 So the first thing that we're going to do with the Gibbs first and second equation that we put into differential form is we're going to apply it to calculate entropy of liquids and solids. Now we'll treat liquids and solids separate from gases and the reason for that is we can make an approximation about the specific heats for both liquids and solids. And that is given that liquids and solids are incompressible. So looking at the differential form that we derived from Gibbs equation, what we can do first of all if we assume that these are incompressible substances, the dv term goes away. So the second term from our equation disappears. The other thing that we can do for the internal energy, we can make a substitution in terms of our definition that we had for the internal energy in terms of the specific heat at constant volume. Now one thing that we'll say about specific heats for both liquids and solids is the specific heat at constant pressure and constant volume we will assume to be the same. Now this is an approximation, it's a better approximation for solids than it is for a liquid because for example if you take water and you heat it, it will undergo volumetric expansion. So it will change a small amount. However what we will do is we will assume that that change is negligible for our purposes and consequently we will consider the specific heat at both constant volume and constant pressure to be the same for both liquids and solids. And with that we can rewrite our equation, the differential form for the entropy, as being specific heat, now not specific either constant volume or constant pressure. And we get this equation. Now what we're going to do is integrate that between two states, a beginning state and an end state. So we get this integral equation and you'll notice that I've written the specific heat here to be a function of temperature. Integrating that equation we can integrate it if we assume an average specific heat for our process otherwise you need to know how the specific heat will change with temperature for that particular solid or liquid. But if you can assume an average specific heat that would be the equation that you then use to calculate the change in entropy for that solid or liquid. A final comment about this is if we're dealing with an isentropic process, remember that's one where we said that there is no change in the entropy. If that is the case then the left hand side of that equation is zero. If it is zero then that implies that T2 needs to be equal to T1. So that's just a comment that we can derive for an isentropic process involving either a liquid or a solid.