(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a particle confined within a box in the shape of a cube of edges L_{x}=L_{y}=L_{z}. The possible energy levels of this particle are then given by the quantized energy for a particle in a 3D box.

Calculate explicitly the force per unit area (or pressure) on this wall. By averaging over all possible states, find an expression for the mean pressure on this wall. (Exploit the property that the average values of the quantum numbers must all be equal by symmetry). Show that this mean pressure can be very simply expressed in terms of the mean energy of the particle and the volume of the box.

2. Relevant equations

In part (a), it was said that the particle exerts a force on a wall perpendicular to the x-axis such that F_{x}= - dE/dL_{x}(these are partial derivatives).

3. The attempt at a solution

I don't want the final answer, however, I just need guidance on how to get there

1) This is through a quasistatic process such that dW=(mean pressurve)*dV

2) What does it mean when "exploit the property that the average values of the quantum numbers are all equa by symmetry?"

3) I know that the length along the x-axis changing by an amount dL_{x}whereas the area of the wall is A=L_{y}L_{z}=constant. How do I related these values together?

4) I understand how to solve it using Kinetic Theory of Gases, however, my professr prefers using the method of pressure, etc.

5) Just some guidance is greatly appreciated. Thanks!

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# Homework Help: Statistical Mechanics

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