 Thus far in the course, when we've been looking at the second law of thermodynamics, we've been looking at it from a rather conceptualized or idealized perspective. What we're now going to do is we're going to take a closer look at the second law of thermodynamics, but we're going to look at it from a quantitative perspective and consequently what we'll be doing in today's class is looking at a way to be able to compute the entropy for different substances that we'll be considering throughout the course. So the topic that we're going to look at is entropy and what we'll do is we'll begin with the Clausius inequality, which will enable us then to work through the mathematics and come up with an expression, two expressions actually, that will enable us to calculate the entropy or the entropy change within the working fluids that we'll be studying. So entropy itself is just a property. It's similar to other properties that we've studied thus far in the course. And entropy is a property that results from the Clausius inequality, and the Clausius inequality states the following. And the closed sign on the integral here implies that it's either a cyclic or closed integral. So that is the Clausius inequality, and it will become the starting point for our derivation of relationships that enable us to calculate change in entropy. So that is the definition of entropy. It's related to heat transfer over temperature and Kelvin for an internally reversible process. Typically when you look in books in thermodynamics, you'll find tables in the back of the book with entropy tabulated. You can also compute it for ideal gases, and it's also listed in the back of the book for ideal gases as well. So if you're dealing with either steam or refrigerant R134A, you'll want to use the tables in the back of the book. If you're dealing with an ideal gas, it depends upon the temperature change of the process that you're looking at. If it is a small temperature change, we can make an approximation. That will be an equation that we look at in a few moments. If it's a larger temperature, then you'll want to use the tables in the back of the book. So the place where we'll use entropy and entropy generation is we'll use it as a quantitative measure of irreversibilities that occur within any process or cycle that we're looking at.