The differential rates and emissivities of neutrino pairs from an equilibrium plasma are calculated for the wide range of density and temperature encountered in astrophysical systems. New analytical expressions are derived for the differential emissivities which yield total emissivities in full agreement with those previously calculated. The photon and plasmon pair production and absorption kernels in the source term of the Boltzmann equation for neutrino transport are provided. The appropriate Legendre coefficients of these kernels, in forms suitable for multi-group flux-limited diffusion schemes are also computed.