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Questioning The Derivative of Kinetic Theory of Ideal Gases [p=(1/3)(N)(m)(u^2)/(V)]

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science_world
#1
Apr23-12, 07:38 AM
P: 7
The kinetic theory of gas state that p=(1/3)(N)(m)(u^2)/(V).
In one step of its derivative related to change of momentum and force given to the wall (Refer to Cubic Container and molecule movement in x,y,z axes in attachment), the equation is given by:

change in momentum / time = force
delta(p) / (2L/u) = F
2mc / (2L/u) = F
(m)(u^2) / (L) = F

*L= length of cube
m = mass of one molecule
u = velocity of one molecule in x axis

This equation assume that "time" means [time taken for the molecule to move from one side of cube to the other side and back to the first side (2L= distance traveled)] divided by [velocity of molecule = u].

I think this is a wrong assumptions. Time for rate of momentum change actually means the time in which the force take to change the momentum of a particle. This means time in the above equations should be [time when force by wall change the momentum of particle, in other words the collision time] not [time taken to move from one side to another side].

Someone please do explain this. Thank you.

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haruspex
#2
Apr24-12, 06:04 AM
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The total force on the wall is the rate of change of momentum of all the particles taken together. That rate will depend on the frequency each particle strikes the wall, on average, and that depends on the time to travel 2L.
science_world
#3
Apr25-12, 08:45 AM
P: 7
But, in usual cases, such as calculating forces given by an object to a wall, the time used is time taken in collision, not time taken for the object to move from a point to that wall and back to that point again. Why it doesn't apply here?

Refer to formula: delta p / delta t = F
delta t is collision time. This formula is also used in kinetic theory of gases.

haruspex
#4
Apr25-12, 04:35 PM
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Questioning The Derivative of Kinetic Theory of Ideal Gases [p=(1/3)(N)(m)(u^2)/(V)]

Because what is being calculated is the average force over time. If you could look at a perfectly detailed graph of force v time you'd see it made up of gazillions of separate tiny pulses, but that's not of interest.


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