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Guffie
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Homework Statement
Say you have a large column of gas with insulating walls standing on the Earth's surface, which is L high and at room temperature (25degC) at the interface of the surface and column. Assuming the potential energy on the gas is only duel to gravity, U = mgx where x is the altitude of the gas, what's the expectation value of the potential energy?
Homework Equations
U = mgx
<f(x)> = int_{a,b} P(x) f(x) dx where P(x) is the distribution function
The Attempt at a Solution
I am having trouble finding the correct distribution function for the potential energy.
I thought it would be the Maxwell-Boltzman distribution, but that is only in terms of momentum and velocity really,
There is a distribution for Energy itself but I'm not sure that it what I should be using?
Could anyone point me to the correct distribution function for this question?
After finding it the answer is just
<U>=mg int_{0,10} P(x) x dx
Right?
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