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I'm about 90% sure I'm right here. But if you find I'm wrong please let me know.
From what I understand the thermodynamic efficiency (efficiency of heat energy converted to mechanical energy) is:
TE = 1 - 1/CR^k-1
TE = thermodynamic efficiency
CR = compression ratio
k = specific heat ratio
If you do the equation with a CR of 10 to one then:
Nitrogen (k = 1.4) = TE of 60%
Water vapor (k = 1.3) = TE of 50%
CO2 (k = 1.28) = TE of 48%
To get a TE of 60% with water vapor you'd need a CR of 22:1.
And with CO2 you'd need a CR of 27:1.
This is why hellium or argon would be good choices for a closed loop engine like a steriling engine:
Hellium (k = 1.667) at 10:1 CR = TE of 78%!
Argon (k = 1.667) at 10:1 CR = TE of 78%!
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