Consider a cylindrical column of cross-sectional area A and infinit...

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Consider a cylindrical column of cross-sectional area A and infinite height. The column is filled with classical ideal gas of N non-interacting, non-relativistic, indistinguishable point particles of mass m. The gas is in equilibrium at a fixed temperature T. The force of gravity acts upon the particles of gas in the column via the gravitational potential energy U(Z) = mgz, where to is the height within the column, and the constant g is the gravitational acceleration at the surface of the Earth.

a) What is the density of the gas n(2) at height to within the column?
b) What is the pressure of the gas p(z) at height to within the column?
c) What is the chemical potential of the gas (z) at height to within the column?

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