Physical vs Chemical Exergy Explained
Every exergy balance on a jet engine quietly depends on one split: how much of a stream's work potential comes from its state (hot, high-pressure, fast) and how much from its chemistry (it can still react with the environment). Confuse the two and your destruction numbers are fiction. Get them right and the whole second-law picture clicks into place.
Physical exergy: work from state alone
Physical exergy is the maximum useful work a stream delivers as it comes to thermal and mechanical equilibrium with the environment — no chemistry allowed. For a flow stream:
eph = (h − h₀) − T₀·(s − s₀)where h₀ and s₀ are evaluated at the dead state (T₀, p₀). In propulsion we add the stream's kinetic exergy, since a jet at 500 m/s carries real work potential in its velocity:
eflow = eph + V²/2 (+ gz, usually negligible)Compressed, hot gas leaving a compressor is rich in physical exergy. Ambient air has none by definition — it is already dead.
Chemical exergy: work from composition
Even at ambient temperature and pressure, a kilogram of kerosene can do an enormous amount of work — because its composition is far from equilibrium with the atmosphere. That is chemical exergy: the work obtainable by reacting and mixing the substance into environmental equilibrium. Air at the dead state has zero physical exergy; unburned fuel at the dead state is nearly pure chemical exergy.
The grade function: why fuel energy ≈ fuel exergy
For hydrocarbon fuels, chemical exergy tracks the lower heating value closely. The ratio is called the grade function:
φ = ech / LHV ≈ 1.04 for kerosene-type fuels (JP-8, Jet A)Practical consequence: when a jet engine burns fuel, the exergy input is essentially the fuel energy input times ~1.04. There is no thermodynamic excuse — every joule entering the combustor is a joule of pure work potential. This is exactly why the combustor's share of destruction is so damning: it is destroying the highest-quality exergy in the entire system.
How the split plays out around the engine
| Location | Physical exergy | Chemical exergy |
|---|---|---|
| Freestream air | Zero (dead state reference) | Zero |
| Fuel, before injection | ≈ Zero | ≈ LHV × 1.04 — the engine's exergy input |
| After compressor | High (pressure + temperature) | Zero |
| After combustor | Higher, but less than fuel exergy in | Largely consumed — the conversion step |
| Exhaust | Residual thermal + kinetic — mostly lost | Small (unburned species, dissociation) |
The combustor is where the ledger flips: chemical exergy becomes physical exergy, and the irreversibility of reaction and mixing is paid in that conversion. Everything downstream — turbine, nozzle — only redistributes the physical exergy that survived.
Why analysts care: first-law efficiency treats a joule of fuel and a joule of warm exhaust as equals. The physical/chemical split is what lets the second law say the unsayable: the exhaust joule is worth less, the fuel joule was worth more, and the difference vanished inside specific, nameable components.
The dead state: choose one and be consistent
Absolute exergy values depend on the reference environment — T₀, p₀, and reference composition. Change the dead state and every station value shifts, but destruction rates and second-law efficiencies barely move, because they are differences. ExergyJet uses standard atmospheric references and reports the full balance so you can audit the assumption directly.
Frequently asked questions
What is the difference between physical and chemical exergy?
Physical exergy is the maximum useful work a stream can deliver by coming to thermal and mechanical equilibrium with the environment — through temperature and pressure alone. Chemical exergy is the additional work obtainable by bringing the stream's composition into equilibrium with the environment, for example by oxidizing a fuel. Total flow exergy is their sum (plus kinetic and potential terms, which matter for jets).
What is the formula for physical exergy?
For a flow stream, specific physical exergy is e_ph = (h − h₀) − T₀(s − s₀), where h and s are the stream's enthalpy and entropy, and h₀, s₀ are evaluated at the environmental dead state temperature T₀ and pressure p₀. Kinetic and potential exergy, V²/2 and gz, are added separately when velocities or elevations matter — as they always do in propulsion.
Why is jet fuel almost pure exergy?
Because for common hydrocarbon fuels the chemical exergy slightly exceeds the lower heating value — the ratio e_ch/LHV, called the grade function, is about 1.04 for kerosene-type fuels such as JP-8. Every joule of fuel energy is essentially a joule of work potential, which is exactly why aviation tolerates no excuse for wasting it.
What is the dead state in exergy analysis?
The dead state is the environment against which work potential is measured — defined by its temperature T₀, pressure p₀, and reference composition (for air-standard work, standard atmosphere). Two analysts using different dead states will get different absolute exergy values but the same destruction and efficiency conclusions. Consistency matters more than the choice.
Does ExergyJet separate physical and chemical exergy in results?
Yes. Station results report physical exergy from the local state and chemical exergy from composition, with the fuel's chemical exergy computed through the grade function. The component balances show exactly where chemical exergy is converted into physical exergy — and how much is destroyed in the conversion.
See the split in your own cycle
Run an analysis and open any station: physical and chemical exergy are reported separately, and the Sankey shows chemical exergy flowing in with the fuel and physical exergy flowing out with the exhaust. The gap is your destruction.
Watch chemical exergy become thrust — or not.
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