Thermodynamics part 1: Molecular theory of gases

after all the work we've been doing with with fluids at you you probably have a pretty good sense of of what pressure is but now let's let's think a little bit about what what it really means especially when we think about it in terms of a gas in a volume and remember what was the difference between a gas and a liquid they're both fluids they both take the shape of their containers but a gas is compressible while a liquid is incompressible so let's let's start focusing on gases so let's say I have a container say let me draw a cube this is my container and I have a bunch of gas in it and so what is a gas made of well it's just made up a bunch of the molecules of the gas itself and I'll draw each of the molecules by a little dot so just going to have a bunch of molecules in it all right many many many more than what I've drawn but that's indicative and they'll all be going in random directions let me draw they're there you know this one might be going really fast and that direction that one might be going a little bit slower in that direction they all have their their own little velocity vectors and they're always constantly bumping into each other and bumping into the sides of the container and ricocheting here and there and changing velocity but in general especially at this level of physics we assume that these are ideal that this is an ideal gas that that all of the all of the bumps that occur there's no loss of energy or essentially that they're all elastic bumps between the different molecules so there's no loss of there's no loss of momentum so let's keep that in mind and everything you're going to see in high school and on the AP test are going to deal with ideal gases so let's think about what an ideal gas sorry what pressure means in this context so we you know a lot of what we think about pressure is something pushing on an area well if we think about pressure here let's pick an arbitrary area let's let's take this side let's say let's take this surface of its container what is the pressure whereas the pressure going to be generated on to the surface what's going to be generated by just the you know millions and billions and trillions of little bumps every time let me draw a side view so if this is a side view of the container of that same side every second so you know there's always these little these molecules of gas moving around and if we pick an arbitrary period of time they're always ricocheting off of off of the side you know this one might let's say you know we're looking at time over a you know a super small fraction of time over that period of time this one might end up here you know this one may be bumped into it right after it ricocheted came here this one changes momentum goes like that you know this one might already been going in that direction that one might ricochet but what's happening is in any given moment since there are so many gases so many molecules that there's always going to be some molecules that are bumping into the side of the wall and when they bump they have a change in momentum right and all forces all forces is change in momentum over time change in momentum over some change in time right and what I'm saying is in any interval of time over any period any change in time there's just going to be a bunch of particles that are changing their momentum on the side of this on the side of the wall and so that is going to generate force and so if we think about how many on average because it's it's hard to keep track of each particle individually you know in when we did kinematics and stuff we would keep track of the individual object at play but when we're dealing with gases and kind of the you know things on a macro level you can't keep drove any keep track of any individual one unless you have some kind of unbelievable supercomputer but we can say on average this many this many particles are changing momentum on this wall in this amount of time and so the force exerted on this wall or the surface is going to be whatever X and if we know what that force is and we know the area of the wall we could figure out pressure right because pressure is equal to is equal to force divided by area so what does this help us with well let's well I wanted to give you that intuition first and now I'm just going to give you really the two things that actually I'm going to give you the one formula that you really just need to know in thermodynamics and then as we go into the next few videos you'll hopefully get I'll kind of prove to you why it works and hopefully give you more of an intuition so now you understand hopefully what pressure means in the context of a gas in a container so with that out of the way let me give you a formula and I hope by the end of this video you have the intuition for why this formula works so in general if I have an ideal gas in a container the pressure exerted on the gas on the on the side of the container or actually even any at any point within the gas because it's all it'll all become homogeneous at some point and we'll talk about entropy in in future videos but the pressure in the container and on to on its surface times the volume of the container is equal to some constant and we'll see in future videos that that constant is actually proportional to the average kinetic energy of the molecules bouncing around and that should make sense to you right if the molecules were moving around a lot faster then you would have more kinetic energy and then they would be changing momentum on the sides of the surface a lot more so you would have more pressure but let's let me let's see if we can get a little bit more intuition onto why pressure times volume is a constant so let's take one exam we take oh that's not what I wanted to do draw I'll do a different color so let's say I have a container now and it's got a bunch of molecules of gas in it and just like I showed you that last in that last right before I erased you know these are bouncing off of the sides at a certain rate right they all have the same you know some all of these molecules on average each of the molecules might have a different kinetic energy it's always changing because they're always transferring momentum to each other but on average they all have a given kinetic energy right and and they keep bumping at a certain rate into the wall and that that kind of determines the pressure now what happens if I don't know I were able to squeeze the box so if I were to able to decrease if I were able to decrease the volume of the box so let's say I was so this is you know I just take that same box the same number of molecules in it but I squeeze I make the volume of the box smaller what's going to happen well I have the same number of molecules in there I have the very same number of molecules in there and they're the same kinetic energy and so on average they're moving with the same velocity but what so now is going to happen they're going to be hitting the sides more often right at the same time here that say this particle went bam bam now it could go Bam Bam I don't know BAM they're going to be hitting the sides more often so you're going to have more changes in momentum so you're actually going to have each particle is actually going to exert more force on each surface because it's going to be hitting them more often in a given amount of time and the surfaces themselves are smaller so you have more force on a surface and on a smaller surface so you're going to have higher pressure so hopefully that gives you an intuition that if I had some amount of pressure in this situation if I squeeze the volume the pressure increases and and another intuition if I have a balloon right the what blows up a balloon was the internal air pressure of you know the helium work or your your own exhales that you put into the balloon and the more and more you try to squeeze a balloon let's say if you squeeze it from all directions you have to be it gets harder and harder to do it right and that's because the pressure within the balloon increases as you decrease the volume and that so if volume goes down pressure goes up right and that makes sense that falls you know they multiply each other you have to have a constant and so let's take the same example again what happens if you make the volume bigger so let's say I have now that's you know huge like that I should have done it more proportionally but I think you get the idea I have the same number of particles and so let's say I had a particle here and some period of time it could have gone Bam Bam Bam right it could hit the walls twice or whatever and now in this situation with larger walls it might just go Bam and that same amount of time it'll maybe get here it won't even hit the other wall so the particles in on average we're going to be colliding with the wall less often and the walls are going to have a larger area as well so in this case when our volume goes up the average pressure the pressure in the container goes down hopefully that gives you a little of intuition and so you'll never forget this that pressure times volume is constant and and then we can use that to do some pretty common problems which I'll do in the next video because I'm about to run out of time see you soon