What is the exhaust temperature of a liquid oxygen + liquid hydrogen vacuum engine?

Question

Ideally the exhaust of stochiometric liquid oxygen + liquid hydrogen rocket would be fast moving chunks of ice at zero kelvin. In this way all the potential chemical energy in the fuel/oxidizer is converted into linear momentum with nothing wasted as heat.

I assume the combustion chamber's job is to completely burn the hydrogen and oxygen together to produce very hot molecular water vapor with a minimum of ionization. The vacuum nozzle's job is then to redirect the molecules into a unidirectional stream. This means removing all the random motion and rotational and vibrational modes and redirecting the energy into linear motion. This probably requires an infinitely large nozzle bell that perfectly reflects any impinging molecules (and thus doesn't itself get hot).

Real rocket engines are presumably far from ideal, so I assume the exhaust is quite hot - though not hot enough to radiate at optical wavelengths. So my question is: assuming a thermometer co-moving with the exhaust gas, what temperature would it register?

Answer 1

In the 1990s there was an effort to produce diagnostic equipment that monitored the Space Shuttle Main Engine plume to look for early signs of engine degradation (i.e., see if the system was starting to run "engine rich").

I thought one of the many papers written around this effort might have your answer. I was hoping for measured values, but so far I've only found one that gives calculated ones.

To estimate the performance of the conceived diagnostic system, the flow conditions at the nozzle exit plane were taken from the results of TDK code calculations supplied by Klaus Gross (NASA/Marshall). These calculations indicate that the flow at the exit plane is composed of 76.2 mole percent water vapor and 23.6 mole percent molecular hydrogen. Atomic and radical species concentrations such as OH, H, O and H202 are below 100 parts per million. ... Figure 2 shows the calculated gas temperature varies from 850 K (1600R) on the centerline to about 1400K (2660R) at the wall.

(emphasis mine)

(TDK stands for Two Dimensional Kinetics)

From Investigation of the feasibility of optical diagnostic measurements at the exit of the SSME