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\sect{Pressure of gas in a box with gravitation}

Consider an ideal gas in a 3D box of volume ${V=L^2 \times (Z_b-Z_a)}$. 
The box is placed in an external gravitational field that points along $-\hat{z}$.

\Dn

a) Find the one-particle partition function $Z_1(\beta,Z_a,Z_b)$.

\Dn

b) What is the $N$-particle partition function $Z_N(\beta,Z_a,Z_b)$.

\Dn

c) What are the forces $F_a$ and $F_b$ acting on the floor and on the ceiling of the box?

\Dn

d) What is the difference between these forces? explain your result.


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