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The PV relationship that comes out of Kinetic Molecular Theory is consistent with the Ideal Gas Law.

		PV = nRT
At constant P and T (therefore u),V increases with and increase of number of gas particles "N" due to an increase in the number of collisions.		Avagadro's hypothesis: at constant P and T, V = kn
A decrease in V at constant T (and therefore u) and N results in an increase in pressure due to an increase in the frequency of collisions, and a decrease in the surface area over which the force of each collision is dispersed (huh ).		Boyle's Law: at constant composition (n) ant T, PV = k
Increasing the Temperature increases the speed the molecules are traveling and this increases the force exerted by the collisions (because each collision involves a larger change in momentum).
To keep the pressure constant the volume must increase so that (1) there are fewer collisions per unit time, and (2) the force of each collision is distributed over a larger area.		Charle's Law: at constant composition (n) and pressure V = kT
At constant volume an increase in the speed of the molecules results in an increase in pressure because (1) as the speed of the particles increases each impact exerts more force on the container, and (2) there are more impacts per unit time.		No one's Law: at constant compostition (n) and volume P = kT

Other things that come out of KMT

n is number of moles, and N is number of particles

The relationship between the velocities of two samples of gas containing the same number of particles at the same temperature, pressure, and volume.

KMT tells us that if the pressures of two gases are the same then the force one gas exerts against the wall of its container must be equal to the force that the other gas exerts against the wall of its container. That is, the total force exerted by all the particles must be the same in the heavy gas and the light gas. Since the number of particles is the same the lighter gas must be moving faster than the heavier gas even though the temperatures of the gases are the same.

The relationship between mass and speed can be demonstrated mathematically as the root mean squared velocity of a gas.

Root mean sqaured (RMS) velocity is not the average velocity, but it is as close as we can get to the average velocity with out knowing the distribution of the velocities of the particles. However, at low temperatures the RMS velocity is close to the average velocity.

Since the distribution of the velocities is a Boltzman distribution it is possible to calculate the average velocity, but this is beyond the scope of this class.

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