 Hi, I'm Zor. Welcome to Unisor Education. I would like to talk about how to measure heat, how it used to be measured, how it is measured right now. Well, this lecture is part of the course, Physics for Teens, which is presented on Unisor.com. And on the same website you can find the prerequisite to this course, which is Maths for Teens. Maths is very important for physics, as you know, especially something like calculus, vector, algebra. Now, if you found this lecture somewhere else on some other website instead of Unisor.com, let's say on YouTube, for instance, well, I do suggest you to use Unisor.com instead. First of all, because on Unisor it's a course, not just one particular lecture, but one particular topic. So it's a course, which is obviously logically dependent upon itself. The lectures are ordered in the proper order, etc. Now, every lecture has also a textual explanation on this website on Unisor. And also there are exams for those people who would like to challenge themselves. So it's much more beneficial for you to study using the website, Unisor.com, rather than any kind of other website, where just the lecture, basically, or only the video presentation, actually, is present. And by the way, the website is completely free, there are no advertisements. You don't even have to sign in if you don't want to. For those who do sign in, there is a possibility of actually studying under a supervision of a teacher or a parent. But anyway, that's not necessary. No financial strings attached at all. All right, so we'll talk about heat. Well, you see, people did know about the heat significantly earlier than they realized something about molecular movement, theory, kinetics of molecules. So the heat is actually related to mechanical movement of the molecules inside the body. So since they didn't really know about anything about kinetic energy of the molecules, they approached heat completely differently, as a special kind of an entity, physical entity, and they wanted to measure it. So how to measure the heat? Well, they have actually discovered experimentally that if you take one gram of water and you would like to increase its temperature from, let's say, 20 degrees Celsius to 21 degrees Celsius, certain amount of heat actually will basically be consumed by this gram of water. So they have decided to use this as a unit of heat. So amount of heat which is needed to heat by one degree, one gram of water, was basically set as a unit of heat measurement. Well, obviously when the water actually cools down from, let's say, 30 degrees Celsius to 29, it releases certain amount of heat, which is exactly the same. Now, it was not easy to establish the fact that amount of heat necessary to increase the water temperature from 20 to 21 degrees is the same as, let's say, from 50 to 51, at least approximately the same. So basically all these efforts were directed towards explaining really to themselves that there are certain laws actually, and the heat can be actually measured using this unit of heat, which is amount of heat necessary to heat up the water by one degree Celsius. Okay, so they have established this, obviously not without flaws, because they probably didn't realize it in the very beginning, at least, that the amount of heat to heat the water by one degree actually depends on many different factors. Well, for instance, the purity of, chemical purity of water. It also depends on the place on earth where exactly you measure this and on height above the earth. There are certain flaws in this, but to the extent of precision accepted at that particular time, it was fine. So they have established one unit of heat, which is called one calorie, and the calorie is amount of heat needed to heat up the water by one degree Celsius. Okay, so that's basically definition of a calorie. Now obviously there is another unit which is also kind of used, kilo calorie, which is 1000 calories. So we have one calorie equals to amount of heat needed by one gram of water plus one degree Celsius. Now one kilo calorie is obviously 1000 calories. So that was established, as I was saying, long before kinetic theory of molecular movement was applied to the heat. Now then the science developed into understanding that the heat is actually a molecular movement. It's an intensity of the molecular movement, that the temperature is actually average kinetic energy of the molecules. So mechanical energy is measured in our standard system in joules, right? Joules, which is one joule is actually one Newton times one meter, right? Where Newton is kilogram meter to second square, right? This is the force, which is according to second law of Newton is mass times acceleration. Now this is the distance, this force is actually acting, so that's how you derive one joule. Alright, so we have this one joule as a unit of energy, mechanical energy in this particular case, which is actually an essence of heat. Heat is mechanical energy of the molecules. So it was necessary to establish certain equivalence between the historical measurement of the heat in calories and something which we basically know as the unit of mechanical energy in the system of measurement called C, Systema Internationale. So how can we establish the correspondence? How do we know that certain amount of energy which we can actually supply to the molecules, let's say water of some other objects, that it's actually converted into certain amount of heat measured in calories. And here is a very clever experiment. Let's imagine that you have a reservoir of water standing on the ground of the earth. Now what if, let's say the mass of the water is M, capital M. Now I have a small stone which is on the surface of this. I'm just holding it right on the level of the surface of this water. Now this stone according to regular mechanics has potential energy because it's about the level of the earth, right? So if this is H, then M times G times H is potential energy of this stone. Now let's let it go so the stone goes down. Here is our stone. Now what we used to have is no kinetic energy. The stone was basically standing still and potential energy. Now when it's on the bottom of this reservoir it has again no kinetic energy and no potential energy because on the level of the ground, right? So where is the energy going? Obviously this potential energy was converted into kinetic energy of the stone itself. Which means it moves basically, right? Since it's moving down, it's falling down within the water. It has its own kinetic energy. But then at the very end there is no kinetic energy. So the kinetic energy this potential is converting into as the stone is falling down is actually transferred into kinetic energy of the molecules of the water, right? Because it should push these molecules around while it's falling down. And at the very end basically all the kinetic energy which it possessed which is basically result of the potential energy it had in the very beginning is distributed among molecules of the water. And since the water molecules started moving it means that the temperature must have been increased, right? So we have certain increase of the temperature, delta T of this water after the stone comes down. And we can measure it. T means it's temperature, right? Temperature can be measured in degrees of Celsius or anything else. So the water has increased the temperature and the amount of heat which is actually amount of kinetic energy of the molecules which is supposed to be equal to the original potential energy. They are supposed to be equal. So this is the same as mass of the water times increment of the temperature. Now, but this is in joules and this is in calories, right? Because one gram times one degree is one calorie. So when we have total amount of water, let's say in grams in this case and the difference in the temperature in degrees of Celsius if we multiply we get the calories. Now, if the same we will have here this is kilograms this is 9.8 meters per second squared this is meters so this is joules. So that's how by comparing this, I mean I put this equal sign but it's not really equal sign because it's different units of measurement. So it's supposed to be basically the basis for conversion so it should be some kind of coefficient here. Coefficient which converts calorie into joules or joules into calories. Now, by making this experiment measuring lower case M which is mass of the stone GVNO HV again measure M mass of water in grams and delta G in degrees of Celsius measuring this and this we can establish what is the ratio factor which we have to multiply this to get this or this to get that. And finally it was actually established that one calorie is equal to 4.184 joules. One calorie is 4.184 joules. Well, obviously this is I would say a little bit approximate a little approximation because as I was saying before it's very difficult to make this experiment clean. It all depends on many different factors like chemical composition of the water, purity of the water, place on earth where we conduct the experiment because the G actually depends on this. So within certain precision let's put it this way reasonable precision you can basically assume that for whatever the calculations historical unit of measurement of the heat which is calorie is related to scientific measurement of the energy by this particular equation just slightly more than 4 joules comes into one calorie. Okay, so now traditionally certain heat is still measured in calories. For instance the amount of energy in food which is somehow converted by our body into energy is measured and by the way I have no idea how they measured it but anyway they measured certain amount of energy in every food. It's traditionally measured in kilo calories which is 1000 calories. However, they call it large calories. So kilo calories sometimes it's called large calories and plain calories is called small calories. So basically when they're talking about energy in food they're measuring it in kilo calories or large calories and in practical life they just skip the large. So they're saying it's calorie but it's not really this calorie it's really kilo calorie it's a large calorie. This is misunderstanding but whatever it is it is. That's kind of a traditional thing. So when they're saying that this particular sandwich contains this particular number of calories it actually means kilo calories and every kilo calorie which is 1000 calories contains 4184 joules. So that's kind of a I would say misunderstanding. Now since the word calorie is always related to water which is heated by one gram of water heated by one degree of Celsius or Kelvin doesn't really matter right because the unit's exactly the same the size of the unit. It's not as scientific as people would prefer. So for purely scientific reasons what physics have decided to do is they cannot really use the word calorie by itself because again it's related to water etc etc. So they have a unit which is called thermo calorie. Thermo calorie. It's just a new word which is supposed to replace the word calorie just because this is a scientific definition and this is a very experiment dependent definition. And this by definition is equal to 4.1833 joules. So basically they have established a new unit of measurement which is equal to 4.1833 joules and call it a thermo calorie which is approximately equals to a calorie but the calorie is kind of a little bit different under different conditions so they have decided okay this is a scientific unit and if anybody wants to measure anything scientifically in calories this is how it's supposed to be done. You don't have to remember it obviously but again you understand the difference between purely scientific definition which is this. Without any kind of experiments no water reservoir, nothing like this. Just by definition established one thermo calorie is equal to this end of story and the calorie which is kind of an experiment dependent and approximately its value is somewhere around this but again under different conditions it can be a little bit more, a little bit less than 4.1834. In this case it's just a little bit less. Basically that's it, that's how the heat is being measured again historically in calories and kilo calories, large calories, small calories, large is emitted and scientifically it's basically in joules or if you really want to go into the calories this is the coefficient of transformation. I do suggest you to read the textual part of this lecture on physics for teens you just go to energy, the heat and heat measurement sub-chapter. That's it for today thank you very much and good luck.