 So now that we understand free energy in particular f equals e minus ts it turns out that we can start to reason about things Let me compare one set of atoms, but in kind of different states on the one hand we have ice a small piece of ice and The structure of these water molecules will look something like this ice 11 under fairly normal conditions even though it's melting away here a bit And on the other I might take a glass of water also water molecules But in the glass of water they behave something like this So it's the same type of atoms, but if we at least assume that well this is definitely below freezing even though it's melting So what is the difference between these two systems and the states and why do this one prefer to be an ice? At least as long as it's below zero centigrade and why does this one belong to be liquid? I'm gonna put that down and try to remember not to drink it well Any time you have questions like that now, you know what you're gonna do you should compare What is the energy of this system? And what is the entropy of that system and similar here? What is the energy of this system? Oops, sorry energy and Entropy how many hydrogen bonds do we have here if you remember from last lecture in perfect ice You would have exactly two full hydrogen bonds per water So you would have very low energy and the kinetic energy is even lower because that they're not moving They're definitely not moving at this slide. It's exactly zero Kelvin. So energy is low low low here Let's stick to the energy first here. We do not have as many hydrogen bonds So we definitely have higher and I wouldn't say high because it's not gas So let's say that it's intermediate energy and they're also moving a bit. So there's a bit of kinetic energy So the energy is intermediate or slightly higher here and energy is significantly lower there Entropy well again, it's not moving. So you just have one single state the entropy would be zero here In this case the entropy. Well, just if you're really fast you can count them. I can't there are many states here So the entropy here is higher because the number of microstates the ways we organize these molecules is definitely higher. So The same system ice here under some external conditions in particular the temperature. We have low energy and Low entropy and in other conditions. We have higher energy and higher entropy and That's the way it should be because now we need to add our friend f equals e minus ts If there's one equation that you can't think enough about that's this one So what happens now if t is very very low? even Zero if t is zero that entire second term is going to disappear and then everything is going to be controlled by energy and In that case the system will prefer to be in a state that has the lowest energy because again entropy doesn't matter That's that one. That's the ice as The temperature goes up eventually the second term here will become more and more and more important eventually they will be exactly equal and When that term then starts to become more important suddenly the system will instead favor the system That's better for the entropy. So suddenly we're going to favor the system that has higher entropy because that total term is negative Right, so suddenly at some crossover point in temperature. It's going to be better to be in another state That rather has lower entropy and that's why we have the phase transition and go over to liquid water Eventually you would have at boiling point the same thing would happen But then we would have even higher entropy when you completely boil it and have the atoms escaping each other So armed with this equation we can start to explain simple phase transitions. This was easy Let's try something harder such as hydrogen bonds. We're going to be over with this class in 10 minutes