What if we were to hold volume and the number of moles constant, and we wanna think about the relationship between pressure and temperature. To volume, or vice versa, if you hold everything else constant, that's often known as Boyle's law. And this relationship, that pressure is inversely proportional And that's going to increase the pressure, so volume goes down, pressure goes up. That same number of particles with the same average kinetic energy, they're just gonna bump into the container that much more often. And you can think about it the other way. If the volume goes up, the pressure is going to go down. Room to go in that volume, and even the surface area of the container is going to be high as well. Then at any given moment, you're just gonna haveįewer bounces of particles off of the container. The same temperature, in a larger container, So, if I were to make the volume go up, so I were to some how expand this, or maybe put the exact number, the same particles with And I had the same number of particles, they have the same average kinetic energy, but let's say I were Theory point of view? Pause this video and think about it. Does that make sense from a kinetic molecular If we divide both sides by P, is that volume is proportional It is is that pressure is proportional to the inverse of volume. If we hold it at constant, I can even just writeĪ K here for constant, but that would also mean we could divide, let's say both sides by V, we can say that pressure isĮqual to some constant over V. Us that pressure times volume is going to be equal to this, How pressure relates to volume if we were to oldĮverything else constant. Whatever gas we're dealing with, the amount of that gas, and then T is the temperature in Kelvin, and R is just the ideal gas constant, that's just whateverĬonstant you're doing, so that the units all work out together. Pressure, V is volume, n is the number of moles of Gas law, PV is equal to nRT, make sense when weĬonceptualize the world here. Kinetic molecular theory and to understand why the ideal Video is take these ideas that we conceptualize in Some force, collectively, on this area, so the pressure is because of these particleĬollisions on the surface. And these are perfectlyĮlastic collisions, they're preserving kinetic energy. This side of the container, actually all sides of the container. You're having some particles that are bouncing off of Then what I have drawn here, so at any given moment, And you have your particles, let me do this in a different color, these particles areĬonstantly bouncing off of it and there's way more particles Surface of our container, this could be some type of a cube so I can draw it in 3-dimensions here, so there's some area over here. And pressure, the pressure, remember, pressure is nothing butįorce per unit area. But, the average of these kinetic energies across all of these particles, that is proportional to temperature Types of particles, they can have different masses as well. Would have some mass and some velocity, but they could all haveĭifferent velocities for sure, even if they're the same type of particle. You calculate that as MV squared over two. Moving around, zooming around, and they each would have And the temperature we're dealing with is related to the average Where their collective volume is much smaller than the You can imagine the gas as being these particles If you imagine a container, I'll just draw it in 2-dimensions here, that it contains some gas, We touched on the notion of kinetic molecular theory, So, no pressure and temperature don't have a square root relationship. Which is just the original proportionality relationship. This yields sqrt(P) α sqrt(T), where the square roots can be removed by squaring both sides yielding P α T. We can do the same operation with the pressure-velocity relationship and say that sqrt(P) α v, and only know we can relate pressure and temperature together through the transitive property using velocity. Which doesn't follow since there is no way to link the square root of temperature with pressure, except through velocity. So therefore we can say that pressure is also directly proportional to the square of the particle's velocity through the transitive property, or P α v^(2).įor some reason you're taking the square root of the temperature-velocity relationship, essentially getting sqrt(T) α v, and then saying that now the square root of temperature is directly proportional to pressure, or sqrt(T) α P. So we can say that temperature is directly proportional to the square of the particle's velocity, or T α v^(2). And temperature is directly proportional to kinetic energy where kinetic energy has the formula K.E. Pressure is directly proportional to temperature, or P α T.
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