In this lesson, we're going to be describing basic thermodynamics, and we'll be able to apply these concepts that we're learning in this lesson to the remainder of the course. First, before we start, we're going to begin with the system and I'm going to provide a few definitions. First, with respect to the system, the system represents our material. And in this case, if we talk about putting heat into the system, we're going to refer to that heat going in as being greater than 0. And if our system happens to do work, then the work that is associated with the process that we're studying is greater than 0 when the system does the work in the system. So, heat in and work out are both positive quantities. And depending upon the magnitudes of those two terms we will have, or possibly have a change in energy. Now since we've defined heat in a very careful way with respect to heat into the system, we need to come up with some formal definitions of what we mean by that. When q is greater than 0 we refer to this process as endothermic. That is, we're putting some heat in, or causing the system to change, and when that does we refer to this process as an endothermic process. When we look at q being less than 0, that's actually an exothermic process. So, as a result of what's happening in the system, if the system is creating heat, then the process has undergone an exothermic reaction. When we look at the work process, again, work greater than 0 is being done by the system, work less than 0 is being done on the system. Now we can write our first law in terms of mathematics, and we'll do that by writing it as I've indicated on the visual. We have two different types of terms, one that are on the left and one's that on the right. And we're going to describe why those are different. In the case of the left, what we have is a lowercase d and that lowercase d is indicating that the energy change is going to be path independent. So we're only interested in the difference in the energy at the beginning of the process and the energy after the process. Now when we look on the right-hand side, rather than having a d we have a delta or a lowercase delta. And that indicates that we're dealing with path dependent quantities. So we need to specify the particular path. So for example, what we can do is we can describe an adiabatic process. And in an adiabatic process it means that we're having no exchange of heat. Or what we can do is we can look at work being done by the system and we can look at it in terms of an isothermal process, or an adiabatic process, or a constant volume process. So we need to specify the particular path, but once we've done that, then we are able to do calculations that we are trying to identify and looking at the variables that we're trying to calculate. So we have our path dependent on the right, and we have on the left-hand side, the path independent. Let's continue with this, and this time what I'm going to do is I'm going to introduce the second law. So let's take a look at the first. So as again, it's written as dE is dq- dw. Now the second law introduces the concept of entropy and we already have, I'm sure, a qualitative feel for what we mean by the term entropy. It's really the amount of disorganization or disorder that we have in the system. So if I were to ask you the question which material would have the higher entropy, a liquid or a crystal and solid, and you would most likely say that the liquid would be a material that would have a higher entropy or it has associated with it more disorder. So when we look at the way this is presented, we have dS, again, we have d on the left-hand side, and what this is telling us is that the entropy, like the energy, is a path independent quantity. On the right-hand side, we have again dq, which we need to specify the particular path. But what we've done here is, by applying an integrating factor of one over two, we have now made that a property that's on the left-hand side, that property is now path independent. So we can rewrite and we can combine the first and second laws. And when we do that we get an expression that tells us that the energy is going to be related to the temperature, the entropy, the pressure, and the volume. Now mathematicians would say then that the energy is a function of the natural variables S and V. So what does that mean? Well that means if we wanted to describe in some way the change in energy associated with a particular step, we can monitor, for example, the volume and we can control the volume to a certain degree. In the case of a gas, controlling the volume is very easy. However, when we start looking at condensed materials like liquids and solids, trying to keep the volume constant during a particular process is very difficult to do, because we have already been introduced to the concept of thermal expansion. When we look at the entropy part of the natural variables we don't really have a meter that's going to permit us to fix the entropy of the system. So consequently, though this is a very good expression for the change in energy, we're now going to start looking for the possibilities of having other types of variables that we can use in an equivalent way. And what they are, are referred to as auxiliary functions. And those auxiliary functions have the same sort of behavior that we've just described with respect to the first and second law. And so what we refer to these as alternate statements of the combined first and second law. And the first one we looked at is the enthalpy or the heat term. And when we look at the natural variables that are associated with the enthalpy, they are the entropy and the pressure. Now we can control the pressure, but still, we have the problem that is associated with controlling the entropy. And when we write this in terms of differential form we now have dH is equal to TdS + VdP. So again, we see there, our natural variables are S and P. We can also describe in terms of a function that we refer to as the Helmholtz free energy. And again it's an auxiliary function, it's an alternate statement of the combined first and second laws. And when we write it in differential form we have the expression dA is -PdV- SdT. Now we have introduced the temperature, but we still have the volume. The last one we're going to be looking at, the last auxiliary function, is the Gibbs function. And we finally have arrived at a function, which is going to be very useful to us, because temperature and pressure are both variables that we can easily control In manipulating our microstructures. And the differential form here is dG is- SdT + VdP. So T and P are the variables that we can wind up controlling. In the next lesson, we're going to take these basic principles, and we're going to apply them to the problem of the transformation of liquid to solid during the solidification of a pure substance. Thank you.