Temperature, kinetic theory, and the ideal gas law
Thermodynamics part 3: Kelvin scale and Ideal gas law example
We just finished, hopefully, getting intuition for why my initial pressure times my initial volume divided by my initial temperature is going to equal-- if I change the volume, the pressure, the temperature, or some combination of all of them, it's going to equal my new pressure times my new volume divided by my new temperature. And once again, just remember all of this-- pressure times volume is proportional to the amount of kinetic energy in the system, and temperature is proportional to the amount of kinetic energy per molecule. If we don't change the number of molecules, the amount-- and since by the conservation of energy, the amount of kinetic energy isn't going to change unless we do some work, or get some potential energy-- these quantities and this relationship won't change. Watch the last video, and hopefully you'll get some intuition-- if it's still confusing, I'll make another video for you guys. Before I apply this equation-- this is going to get you pretty far in thermodynamics just knowing this, and even more just having the intuition of what it means. I want to clarify something about temperature-- there's a lot of different ways to measure temperature. We know that in Fahrenheit, what's freezing of water? It's 32 degrees Fahrenheit that's freezing, but that's also 0 degrees Celsius-- actually, that's how the Celsius scale was determined. They said, where does water freeze, and then where does water boil? 100 degrees for Celsius is boiling, and that's how they rated it. You could be colder than the freezing of water, and you'd have to go negative in that situation-- Fahrenheit, I'm actually not sure. I need to look that up in Wikipedia, or that might be something for you to do, and tell me how it came out. I think the boiling of water in Fahrenheit is 212 degrees, so it's a little arbitrary. I think Fahrenheit might be somehow related to human body temperature, but I'm just guessing. You can have different scales in this situation, and they were all kind of a bit arbitrary when they were designed. They were just to have some type of relative to scale-- you could say when things are boiling, they're definitely hotter because they have a higher temperature then when things are freezing. You can't divide 100 by zero, but if something is 1 degree, is it necessarily the case that something that is 100 degrees Celsius is a hundred times hotter, or has a hundred times the kinetic energy? Actually, what we'll see is that no, it's actually not the case-- you don't have 100 times the kinetic energy, so this is a bit of an arbitrary scale. The actual interval is arbitrary-- you could pick the 1 degree as being one hundredth of the distance between zero and 100, but where you start-- at least in the Celsius scale-- is a bit arbitrary. They picked the freezing of water. Later on, people figured out that there is an absolute point to start at. And that absolute point to start at is the temperature at which a molecule or an atom has absolutely no kinetic energy. Because we said temperature is equal to the average kinetic energy of the system, or the total kinetic energy of the system divided by the number of molecules. Or we could also say the average kinetic energy per molecule. The only way to really say that the temperature is zero-- and this is proportional, because the temperature scales are still a little bit arbitrary-- the only way to get to a temperature of zero should be when the kinetic energy of each and every molecule is zero, or the average kinetic energy. So they're not moving, they're not vibrating, they're not even blinking-- these molecules are stationary. The point at which that occurs is called absolute zero. That actually occurs-- absolute zero, which is also called zero Kelvin, and that is the same thing as minus 273 degrees Celsius. Nowhere in the universe, at least that I'm aware of, it is it colder than minus 273 degrees Celsius-- at that temperature, nothing moves, even at the atomic scale. I'm talking that the electrons collapse into the nucleus-- everything is completely stationary at zero Kelvin. It's a theoretical absolute limit-- maybe we'll do a bunch of videos on how you can get close to that, but in laboratory environments or maybe in deep space, it gets really, really close to this. I'm pretty sure nowhere in the universe do we have absolutely zero Kelvin, or at least in any place where we actually have particles, but I might be wrong there-- that's a little bit out of the scope of what we're talking about. The true way to measure temperature is in Kelvin. When you're measuring in Kelvin, if I say-- I have something that is 1 kelvin versus something that is 5 kelvin, since we nailed down the bottom at a point at which really do not have kinetic energy, I can make the statement that this has five times the energy of something that's at 5 Kelvin versus 1 Kelvin. That whole long explanation about Kelvin, that was to just to make the point that whenever we use this formula, or really any formula in thermodynamics that involves temperature, we should convert to Kelvin, unless we're just doing change in temperature. Then you could you could probably keep it Celsius, but when you're doing proportionality, or you're using it for multiplying or dividing by temperature, you have to use Kelvin. Hopefully, I made a little bit clear of why that is. Let's do an example. You'd be surprised how far this takes you. Really, the main trick is just to remember to convert things to Kelvin. That's the number one reason why people miss questions on thermodynamics exams-- is that they didn't convert to Kelvin. This problem is very typical of most of what you'll see-- this is from the Barron's AP physics B on page 226. It says a confined gas is a temperature of 27 degrees, so its initial temperature is 27 degrees Celsius. It has a pressure of 1,000 pascals, or newtons per meter squared, and the volume is 30 meters. I think in one of the early videos, I think I said newtons per meter cubed, but it's newtons per meter squared-- I just want to make sure I didn't confuse people previously, so that's the initial volume. It says the volume is decreased, so then we go to this date, where my new volume is going to be 20 meters cubed. The new temperature is increased, and so the new temperature is now 50 degrees Celsius. They want to know what is the new pressure? Before we just substitute into the equation, and solve for the new pressure, remember-- if they gave it to you in Celsius, convert to Kelvin. If they gave it to you in Fahrenheit, which they seldom do, then convert into Celsius, and then convert to Kelvin. We already know that zero Kelvin is equal to minus 273 Celsius. Or another way you could say it is x Kelvin is equal to-- essentially, whatever degree you get in Celsius, you just add 273 to it. Does that make sense? Think of it this way: if you're at zero degrees Celsius, you're already 273 degrees above zero Kelvin. Think about that, and hopefully that makes sense-- maybe you want to draw a number line just to make sure. Whatever Celsius degree you have, just add 273 to it, and you'll get Kelvin. Add 273 to 27 degrees Celsius, and that's 300 Kelvin, and then 50 degrees Celsius is-- add 273 to it. So 50 plus 273 is 323, so now we can substitute into this formula. P1, 1,000 pascals times V1 times 30 divided by the first temperature-- remember to do it in Kelvin-- 300, is equal to P2. We don't know what that is. P2 times V2 times 20 divided by our new temperature, 323. We can simplify this: we could take two 0's off of here, take two 0's off of here, then you could take a 3 out of here, and then take a 3 out of here, and we're left with 100. This is equal to 100-- that was 30,000 divided by 300, and so that's 100 on the left-hand side. So we have 100 is equal to P times 20 over 323. I'm running out of time. If I were to solve for it, 323 times 100 divided by 20 equals-- so my new pressure is 1,615 pascals. I just solved this equation, and the hard part was converting to Kelvin. See you in the next video.