 So recapping what we've done so far in this course, we spent a fair amount of time talking about gases in various ways, equations of state and PVT properties and things like that. We've also spent some time talking about solids. So now that we're talking about different phases of materials, we haven't talked about liquids yet, but soon enough we'll be talking about liquids as well. So let's make sure we understand what the differences are between different phases of matter, solids and liquids and gases. So to start out with, I'm just going to draw a quick little cartoon of what a solid would look like as opposed to a liquid as opposed to a gas if I were to, liquid is spilled with a Q, if I were to combine them to a container, and gases we certainly understand. We can, gases fill their container, the molecules are far apart from one another, they're randomly distributed around this box, so that would be an illustration of a gas. A liquid, on the other hand, doesn't fill the container, it settles down to the bottom of the container, and the molecules are much closer to each other in the liquid. So they're all done here in the bottom portion of the container. Difference of course between a liquid and a solid is the solid, the atoms in the solid are ordered, they're arranged regularly, so I'll just draw those in a lattice and I won't take the time to fill the entire box. So there's a nice orderly arrangement of some atoms in a solid. The difference between solid and liquid, which settled to the bottom of the container and the gas, which expands to fill the whole container, we call solids and liquids condensed phases, because the gas which spreads out through the container, if I condense it down so that every molecule is next to a bunch of other molecules, then I have either a liquid or a solid. The difference between solid and liquid is in the ordering of the atoms. If the atoms are relatively random or disordered, we call it a liquid. If the atoms are ordered and obey some sort of regular pattern, then we call it a solid. So these would be phases that we could call disordered. The gas is randomly distributed or disordered as well. The solid is an ordered phase. And that's really the next point we're going to discuss in any detail, is what do we mean by order. So it's easy for you to recognize what I mean when I say the solid is ordered and the liquid is disordered, but what exactly does that mean? If I already press you for a definition, you might come up with some terms. You might say, well, there's some symmetry in the solid that's not present in the liquid, but that just raises a similar question. What do I mean by symmetry? What does it mean to say the solid is symmetric and the atoms in the liquid are not symmetric or maybe they're less symmetric? Can I be more symmetric or less symmetric or more ordered or less ordered? So as usual, with PCEM, we need to be careful about the colloquial, regular English use of these words and the more precise definitions that we use in physical chemistry. And in fact, there's a lot of different types of symmetry that we could talk about, a lot of different types of order. I can have translational symmetry or rotational symmetry or reflection symmetry, and we'll need very precise definitions to be able to talk about what exactly do I mean if I say a solid is ordered or a solid is symmetric. And in fact, is it possible for one substance to be more symmetric or more ordered than another substance? So that's the next topic we'll begin to explore is those more precise meanings behind those words, specifically the words around symmetry.