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# Thermodynamics part 1: Molecular theory of gases

Intuition of how gases generate pressure in a container and why pressure x volume is proportional to the combined kinetic energy of the molecules in the volume. Created by Sal Khan.

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• I still didn't get why P.V is a constant. I mean I got what he said in video, but why is it a constant? • While it is the case that the "constant" K in the video really does depend on the number of molecules in the gas and the absolute temperature, one can still easily understand why the product, PV, will be constant if the number of molecules and their average kinetic energy (measured by the temperature) doesn't change. Imagine inserting a partition in the volume, V, which just divides the volume into two equal parts of volume V/2 each. Because the N molecules will be uniformly distributed through the volume, V, before insertion of the partition, the insertion will result in N/2 molecules, on average, in each of the two subdivisions. But each of these two sets of N/2 molecules were exerting a pressure, P, on the walls of their separate subdivisions before the insertion and they will continue to do so after the insertion. Now imagine what would happen if the N/2 molecules in one of the subdivisions were now placed in the other subdivision. Clearly both sets of N/2 molecules would exert the pressure, P, on the walls of the V/2 volume they now share. Consequently, the total pressure would now be 2P. But the total occupied volume would now be V/2, and so the product (2P)(V/2) = PV, just as before. The argument generalizes to inserting (n - 1) partitions to create n subdivisions of volume, V/n, each, containing (on average) N/n molecules each generating equal pressure, P, in each subdivision. Now put all the molecules in just one of the subdivisions to produce a total pressure of nP in that one crowded subdivision. This time (nP)(V/n) = PV. Finally, consider that N/n of the molecules are contributing P/n to the pressure in the original volume,V. Now expand the volume to nV and realize that then only N/n molecules occupy each volume, V, and generate the pressure, P/n, within that volume as they did before the expansion. But then the pressure throughout the volume, nV, will just be that common pressure for each volume, V, P/n. So now we have (P/n)(nV) = PV.
• How is the momentum of the particles changing if in an ideal gas all collisions are inelastic and momentum is conserved? Thank you in advance. • When Sal writes the formula for Force as "Change in momentum over Change in time", why is "momentum" P, and later, Pressure is also P? Are they both correct? Doesn't this get confusing? • another fundamental question, if i heat up a liquid then the volume increases and the density decreases. If the volume is fixed, for example a liquid is in a bottle and I heat it up and the volume can't get even bigger so the pressure increases instead of the volume. Do the density decreases too in a fixed volume? I have a problem by imagineing this.

Thank's for help. • In all of the thermo vids, Sal uses PV diagrams to teach with. Why are P and V used? Why not T and P, or P and S, or V and dirt (I'm being facetious there) or something else? Why P and V? • At , why and how does the particle change its momentum after bouncing off the wall of the container ? • • If CO2 is one of the main components of smoke and it is heavier than air, then why when there is a fire, people try to crawl on the floor so as not to suffocate in the smoke?
Won't you actually suffocate more quickly if you are down because its concentration near the floor will be greater than in then surrounding air? • How does this relate to the Venturi Effect? If Ihave a large diameter pipe flowing into another smaller pipe Bernoulli says the pressure will be greater in the larger pipe than in the smaller and the speed in the smaller pipe will increase and the pressure will reduce. This video however says larger volume smaller pressure. Does this mean only for a closed system ie. no flow in or out? • Yes.

The video is talking about a gas in which there is ZERO BULK MOTION. in other words there is no flow of gas as a large body. The only kinetic energy in this ideal situation is the microscopic kinetic energy of the molecules.
The velocities are so many and so varied that they average out to zero

For the Bernoulli effect to occur, there needs to be a flow of gas. The flow of air outside an airplane for example: the pitot tube (small tube near the cockpit) measures the change in pressure due to change in air speed.
Your example of the venturi effect (in a carburetor) is another example 