 In this lecture, we will learn the following things. We'll learn about the concept of temperature of a material body. We'll learn how to establish a scale and measure of temperature, about the response of material bodies to changes in temperature, and finally about heat energy as the underlying agent connected to changes in temperature. There are many things that are left unsaid in the first two semesters of introductory physics. We're only able to cover a prescribed range of topics, and that range can be described as follows. Motion, force, the laws of motion relating force and acceleration to changes in state of motion, energy, momentum, the conservation of energy and momentum, non-conservative forces, oscillatory motion, and rotational motion. That's typically what we get covered in the first course in physics. In the second course in physics, we're able to cover electric charge, electric force, electric fields, electric potential, and electric currents, and the combination of all those things into electric circuits. And then we explore magnetic field and force and the basic behaviors of light, such as geometric optics or interference and diffraction. Now, as a result of this in introductory physics, there is essentially no time to discuss the laws of heat energy, also known as thermodynamics. But nonetheless, thermodynamics is an essential foundation of modern physics. It ultimately was a branch of physics that helped to lead the way to quantum mechanics, the theory of the very small, and that is the next subject of this course. So in this part of the course, we will establish the second half of the foundations of modern physics, the concept of temperature, the concept of heat energy, and some of the behaviors of heat energy. We all have a fairly solid familiarity with the various concepts associated with thermodynamics. If you go outside on a day when it's cold, you feel like something is being pulled from your body en masse, as if the world around you is hungry to take something away from you and keep it for itself. This feeling, this sensation of the loss of something from our bodies, where we have to trap it to keep it in, is often what we call cold, or the concept of a cold temperature. Of course the flip side of cold is hot. There are environments, there are situations where instead we feel like something is being put into our body and we want to get rid of it. We might shed some clothing in order to help achieve this, to help regulate our own sensation of temperature. When the world around us is hotter than us, we feel that penetrating into our skin in a way that can be uncomfortable, it causes us to sweat and so forth as a mechanism to try to maintain our own state of body temperature. So cold and hot, these ideas are familiar to us even if we cannot articulate the physical reasons why these situations exist. Now connected to these two things is also the concept of establishing a numerical measure of the degree of hotness or coldness of an environment. So for example, the average human being, and this can vary by age and gender and a number of other factors, is typically comfortable, especially for intellectual work, office work, something like that. In a temperature range between 70 to 75 degrees Fahrenheit. Now a human being experiencing an environment where the temperature is observed to be less than that number will often express a feeling of being cold, chilly, chilled, needing to bundle up more to maintain their body warmth. On the other hand, a person who's subjected to an environment above that range, maybe 85 degrees Fahrenheit instead of 74 degrees Fahrenheit, will complain about sweating too much, feeling too hot, wanting to cool off in some way, maybe by drinking an iced beverage of some kind or maybe taking off a jacket if you're in a work environment, something like that. We have a concept of being able to measure the degree of heat or cold in the world around us, including the heat of our own body. Taking our temperature to see if we have a fever is another concept that is pretty familiar in the human world. Now connected to these sensations, these experiences, we have to come up with a series of critical issues and a plan in order for us to be able to quantitatively describe these scenarios of hot or cold. We have a conception of hot and cold. We have a conception that we can measure these things somehow. But we need to establish the basis for actually having that quantitative measure, that quantitative description of these concepts. How do you know something is hot? How do you know something is cold? How do you measure that? And how do you allow other people independently to establish the same scale of measure? Let us begin by establishing that scale on which we can quantify those ideas, like a room is too hot or a room is too cold. Let us then look at the origins of hot and cold and how the underlying concept is really tied to a fundamental concept called heat energy. We will close with a relationship between heat energy of a body and its ability to radiate energy away. But in this particular lecture, we're going to focus on temperature, heat energy, and the effects of heat energy not only on the temperature of a body, but the structure of a material body. Let's begin by establishing a measure of hot and cold. Now, consider the world around you. There are some phenomena in nature that appear to occur at very specific so-called thermal conditions. That is to say, if you could reproduce the environmental conditions under which a particular phenomenon occurs, that phenomenon would occur repeatedly, reproducibly, reliably. So for example, the freezing or boiling of a body of water. The only substance on earth that can exist in solid, liquid, and gaseous states under earth conditions is water. It's essential to life as we know it. And because it's able to coexist under a very narrow range of conditions as either a liquid, a solid, or a gas, it makes an attractive phenomenon on which to establish a range of behaviors that can be used to delineate a scale of temperature measure. Now, that said, of course there are materials other than water, and they also change in response to temperature. For example, in the opening lecture video for this series, I showed you the result of heating a bimetallic strip. Now I'll return to heating or cooling metals later. But we've observed already that two metals bonded into contact with each other will bend, curve, when exposed to a heat source. And that's because it's been observed that different metals expand and contract by different amounts, even exposed to the same change in hot or cold. The stretching and squashing can be used to make mechanical thermometers, devices whose physical changes are a proxy for temperature changes. So, for example, over here on the right is a meat thermometer. The thermometer has been placed into a bucket of water, and the scale on the thermometer tells us something about the temperature of that water at the moment the photograph was taken. So, for instance, if we're to assume that this thermometer is reliably measuring the temperature of the water in the bucket, we might look at this and say that, well, on the outside of the thermometer we have the Fahrenheit scale. And so this is coming in at approximately 90 degrees Fahrenheit. On the inside of the thermometer we have the centigrade or Celsius scale, and on that scale of temperature measure, it's coming in at more like 35 or so degrees Celsius. This thermometer is actually made by taking metal, coiling it, and as it heats or cools, the coil will compress or unwind, pushing the needle on the thermometer around in a circle. This is a mechanical thermometer, taking advantage of the expansion or contraction of a material to move an indicator on a scale. But how do we calibrate that scale? How do we establish a reliable, reproducible scale of measure of temperature so that any two observers anywhere in the world, if they follow the prescriptions to write down that scale, could reproduce the work of the other person? This would be a calibration, a reliable methodological process under which we can establish the same scale of measure of temperature. How do we do that? Well, one way we might do that is by imagining that we carefully control environmental conditions and make water freeze. And at the moment that we observe that the freezing process begins, the moment we can visibly see ice crystals forming in liquid water, we then call whatever we see on our measuring device a temperature of zero. We've established one point on the scale. Then we might take that same water and alter the environmental conditions and try to boil it, not make it go from liquid to solid, but make it go from liquid to gas. And at the moment we see gas bubbles escaping up through the body of the water into the air around us, we might again read off the scale of whatever device we're using to establish a scale, and call that reference point 100. Now, at this point, we have then used two reproducible phenomena to establish two points on a scale. You could argue that anyone else in the world, anywhere else in the world, could take a volume of water of a prescribed amount, expose it to the same environmental conditions that made it freeze, mark that off as zero on their temperature device, boil the water at the moment that process starts, mark that spot off on their temperature device as 100, and simply divide the space in between zero and 100 into 100 equal sized units. Now, of course, it's possible to bring the temperature of an object down below zero. It's possible to go below freezing in temperature. So you'd have to continue extending those equal sized units negative below zero and above 100. Now, stop and think about this for a moment. It seems perfectly plausible to take a material body like water, take it from a liquid state to a solid state, figure out where that happens on some measuring device, take it from a liquid state to a gaseous state, figure out where that process happens on the same device, divide that into 100 equal sized units, and then go above and below by equal sized unit amounts, and that gives us a full range of a temperature scale. What might be some problems with this way of establishing a temperature scale? Pause the video, think about this for a moment, and when you're ready to hear some ideas, go ahead and resume the video. Well, one problem with this idea is that the bottom of the scale doesn't have a physical meaning. It's possible to go to negative one degree centigrade. The centigrade system, or Celsius system, which you can base on the exact phenomena that I've just described, freezing or boiling water, has 100 equally spaced units between the freezing point of water and the boiling point of water. But it can also go negative. You can have a negative one degree centigrade or a negative one degree Celsius temperature object, a negative 20 degree. It's not obvious what the physical bottom of this scale is. It's clearly not the freezing of water. It's possible to cool things well below the freezing point of water. So it's not really clear what the physical meaning of all those negative numbers really is, and so that makes it kind of technologically unsatisfying. That's more of a wonky problem. A more serious problem is that the boiling and freezing of water depends strongly on some other conditions of the environment around you. Anyone who's ever tried to do something as simple as make pasta or rice at altitude in a place like Colorado or any other high altitude mountainous region knows the difficulties of cooking, especially boiling things at altitude, where the boiling point of water is actually lower than it is at sea level. It's much easier to boil water at high altitude than it is at low altitude because the air pressure is lower up there, and water is more easily able to escape a liquid body of water in its gaseous form. Cooking at altitude is a challenge, and one has to reinvent one's cooking at altitude, but that also means that water doesn't boil at the same place at altitude as it does at sea level. And so that means that a person who's 7,500 feet above sea level would establish a different centigrade scale than a person who's down at sea level or even below sea level trying to do the same thing. So rather, it is the convention of the system international, units of measure to employ not the centigrade scale, certainly not the Fahrenheit scale, but rather the Kelvin temperature scale. The smallest value of the Kelvin scale, which is zero, actually has physical meaning. We'll explore the concept of heat energy later and the origins of heat energy in a material body, but it is possible to take, hypothetically, all heat energy out of a material body. And when one does that, one is said to be at exactly zero Kelvin. Now whether that's actually physically achievable is a topic for another lecture, but conceptually the zero point of the Kelvin scale is exactly defined as the point at which a material body contains zero heat energy. Now that establishes one point on the Kelvin scale. Another point on the Kelvin scale is established not by using the boiling or freezing point of water, but rather what is known as the triple point of water. The triple point of water is illustrated here on this graph. The vertical scale of the graph is external air pressure outside the body of water. The horizontal scale of the graph is the Celsius or centigrade temperature scale. Pressure is given in both Pascal's, which are the system international unit of pressure, Newton's per meter squared, but also Barr, which may be more familiar to somebody who has taken a course in earth science or other such sciences. The top line here gives the same temperatures down here in centigrade, but in the Kelvin scale. And we see that the triple point of water is achieved at a particular pressure and a particular temperature. And so if you can find it, you have exactly reproduced both pressure and temperature conditions, and the triple point can be found at any altitude independent of the air pressure at that altitude by reproducing the pressure constraints. Now that said, the triple point of water, the coexistence point where ice and liquid water and water vapor all exist at the same moment, can be established under a specific set of temperature and pressure conditions, and makes a very reliable place to establish a temperature scale. Now for water, this only occurs when the exterior pressure, the force per unit area exerted by the air around the body of water, is 611.657 Pascal's, where one Pascal is one Newton per meter squared. On the Kelvin scale, this is defined to occur at 273.16 Kelvin. Now that may seem like a funny place to specify your second point, but it's a place of convenience. It happens to be the place where the temperature is roughly zero centigrade or zero Celsius at this air pressure. So it has a more convenient interpretation on the Celsius scale, but on the Kelvin scale, it occurs 273.16 Kelvin above zero. So that's how one could establish a temperature scale. And I mentioned earlier how one might establish a mechanical thermometric basis, a thermometer that responds to more heat or less heat, higher temperatures or lower temperatures in a mechanical way, allowing you to read off points on a scale. And that's because materials change physical dimension when exposed to changes in temperature. This principle is used to make many kinds of thermometers. For example, you could use a liquid basis for a thermometer. You could take a fixed volume, like a tube, so a cylindrical shaped volume, and fill it with some amount of alcohol. Now alcohol's volume as a liquid readily changes with temperature. It expands when heated. It contracts when cooled. So if we confine it to a vessel, what we'll observe is that because it can't push out to the left or to the right anymore, and it can't go down below the bottom of the vessel, its level will rise or fall as the top of the volume of the alcohol is moved up or down by the expansion process. So all we have to do is watch where the top of the volume of alcohol is and mark it off, find our two points, and use that to establish our temperature scale. Now metals similarly change length and volume, and this can be used to make a mechanical thermometer. I described one of these earlier. You could make a metal spring, and that spring will tighten up when cooled and expand out when heated. And as a result of that, if you affix some kind of thing to it that can rotate in response to the expansion or contraction of the spring, you can have a moving marker that indicates temperature on a scale. You just have to figure out where the calibration points on the scale are, and you're good to go. Now let's think empirically, observationally, about what is noticed about materials and their response in physical dimension, for instance one dimensionally, their length for example, how that changes with changes in temperature. And it's observed that if one has a material of original length L, and we change its temperature by some amount delta capital T, then its length will change by an amount delta L, and it's proportional to the product of L times delta T. That is to say the change in the length is proportional to L multiplied by the change in temperature, whatever L the original length was. And so because it's proportional, it means there is an empirical, that is one that has to be determined by experiment, coefficient that is the exact multiplicative relationship between L times the change in temperature and the change in the length. And that coefficient is known as alpha, the coefficient of linear expansion of a material. It tells you how much in one dimension the length of a material will be changed by changing the temperature by a certain amount. Now because it's an empirically determinable thing that varies by material, you have to do an experiment. Expose a material to a specific change in temperature, note the original length, note the final length, compute alpha by looking at the change in length. Now if one dimension can change, say length, then so can depth and height, and because materials are three dimensional, in fact each length will separately expand. And finally you can describe the whole volume change of a material by delta capital V, and that's given in proportion to the original volume times the change in the temperature. Here we have the coefficient of volume expansion denoted by the Greek letter beta, and if you crunch the numbers on this, you'll find out that beta is exactly equal to three times alpha. So if you know the change in one dimension of a material, you can predict the change in the volume. If you know the change in the volume of a material, you can figure out how much each length of each side has changed as a result of that. They are nicely related to each other. Over here on the right I show you a way in which expansion is taken into account in engineering the world around us. If you build a bridge, say across a river, and you make it out of a single piece of material, then depending on how hot that bridge gets or how cool that bridge gets with respect to the temperature at which it was constructed, the bridge material might expand or it might contract. Now, this may not be a problem if you have an infinitely flexible material, but concrete and steel are not infinitely flexible. They fracture at some point if you put them under enough pressure. And so it's very much conventional to build the reality of expansion or contraction into, say, bridge construction by putting in these expansion joints. There are places where cars can drive over the gap safely, but the gap is large enough so that in the summer when the bridge heats up, the gap will close without crushing the material together, and in the winter, when it cools, it will expand allowing the bridge to change its shape without causing the bridge to fall apart in the first place. This photo was clearly taken late in the year during autumn temperatures when it's much cooler. We can see here that the pieces of the bridge have each contracted in length, opening the gap up between the two segments of the bridge shown here. Now, let's begin to think about what it is that causes changes in temperature of a system. Temperature isn't some spooky thing. It took a long time to figure it out, but eventually what temperature changes are caused by and what the nature of the thing that causes those changes was identified. Now, we can begin by getting some terminology down that will help us to talk about really any situation in which we have heating or cooling that can happen. Let's begin by defining an object like a cup of coffee or a glass containing an iced drink as an object that's embedded in a larger space, let's say the air in the room around the hot beverage or the cold beverage. In this case, we would call the object embedded in this larger space a system. The coffee cup shown here with what probably started out as liquid that's hotter than room temperature, that would be a system. The glass with ice cubes in it, possibly some soft drink or something like that being contained in the vessel and cooled below room temperature by the presence of these ice cubes, that would also be a system. Now, the enveloping space, that is everything else in the volume around these two systems, that would be defined as the environment. Now, there are some observational facts that are noted about objects, systems that start off at various temperatures. So, let's imagine we observe systems that begin at some temperature, T with a subscript S to denote it as the temperature of the system. Those objects are then placed in an environment. Now, that environment may have its own temperature, T with a subscript E to denote the environmental temperature. Observationally, if you repeat these experiments by taking a hot cup of coffee and putting it in a room hot, meaning it's clearly warmer than room temperature, or taking a cold beverage and putting it in a room where it's clearly cooler than room temperature, if you repeat those experiments over and over and over and over again, you'll begin to make some recurring observations about these systems. First of all, if the system temperature starts out less than the environmental temperature, then you will observe over time that the system temperature will increase until finally the system temperature and the environmental temperature are equal to each other. And at that point, the system temperature will cease to change. It will increase no further. Alternatively, if the system had begun, like a hot cup of coffee, at a temperature that was greater than the environmental temperature, then over time you will observe that the system temperature will decrease until such time that the system temperature and the environmental temperature are equal. And at that point, the system temperature will cease to change. Now this special place where the system temperature is equal to the environmental temperature, this is referred to as the point of thermal equilibrium. That is the point where the two systems have the same temperature and no further temperature changes are observed to occur. Let me show you one such experiment. I have here a coffee cup containing hot coffee. I also have another coffee cup containing water with ice cubes in it. Our experience tells us that compared to a typical room temperature, the liquid in the coffee cup with the coffee in it will be hotter than room temperature. And the cup with the ice water in it will be colder than room temperature. Now let's imagine I rig up these two cups of liquid, each at different temperatures relative to room temperature with some thermometers. I actually have a nice handy meat thermometer with two probe ports. One probe is placed into the ice water and one probe is placed into the hot coffee. And as you can see, two different temperatures are registered for the hot coffee and for the ice water. At the particular moment shown in this still image, the ice water was at a temperature of 41 degrees Fahrenheit. The hot coffee was at a temperature of 149 degrees Fahrenheit. And the room was at a temperature of about 72 to 73 degrees Fahrenheit. Now what I then did was I did a time lapse video watching these two cups of liquid and their temperatures over about five to six hours. And you observe something fascinating. The hot coffee over that period of time decreases in temperature until its temperature matches room temperature and then changes no further. The water with ice in it, it lags in how quickly it changes temperature. But once the ice cubes are melted away, the water in that cup then all entirely in liquid form begins to move much more quickly toward room temperature. Although in the time window I allotted for it, it never matched room temperature. It took energy to melt the ice into liquid and then raise the temperature of all the liquid up to room temperature. But one key observation you can take away from this experiment is that neither the coffee nor the ice water ever achieved a temperature that went beyond the equilibrium temperature, which happens to be room temperature in this case. The coffee never cooled below room temperature and the ice water never went above room temperature. What was discovered was that the cause of all of this is that energy is transferred between the system and the environment in the above examples. So for instance, in the case where the system temperature started out lower than the environmental temperature, what's observed is that energy is transferred from the environment into the system, raising the temperature of the system until such point as the two temperatures are equal and the transfer stops. The energy that's transferred between the environment and the system is referred to as heat energy. A system that's hotter than its environment will give up heat energy to its environment until their two temperatures come to be the same and the transfer of heat energy will stop. A body that's colder than its surrounding environment will receive heat energy from the environment until the two temperatures become equal and the transfer will stop. If a system and an environment start at the same temperature, no transfer of heat energy will occur and their temperatures will remain equal at all times. The quantity of heat energy that's transferred between the environment and the system is denoted Q. U is used for potential energy, K is used for kinetic energy, Q is used for heat energy. Now let's think a little bit more about matter absorbing or releasing heat energy. Different material objects composed of different substances, for instance elements like hydrogen gas or oxygen or helium gas or molecules like water, dihydrogen monoxide, alloys such as brass. If you expose them to the same amount of heat energy Q, you will find that they react temperature-wise in very different ways. Now the reaction can be measured by observing how the temperature changes with the absorption or release of heat energy from or to the environment. That is to say what you can do is you can watch as an environment and a system exchange heat energy changing the temperature of the system and while that process is ongoing observe the physical properties of the material system. So for example you could try depositing the same number of joules of heat energy to a metal or to water and you'll find that even for the same masses of metal and water you get very different changes in temperature. Metals will readily take up that is conduct heat energy taking it up into its volume and that results in a rapid change in temperature. Think about touching a hot metal pan that's sitting on a stove top exposed to an open flame. You know that if your hand makes contact with the metal, the metal will very readily transfer heat energy to your hand which can cause a serious burn because the heat energy is of sufficient quantity to physically damage the tissues in your hands. In contrast, if you wanted to protect yourself from the metal and its dangerous level of conductivity when it comes to heat energy in this case you might instead wrap your hand in a silicone glove. Now silicone is a material that even if it were the same mass as the pan does not take up heat energy very readily. It's a very poor heat conductor and as a result of that it's great for protecting your hand. Touch directly with the silicone glove a very hot surface and it takes a very long time for that heat energy to penetrate through to the skin of your hand whereas it can be almost instantaneous for touching the metal itself. So already because you use things in the world around you to protect you from changes in temperature that are too rapid you have a sense that materials of different kinds will respond even to the same amount of heat energy with different changes in temperature. Water is not as conductive as metals, it's actually an excellent insulator, it's a poor conductor of heat energy and so for water you'll find that the same amount of heat energy can be taken up with not as dramatic change in temperature as compared to the same mass of a metal like iron or aluminum or copper. Now this is described mathematically by the following equation. The amount of heat energy that you deposit in a material will cause some change in temperature and the change is proportional to the amount of heat energy but varies by material and so empirically you have to assess what is the coefficient of proportionality between q and delta t and this coefficient is known as the heat capacity of a material. It's the amount of energy required to get a specific change in temperature for that material. A large heat capacity corresponds to a smaller change in temperature and vice versa a material with a small heat capacity will give you a very big change in temperature. Now don't let the terminology fool you. Heat capacity is not a measure of the maximum amount of heat energy a material can absorb. In fact so far as we know there is not a limit to the absorption of heat energy so long as you can maintain a temperature difference between a system and the environment you can keep transferring heat energy from the environment into the system or vice versa. Phase changes might occur. You might put so much heat energy into a block of copper that it vaporizes into a gas of copper atoms. You might put so much energy into the gas of copper atoms that you tear the electrons off the atoms and create copper ions and a bath of electrons. This is a state of matter known as a plasma. But it doesn't stop the transfer of heat energy from occurring as long as the temperature of the system in this case is less than the temperature of the environment. When they reach equilibrium that is when the heat energy transfer stops. It is nothing to do with the material properties. It is not to do with a limitation imposed by the heat capacity. The heat capacity just tells you about the capability of the material to respond with a temperature change for a given amount of heat energy. Now repeating the equation here that the amount of heat energy that you deposit into a material will have a corresponding effect on the temperature of the material and the proportionality of that effect is given by the heat capacity. The more mass of material that you supply if you take that copper block I mentioned and double the amount of mass that you're exposing to the same amount of heat energy you'll find that it can absorb more energy before achieving a given temperature change. So it's actually convenient to instead define something known as the specific heat of a material, lowercase C. And that's the amount of heat energy per unit mass needed to achieve a given temperature change. So the above equation then becomes that the heat energy will be equal to the mass of the material times the specific heat of the material times the change in temperature. And big C, the heat capacity, is just given by the product of the mass of the material and its specific heat. So in this lecture we've learned about the concept of temperature of a material body and how to establish a scale and a measure of temperature by looking for reproducible phenomena in the world around us, establishing the conditions for their reproducibility and using those reproducible phenomena to mark points on a device whose physical properties are altered in response to more heat or more cold. We've then explored a little bit about the response of material bodies to changes in temperature and in particular we focused on changes in dimension of a material without it changing phase that is without it going from solid to liquid or liquid to gas. We've thought about how those materials can stretch or expand their volumes in response to changes in temperature and the proportionality of that and how that depends on the material in question. And related to this we've then looked at the underlying concept, the thing that's actually transferred from an environment to a system or a system to an environment that triggers changes in temperature and that thing is a kind of energy called heat energy and denoted by the letter Q. It's the underlying agent that's connected to changes in temperature. It's the thing that can be moved from body to body and that in response the temperature of the bodies change. The degree of change of temperature depends on the properties of a material body and these properties are summarized by a constant of proportionality between Q and change in temperature known as the specific heat and specific heat combined with the mass of the material in question will allow you to quite easily relate heat energy and changes in temperature and the degree of each of those things for a given material body.