Entropy

In this video, we're going to go over the concept of entropy. Entropy is often said to be the degree of disorder of a system. And what I'm going to try to do now is explain what we mean by this and why it's important we know that matter is made of particles, matter in all of its forms in solids, liquids, and gases. And those particles have energy. And the energy causes the particles to do different forms of motion or to have different forms of motion. In a solid, the particles are able to vibrate and about fixed positions. In liquids, the particles are able to vibrate and rotate and move around from one place to another with limited ability. We call that translation. In gases, the particles translate an awful lot. They rotate, vibrate, and translate. We call these the degrees of freedom. Now, energy is delivered to particles in a quantized manner. That means in small packets, which we call quanta, or each packet is called a quantum of energy. And these are very, very, very small amounts of energy. And they change the vibrational states of the particles in solids. So if a particle in a solid absorbs a bit of energy, the particles vibrate a little bit more, and they can keep doing this. There are lots and lots of vibrational energy levels. Rotational energy levels are even smaller. So smaller amounts of energy can be absorbed by particles, which will allow them to rotate. And once again, it's quantized. They can rotate a little bit or a bit more, but nothing in between. And there are many rotational levels. Translation, which is moving from one place to another, has very small quanta of energy. And so there are many, many, many tiny amounts of energy that can be absorbed to change the speed of particles as they fly around. Now, energy is distributed over the particles randomly. It's like throwing a. Throwing a bucket of sand into some water. It just goes all over the place. And the most all possibilities are likely. So what happens is when the energy is randomly distributed over all of the particles, it produces a particular state called a microstate. This is a specific arrangement of energy on the particles. And it's obviously very, very complicated when we have a huge number of particles and a huge amount of energy packets or quanta. So to really appreciate what happens, we need to have a look at a very simple situation. We're going to consider a situation here where we've only got five particles, five physical particles of matter, and three quanta of energy to distribute on these five particles. Well, we could choose to put all three quanta of energy on one particle, and that would constitute a microstate and the number of Ways we could make a similar microstate is five. We could have those three particles, or three, sorry, three quanta of energy on each of five different particles. So effectively here we have five quantum, five microstates, all of which are identical. And so these microstates would produce the same result in the macroscopic world. If we move on and look at how we could arrange the particles when there is one quantum of energy on each of three different particles, you'll see that there are now 10 possible ways of doing this. And each of those will produce an identical macro state, will produce an identical effect in the macroscopic world. So it's clear that this is a more likely outcome. There are 10 possibilities for this outcome or 10 possibilities that one of these outcomes will occur. Whereas before there were only five possibilities that one of the other outcomes would occur. So this is more likely than the previous microstates. Now let's think about what happens if we arrange the particles 2 and 1. Now we have a situation where there are 20 possible microstates. And each of these microstates will give the same macroscopic result. You've got particles in which one particle has two quanta of energy and one particle has one one quanta of energy. So we see that there are certain favored microstates when we've got certain numbers of particles and certain amounts of energy. And here you can see that if we, if we just said, okay, let's randomly select one macrostate which is represented by a microstate, well, the most likely macrostate would be produced by one of the 20 microstates that occur here. Now we're dealing with this. When there are tiny amounts of energy and tiny numbers of particles, once we start to move to huge numbers of particles, we then get certain energy distributions that are so much more likely as to be as to make all of the others virtually impossible. So we have our microstates, which are increased in number by having more energy. As we have more energy, we get more microstates possible. As we have more particles, we get more microstates possible. And so what we call the number of possible microstates of a system, we call this the entropy. It's the number of possible ways we can have that we get the same macroscopic result. Now, nature will move towards the situation that has a greater amount of entropy because this is a much more likely outcome. And so nature drives all change in the, in the universe. Now, if we're going to talk about the universe, we have to define what we're talking about. We can Talk about the particles that we are studying. And we can call those the system. This might be a chemical reaction or a physical reaction. But we can discuss it as the system. These are the particles under study. And then we can talk about the surroundings. And the surroundings is everything else outside of the system. Now, heat energy is part of the surroundings. And can flow from the chemical energy of the system to the surroundings. It can also flow from the surroundings to the chemical energy of the system. Now, when a system that is a bunch of particles, some matter, Undergoes an exothermic process. It releases heat energy to the surroundings. This heat energy increases the entropy of the surroundings. It doesn't have any effect on the entropy of the particles themselves. As those particles have the same random nature. Those particles will be given more entropy by the extra heat if they're heated up. But as I said, we can count the heat energy as part of the surroundings. Now, this gives us then our summary of what's going on. Effectively, to increase the entropy of any system, we need to either increase the number of particles. Or we need to increase the amount of available kinetic or heat energy. So any situation which allows this to happen for the universe Is so incredibly likely to occur that it does. Well, it does with one small proviso. And that is that there is not some kind of energy barrier to the process happening. We call that kinetic control. That's also possible. But the reverse certainly is impossible. It is impossible to have a system which reduces the total entropy of the universe. And this gives us the second law of thermodynamics, which says that it is only possible for systems under study to decrease in entropy. If there is a greater increase in entropy in the surroundings. So the second law of thermodynamics states that the universal entropy must increase. For this reason, sometimes people refer to entropy as nature's arrow or time's arrow. Because it's the only law in physics which says that things move towards the future. Now, we represent entropy by the capital letter S. And the change in entropy is represented by delta S. As we've said, the delta s of the universe Must be made up of delta S. Change in entropy of the system plus change in entropy of the surroundings. Changing entropy. Processes may be either exothermic or endothermic. In terms of heat energy. An exothermic process Will transfer heat energy to the surroundings from the system. The chemical potential energy of the system changes to heat energy, which then goes to the surroundings. This increases the entropy of the surroundings and hence the entropy of the universe. So it's a favorable process. An endothermic process, however, decreases the available heat energy in the surroundings. And that means that the entropy of the surroundings is reduced. This can only occur if the number of particles in the system. Hence the entropy, increases by a greater amount. For any process to be feasible, which we say is thermodynamically spontaneous, in other words, possible. The overall change in universal entropy must be positive. So, to summarize, Entropy is the term we give to the number of possible microstates in a system. Giving rise to the macrostate that we see. Remember, nature will move everything to the one of the macrostates. Or a macrostate that is a function of the most probable microstate. Because the most probable microstate will be so incredibly likely compared to the others that there is no choice. Nature moves it that way because it's just much more likely. We use the word disorder. It gives an idea of random behavior. Because we know that the greatest entropy is produced when we have the maximum amount of power. Particles of energy and particles of matter. Systems are only allowed to change in any way. If the overall entropy of the universe is increased as a result of the change. And this can happen in two ways. It can happen by increasing the total number of particles in the system. Or it can increase by increasing the available heat kinetic energy available in the universe. So entropy is given the symbol S. And a change in entropy is delta S.