 So we've been talking about entropy and entropy generation as being a quantification of the disorganization or disorganized state of the system. What we want to do now is take a look at ways by which we can compute the entropy of a fluid. So what we'll do, we'll take a look at a differential form of the first law applied to a closed stationary system. So we're writing out the first law and we'll use the subscript's internal reversible. Now first of all we're talking about a stationary system, so it's not moving and consequently we can neglect kinetic energy as well as potential energy. And looking at the internal reversible work coming out of the system, let's say that the system could expand, it could be a piston cylinder device for example, and so in that case we may have boundary work. And the other thing that we'll do is we'll use the Clausius inequality to come up with a representation for the heat transfer in terms of entropy. So what we're going to do is we're going to work with this equation and we'll use that to formulate the equation that we can use to calculate entropy change within a substance. So substituting in the heat using the Clausius inequality and then the boundary work we result in this equation for our first law. What I'm going to do now, notice that these are capital S, capital U, capital V, this is not per unit mass, so in order to make it per unit mass I'm going to divide by the system mass and when we do this the capital S is going to become a little s. We then have specific volume and we have internal energy on a per unit mass basis and we will call this the first Gibbs equation and we'll come back to that equation in a couple of moments. Now when we looked at enthalpy in an earlier lecture we said that enthalpy is defined as a combination of internal energy plus PV which is essentially flow work. So I'm going to take the differential form of that and in doing so I'm going to apply the product rule and I'll apply the product rule to the PV term. So we're going to take this equation and we're going to substitute it into the first Gibbs equation so the TDS term remains the same. So that was Gibbs first equation with the du and the pdv, now what we can do is we substitute in our enthalpy term and we will call this the second Gibbs equation. Now what we're going to do is we're going to divide the equations by T and we'll result in two equations now so we're going to take the first Gibbs and the second Gibbs equation. So those are two equations in differential form for entropy in relation to other properties that we've already calculated in the course. So this is a relationship between the entropy and other properties that we already know and it is analogous to what we did when we looked at enthalpy and we expressed enthalpy in terms of internal energy pressure and specific volume. So with these two equations what we can do is we can integrate them between two end states and that will tell us the change in entropy between those end states. Now the other thing that I should mention is that this applies to either a reversible or an irreversible process because if you recall when we talk about properties we said that the termination of properties were independent upon the path that you go to get from one state to another. So properties are only dependent upon particular state points and not on process paths. So what we'll be doing is we'll be using these two equations and integrating them to come up with formulations for entropy change within different substances that we'll be looking at in the course.