The previous analysis of the convective Urca neutrino loss process in
degenerate, convective, quasi-static, carbon-burning cores by Barkat and
Wheeler omitted specific consideration of the role of the kinetic energy flux.
The arguments of Barkat and Wheeler that steady-state composition gradients
exist are correct, but chemical equilibrium does not result in net cooling.
Barkat and Wheeler included a "work" term that effectively removed energy from
the total energy budget that could only have come from the kinetic energy,
which must remain positive. Consideration of the kinetic energy in the
thermodynamics of the convective Urca process shows that the convective Urca
neutrinos reduce the rate of increase of entropy that would otherwise be
associated with the input of nuclear energy and slow down the convective
current, but, unlike the "thermal" Urca process do not reduce the entropy or
temperature.Comment: 16 pages, AAS LaTex, in press, Astrophysical Journal, September 20,
Vol 52