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Introduction to Kinetic Theory of Gasses

Patrick Ford
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Hey guys, so you may run across some problems. They ask you to calculate something called the average kinetic energy of an ideal gas. So what I'm gonna show you in this video is the equation for that and we're gonna see that this equation is actually one of the equations that make up what's called the kinetic molecular theory. So I'm gonna break it down for you, show you the equation and we'll do a quick example. Let's check this out. So remember that the kinetic molecular theory is really just a set of equations and they connect the variables for ideal gasses, macroscopic variables like pressure, volume and temperature to the other microscopic variables for individual particles, like velocities and energies and things like that. Now remember back to one of our earliest discussions on thermodynamics, we talked about temperature. We said that one of the definitions for temperature is a measure of how hot or cold something is, but it's not very useful. A more important definition or more sort of useful one is that it's related to the average kinetic energy more specifically the average kinetic energy per particle. So, in this video, I'm actually gonna show you now the equation that describes that relationship and it's that the average kinetic energy given by the capital letter K Is equal to 3/2ves KB times T. So, just be careful here because you're gonna have to kes the capital one is for the energy, the lower case one is for the bolts men constant. That's that KB and then your temperature has to be in kelvin's but this is it this is the equation. It's very straightforward and it's actually pretty fascinating because it tells us that if we know the temperature of a gas, it tells us the average amount of energy per particle Of that gas, which is pretty awesome. So let's go ahead and just take a look at our example here. So, we're gonna calculate the average kinetic energy of oxygen molecules if the gas is at 27°C. So, in part a all we have to do is just use our new equation. This is gonna be pretty straightforward, just gonna plug and chug. So this is our kinetic energy. This is gonna be three halves. This is gonna be the bolts one constant times the temperature. Now, just very quickly here. Remember that this temperature is given to us in Celsius and it has to be in kelvin's. The reason for that is that if you plug a negative number here, right, you can have negative Celsius, then you're going to get a negative energy. And that doesn't make any sense. So, we have to first convert this to kelvin's. So this is gonna be 2 73 plus 27. And you're gonna get 300 Kelvin and that's what we plug into this temperature over here. All right, so this is just gonna be equal to three halves. And this is gonna be 1.38 times 10 to the minus 23 then we're gonna multiply this by 300. If you work the sandwich you're gonna get is 6.21 times 10 to the minus 21. And that's gonna be in jewels. So if you have this gas here at 300 kelvin's, then obviously some of the molecules are going to have more energy, so we'll have less energy. But if you average them all, this is actually the energy that you're gonna get per particle. Alright, so now let's take a look at the second problem here. The second question is a more conceptual one that asks, would the answer be any different if we had a different type of gas? If it were nitrogen instead of oxygen. So if we just look at the equation, we can see the equation only. Just depends on a constant and temperature and nowhere in the equation do we actually have the type of gas, like the mass or something like that? So one important conceptual point to know about this average kinetic energy is that it depends only on the temperature of the gas And actually not the type of gas. So if you have nitrogen at 300 Kelvin, it would also have this amount of energy per particle would be the same exact number. So, the answer here is no. Alright, so that's it for this one. Guys, let's move on