A surface with M absorption sites is in equilibriurn with a rnixed ...

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A surface with M absorption sites is in equilibriurn with a rnixed ideal gas containing rnolecules of types A and B. Each site can take either a single A rnolecule, with energy EA, or a single B rnolecule, with energy E8. The partial pressures of the two gases are PA and p8. O Derive expressions for the fractions of sites ÍA and f B that are occupied by particles A or B, respectively. O Assume that both gases are rnonoatornic. Determine the relation between PA and PB that will give equal nurnber of A and B absorbed atorns. Consider an ideal gas of bosons confined to rnove on a two-dirnensional surface, of area L 2 . O Write the equation for the average nurnber of particles in the excited states as an infinite surn as a function of the fugacity, z, for this systern. O What is the density of state you need to consider to transforrn the surn into an integral? O Find an expression for the total energy, E, of the system as a function of the pressure, P. O Is there a Bose-Einstein condensation in this two dimensional systern? Explain. [Hint: the following integral will be useful: ¡0 + 00 z-i:�-l == - ln (1 - z) ]

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