It looks to me like you slipped a decimal place in your first quotient above.
I get 10^28 J/5.11 x 10^14 m^2 = 1.95 x 10 ^13 J/m^2. This would reduce your
answer temp. by a factor of 10^(1/4) = 1.7783. This makes the mean radiant
temp. at about 1819 K or 1546 deg C. Of course this ignores the effect of
the latent heat of vaporization of the hydrosphere which would consume only
about some 5 x 10^26 J or 5 % of the released energy in boiling off the
oceans. With this amount of H2O greenhouse gas in the atmosphere the surface
temp would probably have to be significantly higher than this so that the
effective radiant temp. higher up in the outer atmosphere could average
around 1800 K. This would also make the atmospheric surface pressure
comparable to the pressure on the abyssal plains under the current oceans and
the superhot atmosphere would be nearly all water. So unless Noah's ark was
a giant balloon it would not float on a liquid ocean; it would sit on the
dry bottom under superhot superpressurized water vapor atmosphere that would
make Venus seem a mountaintop in Antarctica.
BTW, how on earth could the pre-flood lithosphere just decide to sink into
the mantle? Did the mantle supposedly have lots of empty pockets in it
that filled in, or what? What was the stuff (if any) that this oceanic
lithosphere stuff displaced when it subducted into the mantle? Whatever was
displaced would have its gravitational potential energy increased as that
stuff was displaced upward to make room for the subducting material. In
order to have a net energy release and a spontaneous collapse the displaced
stuff would have to be less dense than the sinking lithosphere rock. If this
is the case, what prevented the collapse from occurring immediately after the
earth was formed?
Glenn are the answers to these background questions simple enough to explain
here without us having to go dig up our own copies of these papers?
David Bowman
dbowman@gtc.georgetown.ky.us