In this video, I'm going to return to our energy theme, introduce ways that energy can be transferred between the surroundings and the system, and briefly discuss heat capacity and specific heat capacity. Concepts you will need if you would like to tackle this week's advanced problem sets. We need to have a frame of reference for this energy flow. And our frame of reference is the system. The system has clearly defined boundaries, the boundaries are shown here as this pink box. And we can have energy either flow into the system, or, on the flip side, we can have energy flow out of the system. Everything that is not part of our clearly defined system and its boundaries is considering to be part of the surroundings. It could be possible that the air is part of the surroundings, or perhaps, if our hand is outside of a container that we've designed as a system, then maybe our hand would be part of the surroundings. So the surroundings is everything in the universe that is not part of the system. We can calculate the energy change of the system if we know the system's final energy and the system's initial energy. If energy is flowing into the system, such as on this picture. Is Delta E going to be a positive or a negative value? Think about that in the context of this equation. I've got energy flowing into the system, so is Delta E a positive value, or a negative value? That's right. If energy is flowing into the system, then from the system's perspective, it's gaining energy. So Delta E is a positive number. On the flip side, if energy is flowing out of the system, then from the system's perspective, it is losing something, and delta e is a negative value. So this is actually pretty easy to remember. If the system is losing something, then from its perspective its change in whatever that is, and it could be temperature or it could be energy, for example. Is negative. Let's do some practice and apply this equation delta E equals to final energy minus the initial energy. For each of these five examples, I'd like you to indicate whether the change in the energy is a negative number, a positive number, or equal to zero. Assume that the system is the object mentioned in the problem, and that everything else is part of the surroundings. The first system is a system of water. And that water is being heated, and it's changing its temperature from 25 degrees Celsius to 50 degrees Celsius. Is the system have a positive change in energy, a negative change in energy, or is the energy change equal to zero? Correct, for that system with the water heating up, the energy change is greater than zero, because from the system's perspective, it gains some energy. Here's one that's a flashback to last week's application of Coulomb's Law. In this case, when moving a cation away from an anion. So you need to think about if those opposite charges want to be close together. That would be the low energy state for opposite charges. What do we have to do, then, to move them apart? That's right. In order to move them apart,we need to put energy into this system. So again, the change and the energy of the system is positive if we move the cation from the anion. Number 3 involves a phase change. There is some water vapor. One gram of water vapor is condensing to form liquid water at 25 degrees C. So, the initial state is water vapor and the gas molecules are moving around rapidly in the atmosphere. And the final state is liquid water, where the water molecules are not moving as rapidly, and they're also not moving over as much of a great area. What is the sign of delta E for that situation? Correct, in the case of water vapor condensing, the change in the energy of the system is less than zero, or negative. Here is a physical example number four. If a ball is on the table top, precariously at the edge of the table. Would it's energy go up or down if we move it from the table top to the floor? Is Delta E for this system going to be negative or positive? Again, this one is negative. Finally, for number five, we're going to take a piece of zinc, solid zinc metal, we're going to start that piece of zinc at 25 degrees Celsius, heat it up to 75 degrees Celsius and then cool it right back down to 25 degrees Celsius. For that entire process, the change in the energy is equal to zero because the energy of the zinc at the end of the process is the same as it was at the beginning of the process. These examples bring us to the first law of thermodynamics. And that is conservation of energy. Energy is neither created nor destroyed for all processes. Another way of saying this is that the change in the energy of the universe is equal to zero for all processes. This equation can be written another way. The change in the energy of the universe, equals the change in the energy of the system. Remember system is kind of implied, if it's not written. Plus the change in the energies of the surroundings. So, everything in the universe is included here, both the system and everything else, which we'll call them the surroundings. Because the change in the energy of the universe is equal to zero, we can set this equation equal to zero, we can do a tiny bit of algebra and rewrite the equation like this. The change in the energy of the system, remember, if it's not written, it's the system, is the opposite of the change in the energy of the surroundings. So, from the system's perspective, it is losing energy. Then from the perspective of the surrounding, it's gaining energy. And vice versa. Here we're looking at heat transfer between two things, the system and the surrounding. You might be asking yourself at this point, how can the energy move between the system and the surroundings? Well, let's look back at the examples we just did. For these five examples, how is the energy being transferred to the system or from the system. Well, in the first example, we're heating something up, so the energy is being transferred by heat. In the second example, we are physically moving something, we're doing work. In the third example, when the water vapor condenses, it's giving off heat, in that process. In the fourth example, moving the ball requires work, and in the fifth example, even though the net change was zero, what is described in the sentence for number five involves heat. So, the energy is moving between the system and the surroundings via either heat or work and we can write that as an equation. Here's the equation, the change in the energy of the system, which remember we're often writing as just delta e, equals q plus w. In this case, q is the symbol we're using for heat, you can think of heat as some disorganized energy, but I think you have a pretty good idea of what heat is. It's kind of unfortunate that q is also used for the charges in Coulomb's law, but we're just going to have to remember that a lower case q can be a charge or it can be heat. W is the work. Work is something that's more organized. We have to grab onto something and move it. So, the change in the energy of the system is the sum of the heat plus the work. Now, the heat and the work can be negative or positive numbers. What do I mean by that? Well, let's think about what can happen with the heat. The heat can either be absorbed by the system or the heat can be released from the system. So if I drew my little picture over here again, with the system, using red instead of pink this time, remember that when something's coming out of the system, that sign was negative. When energy was given off from the system, delta e was negative, remember that? The same is true for q, if heat is released from the system, if heat is coming out, than q is less than zero. Well that's nice, that's easy to remember. How about if something's going into the system? So we'll just label this in and we'll label this out. Well, something's going into the system, the delta sign of that process for delta E was positive. And the same is true for q. If heat is being absorbed by the system, then q is positive. So, our signs work out, whether we're talking about energy, whether we're talking about heat, or whether we're talking about work. If work is greater than zero, then that implies that work is done on the system, and if work is less than zero, then that implies that work is being done by the system. So let me just draw the system one more time. [SOUND] Let's think about this from the perspective of work. If work is done by the system, that means work is coming out of the system, right? And so, it would make sense then, that that would be negative. Remember when things are going in, the sign of those things is positive. So, now we have consistency in our frame of reference. We're always saying that if the system is losing something; whether it is losing heat or whether it is losing energy. Or whether it is doing work and therefore losing work, then the sign of that process is always negative. And we're saying that if things are going into the system, whether it's heat going into the system, or work going into the system by work being done on the system, or whether it's energy going into the system in some other form, all of that has a positive sign. So we're being very consistent here. I don't think I could emphasize this enough. When we are talking about energy flow, the sign in the change of energy indicates the direction of the energy flow. Which direction does heat spontaneously flow. Let me ask you this Does heat spontaneously flow from a hot area to a cold area or does the heat spontaneously flow away from the cold area and toward the hot area? What do you think is the spontaneous direction of heat flow? Well, as an example, have you ever sat outside on a stone bench on a very, very cold day? The back of your legs that are touching the bench feel particularly cold, and that's because the energy is flowing away from your body Toward the cold stone bench. So you're correct, that the direction of spontaneous heat flow is away from the hotter system and towards the colder area. As we're talking about energy flow, one of the things we need to consider is as we add heat to a system, it's temperature will rise, or the system will undergo a phase change, and that's shown graphically here. On the Y axis, I have the temperature. The temperature is displayed in two different scales, the metric scale that most of the people in the world like to use, and I've also shown the Fahrenheit scale for people in the United States or perhaps in Great Britain who are new to science and aren't quite comfortable with Celsius yet. So you can see the freezing point of water is zero degrees Celsius and 32 degrees Fahrenheit, and that's where the phase change occurs between the ice and the liquid water, not really labeled, but that's liquid water. So that occurs at this temperature. It's the freezing or melting point of water. And at 100 degrees C, that, of course, is the boiling point of water, which is 212 Fahrenheit, which I never use. At that point, we have the phase change going from liquid water to water vapor, which is called steam. This phase changes are a little more complicated than what we're trying to do right now. Right now let's just think about what happens when we heat a substance that is not changing phase. In other words, what's happening to the liquid water, in this region. Where it's above 0 degrees C but below 100 degrees C, we can see that, in that region, as the heat is added, going from left to right, the temperature is going up, and as the temperature goes up, the amount it rises is prorportional to the amount of heat observed. In other words, it's increasing in a straight line. When there's no phase change. Like density we can use this to determine what type of matter is present. We can look at this slope to make that determination. And there's an equation we use for that, q equals C times T. This is the heat capacity. The heat capacity is the amount of heat that a substance must absorb to raise it's temperature by one degree Celsius. Like density, specific heat is a property of the type of matter. And we can use the specific heat to determine What matter is present, if we have an unknown. Delta T similar, to Delta E is the final state minus the initial state. So here it's the final temperature minus the initial temperature. The heat capacity depends on the amount of material present. You could have different amounts of material present. And the units are usually in Joules per degree celsius. And the SI system units are joules per kelvin, but of course the incremental size of a degree in kelvin and the degree increment in Celsius is the same size, it's just that the scales are offset slightly. The specific heat, on the other hand, is the heat capacity for a given mass of a substance. Usually that mass is one gram. So the typical units are joules per gram degrees Celsius. As an example, for water vapor, the specific heat is 2.0 joules per gram degrees C. So we can combine this information to have two important equations. The heat capacity, C is the mass times the specific heat, which is given the symbol s and q, the amount of heat absorbed. Has to equal the mass times the specific heat times the change in the temperature. This equation right here, in this box, is very useful in doing, thermal chemistry calculations. I accidentally advanced a slide, but that's okay. So what were the equation that we we're using there? We were using this equation, q equals mass times the specific heat times delta t. And delta T is the final temperature minus the initial temperature, and here are some examples of specific heats. Specific heat is a constant for a given substance. It does depend on the phase of the substance. If we look down here where the water is shown, You see that the value for the specific heat is different depending on whether the water is in the liquid phase, the solid phase, or the vapor phase. Metals tend to have relatively low specific heat capacities, while insulators like water have higher specific heat capacities. This equation will be really useful to you as you're working through the advanced problem set this week. So just as a reminder, everyone is welcomed to try the advanced problem sets but please remember that these advanced problem sets are completely optional for students hoping to achieve a regular statement of accomplishment for completing the course. They're required only for students who are working to earn a Statement of Accomplishment with Distinction. And the reason that I set the course up this way is that I don't want people to have algebra get them down if you've been out of school for a long time. And I don't want you to gnash your teeth in frustration and give up on chemistry. If it's been a while since you've had to apply Algebra to solve problems, you can still learn a lot of chemistry in this course. And you can still learn a lot about chemical concepts without being able to do the complicated Algebra.