So now we're going to turn from thermodynamics, the bulk properties materials to what we call kinetic theory, looking at what happens at the atomic level. So I suspect you're all familiar with the periodic table or at least have seen this sometime in your school career. Let me remind you of the basic properties of atoms that we're going to be concerned about in this class. And let me just focus on the four atoms I suspect we'll encounter the most. Hydrogen is made up of a single proton. Carbon, or the carbon nucleus, has 6 neutrons and 6 protons, and then that carbon nucleus is surrounded by 6 electrons so that the total charge is 0. Nitrogen has 7 neutrons and 7 protons. Oxygen, 8 neutrons and 8 protons. And the numbers in the table tell us, first, the number of protons, the atomic number, and then the atomic weight, the total number of protons and neutrons in each of these elements. Now while you're all familiar with the idea of atoms and molecules, I suspect almost all of you if asked, what's this air made of, would answer atoms and molecules. I suspect many of you would be hard pressed to try to explain, how do we know that this air is made of atoms and molecules? After all, people 200 years ago were very smart. They would put there hands through the air. They didn't feel those atoms, they didn't feel those molecules. How could you convince someone from 200 years ago that atoms and molecules exist? Well the experiment that you could do is something called Brownian Motion. The idea behind Brownian Motion is if you have a big particle, say a dust grain in this room. That dust grain in this room is bombarded by nitrogen and oxygen molecules. And these nitrogen and oxygen molecules keep bouncing off this dust grain and make it move around. And sometimes you can stare at dust floating in the sunlight. And you'll actually see the dust grains move around and jitter. This movement is called Brownian Motion. And by the way, it was first explained by this clever young guy named Albert Einstein back in 1905. And he got off to a pretty good start when he explained this effect. And it was a way, he showed it was, you could understand this motion quantitatively by thinking about different atoms and molecules striking it. And let's go look at a movie of Brownian Motion. And so this movie which I've grabbed from YouTube shows the motions of Large particles in water. And you can see, if you focus on an individual particle, you can watch how it moves around, as it is pushed by individual molecules striking each little grain in the water. And we see the discrete nature, of atoms and molecules through this Brownian Motion. Now that we see that this gas in the room is made of atoms and molecules, we can talk, not just about the density of air, about a kilogram per cubic meter, but the number density of individual atoms and molecules. How many atoms and molecules do we have in a cubic meter? And we can estimate that by taking the density of air and divide it by the mass of the atoms in the air or the mass of the molecules. We'll talk about mu, the molecular weight, and the mass of an atom or a molecule is the molecular weight times the mass of a proton. The mass of a proton is about 10 to the- 27 kilograms. Therefore, if we look at a cubic meter of air, which weighs about a kilogram, it would contain of water 10 to the 27 atoms of molecules. Now how many atoms and molecules are there is going to depend upon what the gas is made of. Different materials will have different molecular weights. That will equal the number of neutrons or protons in the atoms or in the molecules. A single hydrogen atom is made of just one proton So the molecular weight of hydrogen atoms, is one. A hydrogen molecule, is made of two hydrogen atoms. So its molecular weight is 2. Nitrogen, is made of seven protons and seven neutrons. So each individual nitrogen atom has atomic weight of 14, so the molecule weight of N2 is 2(14), or 28. Similarly, oxygen is made of 8 protons and 8 neutrons, so it has a molecular weight of 32. While carbon dioxide has a molecular weight of 44 since it's made up of 12 from the carbon, 6 protons and 6 neutrons, and 16 from the oxygen, 8 protons and 8 neutrons. We can now turn from looking at number density and its relationship to gas density to now thinking about pressure. We can now rewrite our ideal gas law as pressure is equal to the number density of atoms times a constant that's the same for all materials times temperature. And this constant, which we've written out here, turns out to be about 10 to the- 23 joules per degree Kelvin. So once I specify the number density of atoms or molecules in a gas, and its temperature, that tells me its pressure. We can now look at what temperature means at the atomic level. And the way you should think about this is, if you've got low temperature material that's cold, the atoms or molecules in the gas are moving slowly. In a high temperature gas, the atoms and molecules are moving quickly. And temperature is just a measure of how fast the atoms and molecules are moving. Now you'll notice in this picture the atoms and molecules are not moving in one direction. There's not a bulk flow associated with temperature. It's not a wind. They're moving seemingly, or really, in random directions. There are equal numbers going that way, and that way, and that way, and that way as they zoom around in the gas. We can relate temperature directly to the average velocity squared of the atoms and molecules in the gas. The average velocity is zero. There's no net flow. But when we average over all the atoms and molecules, and that's what this symbolizes here, you take all the atoms and molecules and ask, what is the typical random velocity? That typical random velocity can be related directly to the temperature times this constant we wrote down before, and the mass, Of each individual molecule in the gas. So once you've told me the temperature and what the gas is made of, I know the characteristic velocity. And recall that this characteristic velocity isn't telling you that all the atoms and molecules are moving at the same speed in one direction, but that roughly half are moving, say with 600 kilometers a second this way, and half moving with 600 kilometers per second this way, and some fraction moving that way, and some fraction moving that way. They're moving in all different random directions. And the temperature tells you what that characteristic rate of motion of the individual atoms and molecules are in the gas. So temperature which is a concept that we think of in terms of hot and cold, and energy flowing from hot regions to cold regions when we think about the bulk properties of matter. When we think about it at the atomic level, we should think about it as the characteristic speed, at which atoms and molecules are whizzing around in all directions. We can now also take an atomic view of pressure. Pressure is telling you how often atoms and molecules are bouncing off the wall of a container. If you have a cold gas, in which the atoms and molecules move slowly, there are relatively few collisions with the edge of the container. If they move faster, the collision rate goes up. If you have more atoms or molecules, even if they're cold, if there are more of these guys, they're going to hit the wall more often. So pressure is just going to go as the number density times KT. So more atoms and molecules, more collisions. Hotter atoms and molecules, higher velocities, more collisions. We can rewrite our pressure relation in terms of the density of the material, K this constant, and the mass, use the relationship between random velocity and temperature that we wrote down on the last slide. And we can see that gas pressure just goes with the density times the random velocities of atoms and molecules. The atoms and molecules move faster, more collisions, higher pressure. There are more atoms, higher density, more collisions, higher pressure. And this pressure is going to determine the basic structure of the atmosphere. Now let's step back and work out some characteristic numbers. And you'll do that on the problems, where we'll get some characteristic numbers for gases on Earth and other planets and then return and apply these concepts to look at what sets the structure of an atmosphere.
