all right before we uh combine enthalpy and entropy to try to figure out if uh something is spontaneous or not a chemical reaction or physical process again that's going to be important too uh let's just talk a little bit more about entropy and how we could figure out if entropy is increasing or decreasing so the examples we talked about yesterday uh are uh phase changes right and that will tend to be true so here's a plot of entropy which again is abbreviated S as a function of temperature and for thermodynamic prop properties we usually uh use Kelvin so it's in kelvin so you can see that as you go from solid to liquid to gas the entropy increases and that is a good rule of thumb okay you got to compare apples to apples but in general as you go from solid to liquid to gas entropy increases so Professor the disorder goes up entropy goes up yep if disorder goes up entropy goes up yep so the disorder is increasing when you go from solid to liquid because suddenly the molecules get to move around and they're more mixed up when we go from liquid to gas this order increases even more because now the molecules have very little interaction with each other they could be anywhere anywhere in the volume of the container not pictured on this graph but another one we saw last time was that when something goes from a solid to aquous entropy increases as well not only does we do we go from a you know ionic compound like sodium chloride which is a crystal very ordered structure of all those cations and anions to Aquis ions swimming around we're also going from a pure substance to a mixture and so that's more entropic more disordered as well uh let's look at um what happened when we were just keeping a sample in the same phase so we're just talking about let's say a solid what's happening to the entropy as we increase the temperature so temperature is going up this way what's going on with the entropy goes up make it's going up yeah so entropy turns out to increase um as we increase U temperature and that's for all three phases and that's generally going to be be true so if entropy goes up as temperature goes up what type of relationship is that directly proportional so we could even write that a little bit mathematically hard to use baby blue let's go orange entropy is proportional to temperature and if you remember uh last time we talked you know we drew little pictures of what a solid would look like and what a liquid would look like we looked at a uh liquid and then a gas and we can kind of see just from these little cartoonish drawings that yeah it's looking more disordered there's less order in that system so let's draw two samples of the same thing all right all right now we're just looking at two samples which one box a sample a a or sample B would you say has the higher temperature B you're I mean there just five little circles poorly drawn might have ADD okay I could have put a lot of effort into those circles you can tell I'm almost on break all right again I got pie on the mine already this is gonna be really weird like for future people who are watching this video like pie on the M what if they're watching like in the spring semester like what's he talking about pie it's Thanksgiving tomorrow future students it's Thanksgiving tomorrow in the year 2017 ad okay yes I'm talking to you from the past that's what they just did that's [Music] what all right so yeah these are just circles being drawn but you could look at it like yeah B would be higher temperature if this was in liquid phase maybe than the gas phas or anything um so B would be higher temp uh which one has more disorder or higher entropy A or B yeah B higher entropy higher temperature higher entropy all right so here's what I want to do all right so let's figure out what happens to the entropy when we change CH the temperature of a solid 10° all right so this is from 0o this is 0 Kelvin and then of course uh water uh freezes or melts at 0 degrees C so what's that 273 so this is 273 all right so this isn't going to be the scale on their scale but I'll try to keep the this the distances the change in temperature the same here so let's say I go from zero to here this is going to be 10 Kelvin so I increase the temperature 10 Kelvin let's see what happens to the entropy the entropy goes from here here's the entropy at zero here's the entropy at 10 Kelvin so that's going to be like right here so this is my entropy change uh when and my delta T went up by 10° 10 Kelvin from 0 to 10 now at the higher temperature the other end of this spectrum okay let's say so is that distance the same as no make it a little bit bigger okay so is this the same as this about yeah that's about so that's 10 on my Axis so this would be 263 Kelvin to 273 so I increased the same amount of temperature 10 Kelvin in each case let's look at what happened to the entropy now 263 the entropy was here I went up 10° so the entrop is here now this is where I need a ruler oh man I'll just eyeball it so there's need a ruler need some of the straight just do this okay we happy with those lines now yeah so here's how much my entropy went up from 263 to 273 it didn't go up that much right the entropy went up a lot more from 0 to 10 then from 263 to 273 okay and we could have just realized that with the slope of this line what's happening to the slope it's starting to flatten now all right so as the temperature increases the entropy doesn't increase that much all right so entropy increases a lot at lower temperatures and a lot less at higher temperatures yes that word what's the difference between the 273 where it's being measured at B compared oh so from what's the difference between here and here that's uh that's when it's a solid down here and now it's a liquid way up here so there's a huge jump in entropy when it goes from a solid to liquid but entropy does increase increase as a temperature all right so that's a phase change entropy goes through the roof when we do those phase changes but the whole ice won't take effect within one second it will take time to melt overall so that would be still small process like that yeah I mean no so yeah it does take time and energy to go from a solid at 0 degrees cels to liquid at 0 degrees that's the heat of fusion it doesn't happen that that's why like how would the jump from 273 to over there would take fast if the well we're not we're not talking about time how long this is but you if you have a solid at 0 deges C or a liquid at 0 de C the liquid is going to have a lot more entropy a lot higher entropy okay all right so it turns out that entropy since entropy doesn't go up as much at higher temperatures entropy is inversely proportional to the change in temperature meaning that changes in temperature make a big diff much bigger difference at the lower temperature than the higher temperatures so how we say that is that the change in entropy the entropy is inversely proportional to the change in temperature all right so those are close but very very different entropy is import blah blah entropy is directly proportional to temperature higher temperature higher entropy entropy changes go up entropy uh smaller with the inverse inversely proportional to change in temperature okay so the bigger the change iner small the smaller the change in the entropy the bigger the change in the temperature no so the the higher the temperature is the smaller the change in entropy that's what I want to say so both cases the sample went up 10° right so we gave it much energy that takes to go up 10° and since it's a solid it's the same amount of energy so I'm giving the the higher temperature sample entropy increases less than the lower temperature sample its enty goes up a lot so basically it matters more to the colder object than it does the hotter object and there's a good analogy to help uh you uh at least me hopefully you as well help you understand this and you know we got to just call on our our good friend uh Bill Gates one more time okay so Bill Gates turns out to be a pretty rich guy he's up here all right he is he's the high temperature sample so he's got a lot of money okay so let's think of somebody with a lot less money H maybe like your local community college chemistry professor okay so I'm down here okay not worth uh $80 billion if you I mean I'm not going to tell you exactly how much I'm worth but it's not $80 billion okay all right so if you give Bill Gates $20 he's up here high temperature is that going to matter much to Bill Gates no it's not going to matter he already has a lot of higher a lot more money now if you give me $20 is that going to make a big difference to me yeah you better believe it's going to going to make a big difference I'm going out to eat all right I'm getting some Subway all right yeah 20 bucks is going to make a bigger difference to me at the uh lower end of the uh net worth scale than big get so the same thing happens for this okay the The Temper the sample with the lower temperature gaining that amount of heat makes a big difference to it whereas the sample with at the higher temperature just doesn't matter as much okay now this is that we need to do this because we're going to use it eventually in an equation when we start calculating entropy that's really why I'm talking about it but it also explains why heat how does heat transfer from the cold object to the hot object or the hot object to the cold object always transfers from the hot object to the cold object why can't the cold object give the hot object energy okay it technically can I mean a cold molecule can bump into a hot molecule and transfer that energy but it could it could but it turns out that the hot molecule the hot object if it gains some heat it entropy doesn't go up that much the cold object if it gains some heat its entropy is going to go up a lot more even if we're transferring the same amount of heat and we are because if you're looking at a system versus surroundings uh law of conservation energy perent so the entropy for the cold object goes up a lot the entropy for the hot object which lost energy so it's actually going down in temperature only lost a little bit of entropy and what's the second law of Thermodynamics entropy always increases so it has to increase if I transfer heat that's a change entropy has to increase so the hot object's going to go down a little bit the cold object's going to go up a lot guess what what entropy increases so that that's why hot the heat always transfers from the hot to the cold because it's a net positive in entropy all right so that's our relationships uh for entropy and specifically uh we're going to use these three quite a bit entropy increases when you go from solid to liquid to gas entropy also increases when you go from solid to aquous ions like dissolving and solubil increases with temperature again we're going to use this in an equation later so just store that you know shelf that somewhere in your brain but these ones are where we're going to use quite a bit actually let's go back here that's what I screwed up I knew I wasn't doing this right just I was saying it and it didn't feel right all right I put my Deltas in the wrong spot so the change in entropy is imply proportional to the the temperature screwing me up this is what I this is relationship I want entropy is proportional to temperature but entropy changing entropy is inversely proportional to temperature that's what I wanted to say there I think I started getting I started thinking about getting 20 bucks just got excited and my my mind was turned off for a second all right it's life changing I might not coming to work tomorrow h