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kpou
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Homework Statement
Thermal Dynamics question, gases?
So I have this box with lengths 20cm on each side. There are 100 balls inside of it with diameter 5mm each. The density in the box is 7.8 g/cm3. The bottom of the box vibrates so the balls bounce around. The top of the box has a movable piston of mass 1kg. What is the root mean square velo of the steel balls if the top of the box is in dynamic equilibrium with the gas of steel balls? Ignore gravity for motion of the balls.
Homework Equations
Equations
pV=NkT,
p=m<v^2>N/V=m(2/3)(U/mN)(N/V)=(2/3)(U/V)
pV=2/3U
(p+a(n/v)^2)((V/n)-b)=RT
U=N<K>=1/2Nm<v^2>
The Attempt at a Solution
What I know is there is const V, const N
And what I am basically stuck on is how can I find pressure without temperature? Or vise versa? I have a feeling the answer might be lying in the statement of the top of the box being in dynamic equilibrium to the gas of steel balls.
Also, what does the mass of the movable piston have to do with this?
All the work I've been doing is likely just garble working with the knowns. I haven't found a formula with <v^2> that works with what I can see.
I feel like if I knew how dynamic equilibrium fit into this it would make this doable. And maybe what the 1kg piston has to do with it as well.
Not being able to find T or p is starting to get to me (sad face)
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