 Hi, I'm Zor. Welcome to a new Zor education. I would like to continue talking about heat as the form of energy. The previous lecture was kind of introductory, where I introduced the terms of heat, temperature in a more qualitative way. Today, I would like to put some more quantitative characteristics of heat and temperature. Now, this lecture is part of the course called Physics for Teens. Physics for Teenagers. It's presented on Unisor.com website. If you wish this lecture somewhere else, like on YouTube, for instance, you found it, just be aware that this lecture is just a part of the whole course. And the course is presented on the website Unisor.com. The site is free, by the way, no strings attached, no advertisement, etc. Now, there is a prerequisite for this course, which is called mass for teens on the same Unisor.com website. And I do recommend you to refresh your mass before you do physics. Well, primarily, for instance, like vector algebra and calculus, they are a must for this course of physics. All right. So we talk about heat, we talk about temperature. And now I would like to connect with some quantitative characteristics, these properties with something else, which is kind of more familiar. In this particular case, it's a speed, basically. Now, we all know that we are talking about molecules which are moving inside the object, whether this is a solid or a liquid or gas. And the movement of these molecules actually causes the heat to be observed inside. Now, I was talking a few times about the heat and I use the term intensity. So intensity of the movement of the molecules inside the object is actually related to basically something which we call the heat or something which we can measure with a thermometer as a temperature. Now, what's very important to understand is that this is not really a proper definition. The definition of the temperature is something which we can measure with a thermometer. So without the thermometer, we cannot talk about the temperature. Now, if that's true, then how is this our creation, basically, a thermometer is an instrument which we have created? How is it related to some objective characteristics as movement of the molecules inside the object? Now, the purpose of this lecture is to demonstrate this relationship between the temperature as we measure it and the intensity of the movement of the molecules. And when I'm talking about intensity, I primarily talk about speed. Okay, now, since we are talking about relationship, we need some kind of an equation, right? Here is the temperature, here is the speed of the molecules, how they are related. Well, that's not easy actually to talk in these terms, primarily because molecules inside of an object are numerous. I mean, they all are moving in different directions, kind of chaotically, especially in case of gases, for instance, not as much in case of crystallized metals, for instance. But in any case, they are moving in different directions with obviously different speed, etc. Now, when we are measure the temperature, we have on the thermometer a concrete temperature on some scale, whatever the scale is Kelvin scale or Celsius or or Fahrenheit. So how are they related? I mean, this is something like a temperature, something like a one number, like 10 degrees Celsius, right? And molecules are numerous. Okay, let's just talk about how the thermometer is actually created. And I will talk about the simple thermometer, which is kind of classical thermometer, the one which has certain reservoir and the tube. And this is mercury inside. And when the temperature of this thermometer is increasing, this level of the mercury in the tube also increasing or decreasing the temperature decreasing. Why is it working? And what is basically the connection between the temperature and and the rise of the thermometer? Okay, here is what's very important. Let's talk about something which we have observed that this particular mercury is increasing basically in size when it's heated up. Now, why? This is the most important question. Why? Well, here is the model which probably explains it in a relatively good level. At least it satisfies my curiosity. Just think about all the different molecules inside this object inside mercury in this particular case, they are moving in all the different directions with different speeds, etc. However, if we are increasing the amount of heat, they start moving faster. That's what we were talking about that the heat is actually the intensity of the movement. Now, if you imagine the molecule which is flying among other molecules with a higher speed, but what prevents it from basically going outside of this wall or outside of this level of the mercury? Well, other molecules, so there is a collision every time it collides with something else, it changes the direction and goes back. Collision with the wall, and collision with the surface. Well, every surface has certain things which we call tension, surface tension. And there are reasons for this surface tension because the molecules are kind of gravitating down in this particular case and there is nothing which pulls them up. So if this is the level, these molecules, they are attracted down, but not up. There is no upwards attraction. However, if the molecule is inside, then it's actually attracted to all the different directions. So the surface molecules are gravitated down so that creates certain tension. So this tension, it works like a net, which is on the top of the surface. And it does not really allow molecules to go outside. Well, up to an extent. I mean, if the molecule is moving very fast, it really goes against this net and the net is bent a little bit upwards, right, like this. And then another molecule. So it bends this way. And then the molecules from inside are bumping to these molecules. And that's what actually raises the level of the of the mercury in this particular case. So this is something which explains why the the objects with higher intensity of the movement of the molecules, they are tend to increase in size, because the molecules are moving faster, and they're pushing harder to all the different directions. Now, these directions are fixed because there is a boundary, the walls, actually, like a glass wall, for instance, this is soft, so it goes up. So there is definitely a connection between the intensity between the speed of the movement of these molecules and the level of the mercury in the thermometer. So how are they related? Here is my analogous kind of a model of this process. Imagine you have certain force which prevents them to go all the way up. Well, if the molecule has certain amount of energy, and it goes, let's say, this way, it actually is obstructed by other molecules and by the surface tension. Now, so there is a force which basically prevents the molecule to go all the way up. Now, it's analogous to, for instance, if you are on the ground, and you have a stone which you throw upwards, what is the force which prevents it to go all the way up? Well, the force is gravity in this particular case. So I'm trying to use this analogy to explain what happens in this case. So there is a force which basically prevents them to go all the way up and fly away. And obviously, one of the forces is gravity. That's true. Another force is this resistance from other molecules and from the surface tension. So this force actually finally slows down and stops this molecule or maybe reflects it to some other directions instead of going all the way up. So what happens in this case? In this case, if we throw this stone with certain speed v and the stone has a mass m, what happens with from the energy standpoint? At this level, there is no potential energy relative to the ground. And there is only the kinetic energy, right? Now, then it goes up, it slows down because the gravity pushes it down. Same thing as here, the resistance of other molecules and the and the tension from the surface actually, it slows it down, this particular molecule which wants to fly away, and it stops eventually. Same thing here, the gravity eventually stops it. It stops it on certain height. On the highest point, the kinetic energy is zero because the speed is zero, right? But there is a potential energy and it's equal to mgh. And we know that the full mechanical energy is preserved. So in this case, this is potential. So in this case, we have only kinetic energy and this is the full mechanical energy because the potential is zero. In this case, full mechanical energy is this because kinetic energy is zero. So these guys must be equal to each other. So mgh equals to mv square over two, from which h is equal to v square divided by two g, where g is the free fall acceleration. So what do we see here? That the height of the maximum height of the stone, when you throw it upwards, depends on the square of the speed. It's very, very similar to this situation. So if you take a particular molecule, and let's say it goes vertically up because of all because of all these collisions and surface tension, etc., it slows down. And the amount on which it allows actually to go through this upper surface, this amount, it bends it upwards, it actually depends on initial speed, it reached when when you when you're here. So all I'm saying is that the amount of the rising of the of the mercury in this particular case depends on the square of the speed. But not why it depends on the square of the speed because the square of the speed is actually a reflection of the kinetic energy. It's energy, right? Now, whenever you are bending upwards, the surface, there is a tension which is actually acting on the molecule in a very similar way to this gravitation acting on the stone. So the potential energy of this particular molecule is rising because it's like a rubber net, basically. So at the very top, when it stops actually bending, it has certain potential energy because this rubber net will push it down again with certain speed. So the potential energy is accumulated and the kinetic energy is going down. And on the top, the process is reversed. Potential energy of this rubber net, which is the surface tension, starts converging into kinetic energy and pushes back down. Well, same thing is in case of the walls, actually. But the wall is maybe a little bit harder than the surface. And you don't really see it on the same scale. But it's still the same thing. What happens when the the molecule hits the wall, the same thing, actually, the wall bends a little bit. And then it reflects it back. So we're talking about elastic reflection. Same thing with any other molecules. The molecules are, again, are elastically reflecting against each other. What's very important is this conversion from potential energy into kinetic and from kinetic to potential. kinetic energy is always proportional to the square of the speed. And potential energy is always proportional to deformation. In this case, it's the height above the ground. In this case is some kind of deformation of this horizontal level. In the case of the wall, there is a tiny deformation of the glass, which basically is causing this elastic reflection. So that's what basically is the most important conclusion of all this explanation that our temperature, which is basically related to this deformation, because we see this deformation, right? It's supposed to be proportional to the square of the speed. Well, that's not exactly correct because we're talking about speed of one molecule. And this is the temperature, right? So we cannot talk about one particular molecule, we have to talk about the average energy of the molecules, average square, average of the square of the velocity. Now, if we have somehow measure this average square of all the molecules inside the thermometer, then that would actually be the corresponding to a temperature. Now, when we're talking about proportionality, we obviously have to assume that if this is equal to zero, then this is equal to zero, and vice versa, right? So that means actually that we're talking about the Kelvin scale, when absolute zero, which is like temperature when nothing actually is outside as a source of energy, you're deep in space somewhere, there are no stars nearby, no sources of energy, that's the absolute zero. And when you have this temperature of absolute zero, molecules will just stand still. If you have a metal, the metal will be completely frozen, so there is no inner oscillation of the molecules. If you're talking about liquid, liquid is supposed to be completely solid. Everything and gas also will be completely converted into a solid state, like helium, for instance, we know we can convert gas, helium into liquid, under a very cold conditions. But if we will go even colder, then the liquid becomes solid. And when it's solid, nothing moves inside, all the molecules are standing still. So this is very important thing. And in this particular case, we're talking about Kelvin scale of the temperature. Now, obviously, depends on the size of the degree, but this is coefficient of proportionality. So the units determine the coefficient of proportionality, but it should start with zero. So zero speed of the molecules means that there is absolutely no temperature at absolute zero. And absolute zero temperature means that there is no movement of the molecules inside. And again, you have to consider this as average speed of all the molecules, square average of the square of the speed, which means that if you have, let's say, one molecule, another molecule, and and molecule, that's their average of squares, quadratic average, sometimes they call it quadratic average. Alright, so that's basically the result of this lecture, that the temperature in degrees of on the scale Kelvin is proportional to the average of the squares of the molecules. By the way, what's interesting in this particular case, it does not depend on the mass of the stone. So that's actually true for the molecules as well. Now, this is the preparation for a little bit more complex, a little bit more involved quantitatively into theory into kinetic theory of ideal gases, which will be the subject of our next lecture. So that's it for today. Thanks very much. And read all this on the explanation, which every lecture has explanation and knows if you wish on the website. And that would be very helpful, obviously. Other than that, that's it. Thanks.