  The two-dimensional steady-state Boltzmann equation for hard-disk molecules
in the presence of a temperature gradient has been solved explicitly to second
order in density and the temperature gradient. The two-dimensional equation of
state and some physical quantities are calculated from it and compared with
those for the two-dimensional steady-state Bhatnagar-Gross-Krook(BGK) equation
and information theory. We have found that the same kind of qualitative
differences as the three-dimensional case among these theories still appear in
the two-dimensional case.
