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## Physics library

### Course: Physics library>Unit 10

Lesson 1: Temperature, kinetic theory, and the ideal gas law

# 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.

## Want to join the conversation?

• 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.
(1 vote)
• 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.
• The collisions are ELASTIC. But it is the total momentum of the entire system that is conserved, not that of each particle. Conservation of momentum only applies to systems of particles, not individuals.
However, in a closed system momentum is conserved for both elastic and inelastic collisions.
• 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.
• Density is mass divided by volume so since the mass doesn't change if the volume doesn't change then the density doesn't change either.
• At , why and how does the particle change its momentum after bouncing off the wall of the container ?
• The momentum changes because the particle is suffering an impulse as it collides. At this model, every collision is elastic, which makes sense, since in the macroscopical world non-elastic collisions lose energy in the form of heat and sound, two things that a microscopical collision can't create, by definition. Thus, when the particle hits the wall, it simply bounces back.
• is PV=k related to the ideal gas law PV=nRT?
(1 vote)
• If T is constant, then nRT is a constant, and if you rename it k, you have PV = k
• 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?
• CO2 is not one of the main components of smoke. Also, while it may be present in smoke, it is not nearly as deadly for us to breathe as the other, major components, like carbon monoxide and other particulates, which are lighter than air and rise.
• 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
• i have heard that the momentum of the whole system is conserved but the momentum of individual particle is not conserved..........
i dont get it actually......
does it mean the product of mass and velocity of all the particles in the system remains constant.. but for and individual particle it is different? correct me if i am wrong...
(1 vote)
• the law of conservation of matter and momentum says that momentum cannot be created or destroyed so in the case of collision between particles. the total momentum prior to the collision and after the collision will remain constant. the momentum is just exchanged between particles.