecules, fraction of molecules having, have common speed. Which is the most probable speed. Most probable speed. At a given temperature. Temperatures of area under the curve. Is constant. Last point. As the temperature increases, it shifts towards the right. Hence, the most probable speed VMP decreases. Pop it up at this point. Ok you see the question that they ask into this. There are only few things that are important to this. The graph that you see. The y-axis is the fraction of molecule. This is the fraction of molecule. And this side we have the speed. Ok, fraction of molecule and speed. You see the graph, it goes like this. Ok, so this point you see. Corresponding to this point. What is this graph? The fraction is maximum, right? No, I can't even see. So it's like the volume of my fraction. You need to say there were 100 molecules. The speed of one molecule divided by 100 molecules. The fraction of that molecule. Ok, now you see corresponding to this point. The speed that we have is this, right? This is the speed. Now this fraction of molecules is maximum, right? So maximum number of molecules corresponding to this. The speed that we have, we call it as most probable speed. This is VMP. Most probable speed. Ok, and we have some velocity here also. You see, this velocity is the VRMS. Root mean square velocity. Root mean square velocity. No, randomly I have given you. Why it is more than this? Because we know VRMS is maximum. Then V average and then VMP. So with this relation, VRMS should be somewhere this side. And in between these two will have the averages, right? So average speed will be somewhere here. This is V average. Ok, so you see as the speed increases, VMP to VRMS. The fraction of the molecules having this speed decreases. That's what the point is that the fraction of molecules is very less with high speed. Similarly, the molecules which has very low speed is also very less. Ok, this is what the Maxwell observation. So fraction just means number of molecules. So suppose we have 100 molecules, right? Out of 100 molecules, 90 molecules will have the same speed and that speed is VMP. So fraction of molecules having this speed is what? 90 divided by 100. This is what this axis is. Understood? Ok. So now this graph is fraction of molecules at V and the speed. So based on this, what is this speed we have? What is this speed we have? They ask one question. Ok. So the molecule, the maximum number of molecules or fraction of molecules corresponding to that, we have VMP, most fabulous speed. And we know VMP is minimum. So obviously VRMS and V average will be more than this. So it will be right side of this point. Ok. So like this. We will discuss that. Ok. So this is at some temperature we have this graph. Ok. Now you see when we draw this graph at two or three different temperatures. Ok. So one point I have given you as temperature increases the curve becomes flatter, right? It shifts towards the right side. So when you draw this graph at different temperature, at one temperature we will have graph like this, another temperature we will have graph like this, and another temperature the graph goes like this. It is very simple and straightforward. As you increase the temperature, kinetic energy increases, kinetic energy increase, this velocity increases, this most fabulous speed also increases. And that is only possible when the graph shifts towards the right side. So you see if this temperature is T1, this is T2, and this is T3, so most fabulous speed is what? This is speed. This is VMP1, and T2 temperature most fabulous speed is this, which should be more than the most fabulous speed is T1 temperature because temperature is increasing, right? And VMP is this corresponding to this. So as the temperature increases you see the most fabulous speed increases and the graph becomes flatter. The fraction of molecule having this speed obviously decreases because the velocity is increasing. So lesser number of molecules will have the same speed. See the fraction of molecules decreases, but the most fabulous speed increases, okay? So that is what we can say at a given temperature we will have this kind of graph, but at different different temperature the most fabulous speed will increase. So if we can write here from this relation T3 should be maximum and T1 should be minimum and corresponding to this VMP3 is maximum VMP1. Understood? So temperature relation is another kind of question they ask on this. Second time. The last thing here. Suppose this is a full graph, we have different graph and we have four different gases suppose O2 and O2, H2 and Helium. So which gas represents which graph? So why is the root mean speed better? Root means speed better. I have discussed this, no we have just formulaized what? Rt by m, averages 8 RT by 5 m and most problem is 2 RT by m. So you can take the ratio VRMS is maximum you will get with this formula. This one? Where VRMS? You have done it in the last class. VRMS speed. VRMS V average and V most problem. Done. So question here is we have four different graph and four different gases we have. Which gas represents which graph? Helium will be the highest. Helium will be the highest. What highest? So lowest VLP. Helium. Hydrogen. Hydrogen. Hydrogen. Hydrogen. Hydrogen. Hydrogen. Hydrogen. Hydrogen. Hydrogen. Hydrogen. Hydrogen. Hydrogen, helium, end to a node. What is the answer? First one is hydrogen. Can you tell me one thing? For this graph VMP is what? VMP here is this. Hydrogen? Hydrogen? Hydrogen? Hydrogen. From this graph we can see what? This is the order we have. VMP4 is maximum right? VMP4 is the maximum? And what is the formula for most problem speed, VMP is equals to what? 2RT by m root over of it, so most travel speed is inversely proportional to the square root of the molecular mass, so the molecular mass is maximum called oxygen, it means it most travel speed should be minimum, so this is O2, this is N2, this is E and this is H2, this is how we assign the gas. Easy. This 2 three types of questions they ask, okay, no, no, no, I mean yeah the first part, till ideal gas, anyways those two will not add on that, after that they have involved the also now they ask theoretical question, conceptual question mostly done, is it clear? So what is the formula? 8 RT by 5M to the power of m Sir is it that 3RT by m? Yes, 3RT by m you can take a ratio and guess 3RT by m is maximum So what is the formula? So what is the formula? So what is the formula? No, RMS is 3RT by m Sir RMS is supposed to be the most Yes, 3RT by m is maximum So you have 3RT by m is maximum It is 8RT by 5M V RMS is root under 3RT by m V average is 8RT by 5M So you see it is 8 by 5 is 2. something you are getting here Right? And V MP is 2RT by m So obviously V MP is minimum RMS is maximum Okay