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\sect{Quasi-Static processes in a mesoscopic system}

Write the basic level energy of a particle with mass ${\mathsf
{m}}$, which is in a box with final volume ${V}$. (Take boundary
conditions zero in the limits of the box). In temperature zero,
${\left(\beta^{-1}=0\right)}$, calculate explicitly the pressure
caused by the particle. Use the equation
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\[{p}=\sum_{r}p_{r}\left(-\frac{\partial E_{r}}{\partial
V}\right)\]
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Compare it to the equation developed in class for general
temperature
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\[{P}=\frac{1}{V}\beta^{-1}\]
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and explain why in the limit ${\beta^{-1}\rightarrow 0}$
we don't get the result you calculated. (Hint - notice the title of
this question).



