Combustion and thermal cycles: how fuel becomes work

Combustion is the rapid oxidation of a fuel, releasing energy as heat (and light) and producing oxidized products. For hydrocarbon fuels:

$\text{C}_x\text{H}_y + \left(x + \frac{y}{4}\right)\text{O}_2 \rightarrow x\,\text{CO}_2 + \frac{y}{2}\text{H}_2\text{O} + \text{heat}.$

The heat released per mole of fuel comes from the difference between bond energies in the fuel and bond energies in the products. Carbon-oxygen and hydrogen-oxygen bonds in CO₂ and H₂O are stronger than carbon-hydrogen and carbon-carbon bonds in the fuel; the surplus energy emerges as heat.

Key quantitative values:

• Methane (CH₄) combustion: releases ~890 kJ/mol, or ~55 MJ/kg. Produces 1 mol CO₂ per mol CH₄.
• Octane (C₈H₁₈), representative of gasoline: ~5470 kJ/mol, ~46 MJ/kg. Produces 8 mol CO₂ per mol fuel.
• Carbon (coal proxy): ~32 MJ/kg. Produces 1 mol CO₂ per mol C.

The carbon-to-energy ratio differs across fuels because of the hydrogen content. Methane is mostly hydrogen by atom count (4 H per 1 C), so a large share of its energy comes from H-O bond formation, releasing relatively less CO₂ per unit of energy. Coal is mostly carbon (essentially zero H per C in pure-graphite limit), so all its energy comes from C-O bond formation. This is the structural reason natural gas emits roughly half the CO₂ per unit electrical energy as coal.

Combustion products include water vapor, whose latent heat of vaporization is significant. Two conventions for accounting:

• Higher heating value (HHV). Includes the latent heat — assumes water vapor in exhaust condenses back to liquid, releasing its phase-change energy.
• Lower heating value (LHV). Excludes the latent heat — assumes water leaves as vapor and the energy of vaporization is lost.

The difference matters: HHV is roughly 5–10% larger than LHV for hydrocarbon fuels. In practice:

• Industrial heating with condensing boilers captures latent heat; efficiency naturally quoted relative to HHV.
• Power generation with steam cycles typically does not recover exhaust latent heat; LHV is the conventional basis.
• Hydrogen has a particularly large HHV-LHV gap (~18%) because of its high water-vapor output.

Stated thermal efficiencies can refer to either basis. A 60% efficient gas turbine combined cycle on LHV becomes ~54% on HHV. Cross-source comparisons require a common basis. The convention in most professional energy literature is LHV for electricity, HHV for fuel sales (so natural gas is often sold per HHV-million-BTU). The mismatch is a small but real source of confusion in efficiency comparisons across regions and reports.

Most large fossil and nuclear plants produce electricity through the Rankine cycle, which uses water-steam as the working fluid.

The cycle has four steps:

1. Feed pump raises pressure of liquid water to boiler pressure.
2. Boiler absorbs heat from the fuel and converts water to high-pressure steam (and superheats it).
3. Turbine expands the steam, extracting mechanical work; the steam exits at low pressure as a wet vapor.
4. Condenser rejects waste heat to a cold reservoir (usually river, lake, or cooling tower), condensing the steam back to liquid. The cycle repeats.

The efficiency is the work extracted divided by the heat absorbed in the boiler, bounded by Carnot. Real coal plants reach 35–47% thermal efficiency; modern supercritical (steam above its critical pressure of 22.1 MPa) and ultra-supercritical designs (~30+ MPa, steam above 600°C) push toward 45–48%.

Key constraints:

• Materials. Higher steam temperatures and pressures raise efficiency but require better metallurgy. Nickel-based superalloys push the practical ceiling around 700°C steam.
• Cooling. The cold reservoir's temperature limits the bottom of the cycle. Plants on rivers in summer face efficiency losses and sometimes regulatory shutdowns when ambient water temperatures rise too high.
• Heat-rate degradation. Over years, fouling, leaks, and aging components erode efficiency by 1–3% from new.

Nuclear plants also use Rankine cycles but typically at lower temperatures (steam at 270–290°C in light-water reactors), bounding their thermal efficiency near 33%. Generation IV designs (sodium-cooled fast reactors, high-temperature gas-cooled reactors) target higher steam temperatures and consequently higher Carnot bounds.

Gas turbines (also called combustion turbines or jet engines) use the Brayton cycle, with air as the working fluid.

Four steps:

1. Compressor raises air pressure (typically 15–40× atmospheric for industrial turbines).
2. Combustor burns fuel (natural gas or distillate) in the compressed air, raising temperature dramatically.
3. Turbine expands the hot gas, extracting work to drive both the compressor and a generator (or a fan for jet engines).
4. Exhaust rejects waste heat at the turbine outlet.

Modern industrial gas turbines reach 38–42% efficiency on the Brayton cycle alone, with turbine inlet temperatures pushing 1,600°C (constrained by single-crystal nickel-superalloy blades with internal cooling).

Gas turbines have practical advantages:

• Fast startup. A combustion turbine can go from cold to full power in minutes (versus hours for a steam plant). This makes them valuable for peaking and balancing variable renewable output.
• Modular construction. A 50–500 MW gas turbine is roughly a factory-built unit, not a custom power-plant build.
• Lower capital cost per nameplate than coal or nuclear; higher fuel cost per kWh.

Limitations:

• Fuel quality. Gas turbines need clean fuel (gas, distillate). Coal-firing requires combined-cycle gasification or fluidized-bed combustion intermediaries.
• High exhaust temperatures. The turbine exhaust is ~600°C — still hot enough to do useful work. This is what motivates combined cycles.

A combined-cycle gas turbine (CCGT) plant runs a Brayton-cycle gas turbine, then uses the still-hot exhaust to boil water in a heat-recovery steam generator (HRSG) that drives a Rankine-cycle steam turbine.

The two cycles in series:

• Gas turbine extracts ~40% of the fuel's energy as electrical work.
• HRSG recovers a large fraction of the remaining exhaust heat as steam.
• Steam turbine extracts another ~20% of the original fuel energy as electrical work.

The combined thermal efficiency is the sum: modern CCGT plants reach 60–64% on LHV — the highest efficiency of any thermal power plant in commercial operation.

The structural reason combined cycle works: layering two cycles with different operating temperature ranges captures more of the Carnot-available exergy. The gas turbine operates between ~1,600°C inlet and ~600°C exhaust; the steam cycle operates between ~600°C and ~30°C condenser. Each cycle alone would leave most of its temperature range unexploited; together they span almost the full thermal gradient.

CCGT plants are the dominant new fossil-fuel build in most markets where natural gas is available because:

• Highest thermal efficiency per unit fuel, so lowest CO₂ per kWh among fossil sources (~350 g CO₂/kWh vs ~900 g/kWh for coal).
• Capital costs roughly $1,000–1,500/kW installed, much less than coal ($3,000–4,000) or nuclear ($5,000–12,000).
• Construction time 2–3 years versus 5–10+ for coal or nuclear.
• Flexibility (can run as baseload or load-following).

The CO₂ advantage over coal explains a substantial share of recent CO₂-intensity declines in electricity grids where coal has been displaced by gas.

Internal combustion engines (ICE) power most vehicles. Two main thermodynamic cycles dominate.

Otto cycle (gasoline engine).

1. Intake: piston draws air-fuel mixture into cylinder.
2. Compression: piston compresses the mixture (compression ratio 8:1 to 12:1).
3. Power: spark plug ignites the mixture; expanding combustion gases drive the piston.
4. Exhaust: piston expels combustion products.

Otto-cycle efficiency:

$\eta_{\text{Otto}} = 1 - \frac{1}{r^{\gamma-1}}$

where $r$ is the compression ratio and $\gamma \approx 1.4$ for air. A 10:1 compression ratio gives $\eta \approx 60\%$ idealized; real engines reach 25–35% on practical cycles after accounting for friction, heat loss, throttling, and incomplete combustion.

Diesel cycle (diesel engine).

Similar four strokes but compression is much higher (15:1 to 25:1), and fuel is injected only at the end of the compression stroke, igniting from the heat of compression alone (no spark plug). Higher compression yields higher thermal efficiency: 40–50% in modern truck diesels, 50%+ in large marine and stationary diesels.

Why higher efficiency:

• Higher compression ratios are tolerable because the fuel is not in the cylinder during compression (no pre-ignition knock concern with diesel).
• Lean operation at part-load (Otto must maintain stoichiometric air-fuel ratio for catalytic converters; diesel can run lean).
• Higher peak combustion temperatures.

Electric vehicles, for context, achieve ~70–90% efficiency from battery to wheel (with much of the remainder being motor and inverter losses). The ICE-vs-EV efficiency gap is structural: ICE is heat-engine-limited; EV is direct electrical conversion. The gap shows up in the energy-per-distance numbers — an EV uses 0.15–0.25 kWh/km; a comparable ICE car uses 0.6–0.9 kWh/km of fuel energy.

Generating electricity is only one use of combustion. Many industrial processes need heat directly rather than electricity, and the heat has to be at the right temperature.

Approximate heat-temperature requirements:

The structural problem for decarbonizing industrial energy:

• Low-temperature heat (under ~200°C) can be supplied by electric heat pumps with COP of 3–5, using electricity efficiently.
• Medium-temperature heat (200–500°C) can use electric resistance heating, electric boilers, or industrial heat pumps with COP near 2.
• High-temperature process heat (above 1000°C) is much harder to electrify. Electric arc furnaces work for steel scrap recycling but not for primary steel from iron ore (which needs reducing chemistry from coke or hydrogen, not just heat). Cement, glass, and primary chemicals require similar reconfiguration.

The distinction between 'electrify the heat' and 'electrify by replacing the process' matters because some industries need the chemistry, not just the temperature. Hydrogen, electrified bioreactors, electrolysis, and other process-level changes are required where the heat is in service of a reaction. This is why decarbonization analyses break industry into 'easy to electrify' and 'hard to abate' subcategories with quite different policy implications.

The CO₂ emissions per kWh of electricity depend on both the fuel and the conversion cycle.

Typical numbers (grid-edge CO₂, lifecycle approximations):

A grid that shifts from coal to combined-cycle gas roughly halves CO₂ per kWh. A grid that shifts from coal to wind/nuclear/solar drops CO₂ per kWh by 30–100×.

Lifecycle numbers include emissions from fuel extraction, plant construction, fuel transport, plant operation, decommissioning. For fossil sources the operating emissions dominate; for renewables and nuclear, the construction and material emissions dominate (which is why hydroelectric reservoirs in tropical regions can have surprisingly high lifecycle numbers from methane from submerged biomass).

These numbers are the structural reason the choice of generation mix dominates a grid's emissions trajectory. Efficiency improvements on existing plants matter but are bounded by Carnot; cycle changes (subcritical → supercritical → combined cycle) help but stay within the same fuel class; cross-fuel changes (coal → gas → renewables/nuclear) deliver the largest changes in carbon intensity per kWh.

The next lesson moves to the alternative source whose energy density rewrites the analysis: nuclear fission.