  The velocity distribution function of the steady-state Boltzmann equation for
hard-core molecules in the presence of a temperature gradient has been obtained
explicitly to second order in density and the temperature gradient. Some
thermodynamical quantities are calculated from the velocity distribution
function for hard-core molecules and compared with those for Maxwell molecules
and the steady-state Bhatnagar-Gross-Krook(BGK) equation. We have found
qualitative differences between hard-core molecules and Maxwell molecules in
the thermodynamical quantities, and also confirmed that the steady-state BGK
equation belongs to the same universality class as Maxwell molecules.
