  Neutrino opacities important in the evolution of a proto-neutron star
containing quark matter are studied. The results for pure quark matter are
compared with limiting expressions previously derived, and are generalized to
the temperatures, neutrino degeneracies and lepton contents encountered in a
proto-neutron star's evolution. We find that the appearance of quarks in
baryonic matter drastically reduces the neutrino opacity for a given entropy,
the reduction being sensitive to the thermodynamic conditions in the mixed
quark-hadron phase.
