Learn about Thermodynamics - part 1 Video

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Learn about Thermodynamics - part 1

After all the work we’ve been doing with fluids. You probably have a pretty good sense of what pressure is but now let’s think a little bit about 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? There both fluids. They both stake the shape of there containers but a gas is compressible while a liquid is incompressible. So let’s start focusing on gases. So let’s say I have a container. Let say—let me 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 just made of a bunch of the molecules of the gas itself and I'll draw to you the molecules by little dot. So this is just going to have a bunch of molecules in it, right. Many, many more that what I have drawn but that’s indicative and they’ll be going in random directions. Let me draw their you know, this one might be going really fast in that direction, that one might be going a little bit slower in that direction. They all have there own little velocity vectors and there 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 this level of physics. We assumed that these are ideal that this, an ideal gas that all of the bumps that occur just no lost of energy or essentially that there all elastic bumps between the different molecules. So there's no lost of, there's no lost of momentum. So let’s keep that in mind and everything you’re going to see in high school and on AP test are going to deal with ideal gases. So let’s think about what an ideal gas, oh sorry what pressure means in this context. So 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 take this side. Let say; let’s take this surface of its container. What is the pressure? Where is the pressure going to be generated onto the surface? Well its going to be generated by just the, you knows 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 and at that same side every second. So you know there's always this little molecule of gas moving around and if we pick an arbitrary period of time. There always ricocheting half of the side, you know this one might. Let say you know were looking at time over you know a super small fraction of time. Over that period of time, this one might end up here. You know this one maybe bump into it right after ricocheting it came here. This one changes momentum, goes like that, you know this one might already been going in that direction that one might ricocheted. But what's happening is in any given moments since there are 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 of momentum right and all force is change in momentum over time. Change in momentum over some change in time right and what I'm saying is at any interval of time over any period or any change in time. There’s just going to be a bunch of particles that are changing there momentum 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 its hard to keep track of each particle individually, you know when we did kinematic and stuff. We would keep track of the individual object to play but when we're dealing with gases and kind of the you know things on a macro level. You can't keep draw any, keep track of any individual one unless you have some kind of unbelievable super computer but we can say on average. This many particles are changing momentum on this wall and this amount of time, and so the force exerted on this wall or this surface is going to be whatever X. And if we know what the force is and we know the area of the wall, we could figure out pressure right. Its pressure is equal to force divided by area. So what is this helped us with? Well its, well I want to give you that intuition first and now I'm just going to give you really the two things. Actually I'm going to give you the one formula that you really just didn’t know in thermodynamics and then as we go into the next few videos. You’ll hopefully get a kind of prove why it works and hopefully you give you more intuition. So now you understand hopefully what pressure means in the context of a gas in the 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 and on the side of the container or actually even at any point within the gas because its all, there all become homogenous at some point and well talk about entropion in future videos but the pressure in the container and on its surface times the volume of the container is equal to some constant. And well see in future videos that constant is actually proportional to the average kinetic energy of the molecules bouncing around and that should makes sense to you right. I f 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. Let see if we get little bit more intuition onto why pressure times volume is a constant. So let’s take one example. Let me take, oh that’s not what I wanted to do. I'll do a different color. So let say I have a container now and it’s a got a bunch of molecules of gas in it and just like I showed you in that last all right before I erased. You know these are bouncing off of the sides at a certain rate, right. And they have all the same you know, all of these molecules on average. Each of the molecules might have a different kinetic energy. It’s always changing because were transferring momentum to each other but on average they have all given kinetic energy right. And they keep bumping at a certain rate into the wall and that kind of determine some 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 lets say I was; this is you know I just take that same box to the same number molecules in it but I squeezed. I make it the volume of the box smaller. What's going to happen? Well I have the same number of molecules in there and the very same number of molecules in there under the same kinetic energy and so on average there moving with the same velocities. So now what's going to happen? There going to be hitting the sides more often right and the same time here that say this particle went bum, bum. Now it go bum, bum I don’t know bum. There going to be hitting the sides more often. So you’re going to have more changes in momentum. So your 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 at a given amount of time and the surfaces is them smaller. You see have more force on a surface and on a smaller surface. So you’re going to have higher pressure. So hopefully that gives an intuition that’s if I have some amount of pressure in this situation. If I squeeze the volume, the pressure increases and another intuition if I have a balloon right, what would blows-up a balloon? Well it’s the internal air pressure of the helium or your own exhales that you put into the balloon and the more and more you try to squeeze the balloon. Let say if you squeeze it from all direction. 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. So if volume goes down, pressure goes up, right and that makes sense that falls. When you know when they multiply each other. You have to kind of constant and so let’s take the same example again. And what happens if you make the volume bigger. So let say I have—now that’s you know, huge like that. I should have done that more proportionally but I think you get the idea and the same number of particles. And so we say you had a particle here and in some period of time it could have gone bum, bum, bum right. It can hit the walls twice or whatever and now in this situation with larger walls. It might just go bum and at that same amount of time it will maybe get here or you can hit the other wall. So the particles on average were 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 or 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 then we can use that to do some pretty common bumps which I'll do in the next video because I'm about to run of time. See you soon.

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After all the work we’ve been doing with fluids. You probably have a pretty good sense of what pressure is but now let’s think a little bit about 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? There both fluids. They both stake the shape of there containers but a gas is compressible while a liquid is incompressible. So let’s start focusing on gases.

So let’s say I have a container. Let say—let me 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 just made of a bunch of the molecules of the gas itself and I'll draw to you the molecules by little dot. So this is just going to have a bunch of molecules in it, right. Many, many more that what I have drawn but that’s indicative and they’ll be going in random directions. Let me draw their you know, this one might be going really fast in that direction, that one might be going a little bit slower in that direction.

They all have there own little velocity vectors and there 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 this level of physics. We assumed that these are ideal that this, an ideal gas that all of the bumps that occur just no lost of energy or essentially that there all elastic bumps between the different molecules. So there's no lost of, there's no lost of momentum. So let’s keep that in mind and everything you’re going to see in high school and on AP test are going to deal with ideal gases.

So let’s think about what an ideal gas, oh sorry what pressure means in this context. So 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 take this side. Let say; let’s take this surface of its container. What is the pressure? Where is the pressure going to be generated onto the surface?

Well its going to be generated by just the, you knows 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 and at that same side every second. So you know there's always this little molecule of gas moving around and if we pick an arbitrary period of time. There always ricocheting half of the side, you know this one might. Let say you know were looking at time over you know a super small fraction of time. Over that period of time, this one might end up here. You know this one maybe bump into it right after ricocheting it came here. This one changes momentum, goes like that, you know this one might already been going in that direction that one might ricocheted.

But what's happening is in any given moments since there are 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 of momentum right and all force is change in momentum over time. Change in momentum over some change in time right and what I'm saying is at any interval of time over any period or any change in time. There’s just going to be a bunch of particles that are changing there momentum 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 its hard to keep track of each particle individually, you know when we did kinematic and stuff. We would keep track of the individual object to play but when we're dealing with gases and kind of the you know things on a macro level. You can't keep draw any, keep track of any individual one unless you have some kind of unbelievable super computer but we can say on average. This many particles are changing momentum on this wall and this amount of time, and so the force exerted on this wall or this surface is going to be whatever X.

And if we know what the force is and we know the area of the wall, we could figure out pressure right. Its pressure is equal to force divided by area. So what is this helped us with? Well its, well I want to give you that intuition first and now I'm just going to give you really the two things. Actually I'm going to give you the one formula that you really just didn’t know in thermodynamics and then as we go into the next few videos. You’ll hopefully get a kind of prove why it works and hopefully you give you more intuition.

So now you understand hopefully what pressure means in the context of a gas in the 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 and on the side of the container or actually even at any point within the gas because its all, there all become homogenous at some point and well talk about entropion in future videos but the pressure in the container and on its surface times the volume of the container is equal to some constant.

And well see in future videos that constant is actually proportional to the average kinetic energy of the molecules bouncing around and that should makes sense to you right. I f 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. Let see if we get little bit more intuition onto why pressure times volume is a constant.

So let’s take one example. Let me take, oh that’s not what I wanted to do. I'll do a different color. So let say I have a container now and it’s a got a bunch of molecules of gas in it and just like I showed you in that last all right before I erased. You know these are bouncing off of the sides at a certain rate, right. And they have all the same you know, all of these molecules on average. Each of the molecules might have a different kinetic energy. It’s always changing because were transferring momentum to each other but on average they have all given kinetic energy right. And they keep bumping at a certain rate into the wall and that kind of determine some 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 lets say I was; this is you know I just take that same box to the same number molecules in it but I squeezed. I make it the volume of the box smaller. What's going to happen? Well I have the same number of molecules in there and the very same number of molecules in there under the same kinetic energy and so on average there moving with the same velocities. So now what's going to happen? There going to be hitting the sides more often right and the same time here that say this particle went bum, bum. Now it go bum, bum I don’t know bum. There going to be hitting the sides more often.

So you’re going to have more changes in momentum. So your 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 at a given amount of time and the surfaces is them smaller. You see have more force on a surface and on a smaller surface. So you’re going to have higher pressure. So hopefully that gives an intuition that’s if I have some amount of pressure in this situation. If I squeeze the volume, the pressure increases and another intuition if I have a balloon right, what would blows-up a balloon? Well it’s the internal air pressure of the helium or your own exhales that you put into the balloon and the more and more you try to squeeze the balloon. Let say if you squeeze it from all direction. 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.

So if volume goes down, pressure goes up, right and that makes sense that falls. When you know when they multiply each other. You have to kind of constant and so let’s take the same example again. And what happens if you make the volume bigger. So let say I have—now that’s you know, huge like that. I should have done that more proportionally but I think you get the idea and the same number of particles. And so we say you had a particle here and in some period of time it could have gone bum, bum, bum right.

It can hit the walls twice or whatever and now in this situation with larger walls. It might just go bum and at that same amount of time it will maybe get here or you can hit the other wall. So the particles on average were 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 or 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 then we can use that to do some pretty common bumps which I'll do in the next video because I'm about to run of time. See you soon.

Transcription by: Scribe4you Transcription Services