The second virial coefficient, correct to the fourth power in Planck's constant, is derived for a twohyphen;dimensional gas in an external potential field. The molecules of the gas are assumed to interact via either a renormalized (12,6) potential or the Sinanogcaron;lundash;Pitzer (12,6,3) potential, where the inverse cube term accounts for the perturbation of the gasndash;gas interactions by the field. As the magnitude of the perturbation increases the quantum defects at a given temperature are enhanced. The models are applied to data for CH4, CD4, H2, and D2on a uniform graphitic surface. The results are inconclusive, since uncertainties in the data for the hydrogens preclude a (12,6,3) analysis for these gases.
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