Exhaust temperatures

We can assume the flow is adiabatic, and so isentropic. Thermal+mechanical power transmitted down the nozzle is also a constant at any plane for a constant flow. If so, (specific) kinetic energy+enthalpy is constant. Enthalpy is proportional to temperature for an ideal gas, so in that case you get something that suggests Carnot. Trivial thought experiments with non constant specific heat, phase changes or dissociation will show, in too many examples ideal efficiency beyond what the misapplication of Carnot's law would imply.

Lets try stoichiometric H2 O2 gaseous rocket at 298K@1000PSI in Guipep.
chamber 3680K@1000PSI
exhaust 2556K@14.7PSI
so Carnot eff=30.5%

v=3614m/s=6.53MJ/kg
out of what is chemically 286KJ/mol, 15.9MJ/kg
so that's 41.1% efficiency.
Frozen ISP would be 3404m/s so 5.8MJ/kg. That leaves efficiency at only 36%.

Stoichiometric carbon and oxygen 1000PSI@298K.
Chamber 4163K@1000PSI
exhaust 2960K@14.7PSI
Carnot says 28.9% (or rather I think he doesn't)

The chemical energy something like 8.95MJ/kg
shifting ISP 2711m/s=3.67MJ/kg=41%
frozen ISP 2516m/s=3.17MJ/kg=35%

I've cherry picked two data points from NIST to give an example where the issue could only really be specific heat increasing with temperature about 20% over the range. Not really to do with chemical energy per se.

http://webbook.nist.gov/chemistry/fluid/
Nitrogen 1700C/1973.15K 10MPa entropy 7.6141J/g/K enthalpy 2290.1kJ/kg
Looking at the isobaric data@0.1MPa same the entropy is found at 349.6C/622.75K, enthalpy 651.50kJ/kg.
Carnot efficiency=68.4%
from entropy=71.5%

Haven't checked these very well. Caveat Emptor.

Thanks for going through some of the calculations.

I didn't really check very much, so if I've created the impression there are no mistakes, no chance of error, and pure sarcasm it's something that wasn't intended. I was aiming at an slightly improbable but possible degree of fallibility on all the figures and methods involved. Probably mixed with irritation.

From my perspective, particularly if you look a rocket example with a constant temperature/ liquid->solid phase change it's obvious that Carnot could not apply as a limitation on work done. Made into a thermodynamic cycle on the other hand(returning exactly the way it came), that would be completely non-viable because the Carnot cycle you'd end up with encloses no volume.
Might have some more constructive thoughts later.

This is one of the areas where its clear GUIPEP is "horribly flawed". For example, its "condensed species" list is clearly way off base in many cases.


Computing case 1
Frozen equilibrium performance evaluation

Propellant composition
Code Name mol Mass (g) Composition
685 OXYGEN (GAS) 2.0000 63.9976 2O
635 NITROGEN (GASEOUS) 8.0000 224.1078 2N
578 METHANE 1.0000 16.0425 1C 4H
976 WATER 12.0000 216.1834 2H 1O
Density : 2.047 g/cm^3
4 different elements
O N C H
Total mass: 520.331258 g
Enthalpy : -6760.25 kJ/kg

148 possible gazeous species
3 possible condensed species

CHAMBER THROAT EXIT
Pressure (atm) : 340.230 184.275 0.068
Temperature (K) : 637.973 550.506 65.618
H (kJ/kg) : -6760.252 -6893.966 -7580.415
U (kJ/kg) : -6994.722 -7096.289 -7604.531
G (kJ/kg) : -11676.016 -11135.770 -8086.023
S (kJ/(kg)(K) : 7.705 7.705 7.705
M (g/mol) : 22.623 22.623 22.623
(dLnV/dLnP)t : -1.00000 -1.00000 -1.00000
(dLnV/dLnT)p : 1.00000 1.00000 1.00000
Cp (kJ/(kg)(K)) : 1.54836 1.50948 0.96269
Cv (kJ/(kg)(K)) : 1.18084 1.14196 0.59517
Cp/Cv : 1.31124 1.32184 1.61751
Gamma : 1.31124 1.32184 1.61751
Vson (m/s) : 554.47806 517.14452 177.82623

Ae/At : 1.00000 130.33903
A/dotm (m/s/atm) : 2.12309 276.72117
C* (m/s) : 722.33770 722.33770
Cf : 0.71593 1.77307
Ivac (m/s) : 908.37648 1299.58233
Isp (m/s) : 517.14452 1280.75258
Isp/g (s) : 52.73407 130.60042

Molar fractions

CO2 4.3478e-002 4.3478e-002 4.3478e-002
H2 1.9570e-006 1.9570e-006 1.9570e-006
H2O 6.0870e-001 6.0870e-001 6.0870e-001
NH3 1.2539e-008 1.2539e-008 1.2539e-008
N2 3.4783e-001 3.4783e-001 3.4783e-001