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# Thermodynamics part 2: Ideal gas law

## Video transcript

welcome back in the last video I told you that that pressure times volume is a constant that if you increase the pressure or if you increase the volume you're going to decrease the pressure and hopefully you got an intuitive sense why or or likewise if you squeezed the balloon or the box and there are no openings there then the pressure within the box would increase so with that said let's see if we can do a couple of fairly typical problems that you'll see so let's say that I don't know I have a box or a balloon or something and let's say it has a volume so let me call this the initial volume let me let me erase all of this so let's say my initial volume is 50 cubic meters and let's say my initial pressure my initial pressure is 500 Pascal's just so you remember what's a Pascal that's 500 Newton's per meter 500 Newton's per meter cubed and then what is and then let's say that I take that box or balloon or whatever and I compress it down to 20 meters cubed so let's say I compress it so I squeeze it so that was like the first example I gave last time but it's the same container and I squeezed it down to 20 meters cube what's going to be the new pressure well you should immediately have an intuition that what happens when you squeeze the balloon it becomes harder to do it sorry I just had some peanuts I should have had some water with it um my throat's very dry but anyway I'll try to soldier through this this this video so what's going to be the new pressure well it's definitely going to be higher right when you decrease the volume the pressure increases they're inversely related so the pressure is going to go up and let's see if we can calculate it well we know that p1 times v1 is equal to some constant and and since we have no aggregate change in energy right I'm just telling you that the box is squeezed I'm not telling you whether it did any work or anything like that that the same constant is going to be equal to the new pressure times the new volume is going to be equal to p2 times v2 so you could just have the general relationship p1 times v1 is equal to p2 times v2 assuming that no work was done and there was no exchange of energy from outside of the system and in most of these cases when you see this an exam that is the case so the old pressure was 500 Pascal's times 50 meters cubed and one thing to keep in mind because we're using both the same units on the same side because this is an equivalent this equivalence is not equal we're not saying it has to equal to some necessary absolute number for example we don't know exactly what this K is although we could figure it out right now as long as you're using one unit for pressure on this side and one unit for volume on this side you just have to use the same units so we could have done this same exact problem the exact same way if instead of meters cubed they said liters and as long as we wanted we had liters here you just have to make sure using the same units on both sides so in this case we have 5500 Pascal's of pressure the volume is 50 meters cubed that's going to be equal excuse me to the new pressure p2 times the new volume 20 meters cubed and so let's see what we can do we can divide both sides by 10 so we can name you know just take a 10 out of there and then we could divide both sides by 2 so that becomes a 250 and so we we get 250 times 5 is equal to p2 and so p2 is equal to 1200 and 50 Pascal's and if we kept with the unit's you would have seen that so when I decreased the volume by more you know by roughly 60% is how much I decrease the volume I have the pressure actually increased by two and a half so that that gels with what we talked about before now let's let's add another variable into this mix let's talk about temperature and and like pressure and like volume and like a work and a lot of concepts that we talk about in physics temperature is something that you probably are at least reasonably familiar with right temperature I mean you how do you view temperature temperature I think if a high temperature means something is hot and a low temperature means something is cold and I think you that also gives you intuition that that a higher temperature object has more energy right higher temperature has higher energy right the Sun has more energy than a then an ice cube right I think that's fair enough and I think you also have the sense that what what would have more energy a a hundred degree a hundred degree let me think of something a cup of tea a cup of tea or or a hundred degree let me do I don't know that of that of a you know barrel of tea I want to make them equivalent in terms of what they're holding so I think I think you have the sense even though they're the same temperature they're both pretty warm let's say this one hundred degrees Celsius so they're both boiling that the barrel because there's more of it it's going to have more energy right it's it's equally hot and it's just there's just more molecules there and so that's what temperature is temperature temperature in general is a measure roughly is is equal to some constant times the kinetic energy the average kinetic energy kinetic energy per molecule for molecule sorry it's the average kinetic energy for molecule so the average kinetic energy of the system divided by the total number of molecules we have so if I took so it's it you I guess another way we could talk about it is temperature is essentially energy for molecule so something that has a lot of molecules where n is the number of molecules right so another way we could view this is that the kinetic energy of the system of the system is going to be equal to the number of molecules times the temperature and you know this is just a constants of you know times 1 over K but 1 over K we don't even know what this is so we could say that's still a constant so the kinetic energy of the system is going to be equal to some constant times the number of particles times temperature right and we don't know what this is and we're going to figure this out later so this is another interesting concept we said that pressure times volume is is proportional to the kinetic energy of the system of the system the aggregate if you take all of the molecules and combine their kinetic energies and these are the same case I mean I could put another constant here I call that k1 and we also know we also know that that the kinetic energy of the system is equal to some other constant I don't know times the number of the number of the number of molecules I have times the temperature right so if you think about it you could also say that you know this is proportional to this and this is proportional to this so you could say that pressure times volume is proportional to the number and these are all different proportional constants we'll figure out this exact constant later but we can say the pressure times volume is proportional to the number of molecules we have times temperature and recent kind of temperatures is we can kind of view it as energy per molecule or another way we could say that if this constant is constant which it is by definition let me change colors and the number of molecules is constant we have PV over temperature pressure times volume over temperature is going to be equal to something times the number of molecules so we could say that's some other constant I don't know k4 so this is another interesting thing to think about we said pressure times volume is equal to pressure times volume now we added temperature into the mix so let's let me clear this up I think I got my throat back so we could say p1 times v1 times over t1 is equal to p2 times v2 over t2 and does this make sense to you let's say what happens if if I have another box and you know I have my particles bouncing around like always and they're you know I have some volume and some some amount of pressure what happens when the temperature goes up what am I saying well I'm saying that the average kinetic energy per molecule is essentially going to go up so they're going to bounce against the walls more so if they bounce against the walls more the pressure is going to go up right assuming volume stays flat right another way you could you could think about it let's say let's say the temperature goes up and I increase and let's say the pressure stays flat so what did I have to do well I just said if the temperature goes up the average kinetic energy of each molecule they'll bounce more so in order to make them bounce the against the sides of the walls as often I'd have to increase the volume so if you hold pressure constant the only way you can do that is by increasing the volume while you increase the temperature so let's keep this in mind and we will use this to solve some pretty typical problems in the next video