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Q. Consider N atoms confined on a surface of area A at temperature T. The atoms form a two-dimensional (2D) gas of classical, non interacting particles.
(a) Compute the partition function for system.
(b) Calculate the Helmholtz free energy, F, of the gas. Compare it with the 3D case.
(c) Estimate the internal energy of the gas. Compare it with the 3D case.
(d) Calculate the surface tension of the gas, γ=(∂F/∂A)_(T,N).
(e) Calculate the momentum distribution n(p) which determines the number of
atoms N(p) with momenta between p and p + dp: N(p) = n(p)dp.

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