Ummm, no. All the work performed can be measured in the heat produced (adiabatic heating is a byproduct of compression, and no additional work is performed for this heat). You would take the adiabatic (reversible) portion and add it to the non-adiabatic, non-reversible waste heat produced,
The Heating of the compressed air is a combination of both the adiabatic process and the efficiency of the turbo. Separate inputs, but both require power to generate.
OR just use the one process delta T. I have seen 170 degree air compressed to 500 F. This ends up as 250,000 BTU/hr or 98 HP work. That is for 800-900 cfm of 170 hot air intake. It is worse yet for 240 degree intake, over 300,000 BTU/hr. So, yes, non-adiabatic behavior results in more shaft HP. At 120,000 rpm, 98 HP is not unrealistic IMO.
To use this example: Assuming 5000 ft elevation (~12 PSI?) and 20 PSI boost
Adiabatic heating of the air charge would bring it from 170F to 372F. To get to 500F would require a turbo efficiency of about 60%. So that's 202F increase due to adiabatic and 128F due to efficiency.
At 3000 RPM that would be ~2880 lb/hr of air or ~67 HP to compress and another 35 HP dumped into heat. Total 102 shaft HP, close to you 98 HP. Total dumped out the CAC is 222,000 BTU/hr. A little less than your 250,000 BTU/h
But this 98 HP is not parasitic to wheel HP, at least not entirely. EGT's drop up to 500 degrees across the turbine, the exhaust firecracker "free snack" is serving up at least 2/3rds (guess) of that. Still, the cost of this problem, is parasitic HP loss (some) and high EGT, and of course...overheating. But not from high EGT as some people think. From a thermally overloaded stack, on fire at the CAC.
ALL of the work done by the compressor comes from the shaft and is at the mercy of the efficiencies of the turbine and exhaust system before and after it. Tap a turbo pre and post vane. Very enlightening.
But if you agree at all, there is the explanation for the elusive drive pressure canundrum. I always thought that maybe drive pressure was related to the problems of the compression and airflow side, moreso than vane and exhaust related restriction. But who knows? I am planning a CAC tube swap to 3", whick according to some calculations, should remove 2-3 psi of restriction, translating to 2-3 psi less compressor discharge boost, or 10,000 rpm less. Too bad I don't have a drive pressure monitoring. It would be useful.
If this is something you can talk about more, please dust off the old test results from Wisconsin. If you can post a chart of the baseline run, and show ECT, IAT, Drive Pressure and EGT, I have made sense of something that we could never explain in those charts, re the ECT plateau, and the unexplainedsubsequent rise. I don't have the database, or I would do it myself.