The laws of energy: conservation, entropy and efficiency: Exergy and the three stages of energy accounting

5.1 Exergy measures how much work energy can still do

Exergy is the maximum useful work that can be obtained from an amount of energy as it comes into balance with its surroundings. For electricity and mechanical work, exergy equals energy: in principle all of it can do work. For fuels it is close to their heating value. For heat it depends on temperature. The exergy share of heat at a temperature T, in surroundings at T0, is 1 minus T0 divided by T, in kelvin, the same expression as the Carnot limit.

That formula ranks heat by quality. In surroundings at 25 degrees, heat at 1,500 degrees is about 83% exergy; heat at 500 degrees about 61%; steam at 200 degrees about 37%; hot water at 80 degrees about 16%; and warm air at 40 degrees under 5%. Heat at room temperature is all energy and no exergy.

Exergy changes how efficiency looks. A gas boiler heating water to 60 degrees may be 90% efficient by the first law, since 90% of the gas's energy reaches the water. By exergy it is only about 10% efficient, because it burned a fuel capable of reaching 1,900 degrees to make lukewarm water. A heat pump with a COP of 3.5 doing the same job has an exergy efficiency of over a third. An electric resistance heater, 100% efficient by energy, has the same poor exergy efficiency as the boiler, and if its electricity came from a fossil plant it is worse still.

The lesson for investment is to match quality to need. Use high-temperature heat and electricity for jobs that need them, such as steelmaking, motors and electronics. Supply low-temperature needs, such as space heating, hot water and drying, from low-quality sources: waste heat, solar heat collectors, heat pumps. Pinch analysis and cascading heat from hot uses to cooler ones apply the same idea inside factories.

• Smil, Energy in Nature and Society: General Energetics of Complex Systems (2008) · via Smil Mastery Course, M1 'Entropy and the second law'
• Brockway, P.E., Heun, M.K., Marshall, Z., Aramendia, E., Steenwyk, P., Relph, T., Widjanarko, M., Kim, J., Sainju, A. and Irtube, J., 'A country-level primary-final-useful (CL-PFU) energy and exergy database: overview of its construction and 1971-2020 world-level efficiency results', Environmental Research: Energy 1(2), 025005, IOP Publishing, 2024 · World-level primary-to-final and final-to-useful energy and exergy efficiencies, 1971-2020. https://eprints.whiterose.ac.uk/id/eprint/217800/

5.2 Primary, final and useful energy are three different totals

Energy statistics count energy at different stages, and confusing them is a common source of error.

Primary energy, which the Energy Institute now calls total energy supply, is energy as first taken from nature and counted: coal and crude oil as mined, gas as produced, and, by convention, electricity or heat from wind, solar, hydro and nuclear. The world's total for 2024 was about 592 EJ.

Final energy is energy as delivered to users: electricity at the meter, petrol at the pump, gas to the boiler, coal to the steel mill. The gap between primary and final is the energy industry's own conversion losses: power stations rejecting heat, refineries burning part of their crude, pipelines and grids losing a few per cent.

Useful energy is what the user's own device delivers: heat in the pot or the room, light from the lamp, motion at the wheels or the machine shaft. The gap between final and useful is the end-use losses.

A 2024 study by Paul Brockway, Matthew Heun and colleagues built a database of primary, final and useful energy and exergy for countries since 1971. For the world in 2020 it found that about 72% of primary energy reached users as final energy, and about 65% of final energy became useful energy. Measured as exergy the picture is starker: only about 23% of final exergy became useful exergy. Multiply through, using a primary-to-final exergy efficiency of about 70%, and roughly 16% (calculated) of the world's primary exergy ends up as useful work, light and heat of the quality required.

The study also found that final-to-useful efficiency has improved strongly since 1971, from about 37% to 65% in energy terms, so useful energy grew 3.7 times while primary energy grew 2.3 times. The world is getting better at turning fuel into services, even as it uses more fuel.

• Brockway, P.E., Heun, M.K., Marshall, Z., Aramendia, E., Steenwyk, P., Relph, T., Widjanarko, M., Kim, J., Sainju, A. and Irtube, J., 'A country-level primary-final-useful (CL-PFU) energy and exergy database: overview of its construction and 1971-2020 world-level efficiency results', Environmental Research: Energy 1(2), 025005, IOP Publishing, 2024 · World-level primary-to-final and final-to-useful energy and exergy efficiencies, 1971-2020. https://eprints.whiterose.ac.uk/id/eprint/217800/
• Energy Institute, Statistical Review of World Energy 2025 (74th edition), Energy Institute with KPMG and Kearney, 2025 web ↗ · Methodology change p. 8; 'effectively 7% more efficient' p. 9; total energy supply 2023 and 2024 p. 13. https://www.energyinst.org/statistical-review (copy at https://assets.kpmg.com/content/dam/kpmg/tr/pdf/2025/07/Statistical_Review_of_World_Energy.pdf)

5.3 How statisticians count electricity from wind, sun and atoms

Primary energy is easy to define for fuels: count their heat content. It is awkward for electricity that never passed through a fuel. A kilowatt-hour from a wind turbine has no coal pile behind it. How many primary kilowatt-hours should it count as?

Up to its 2024 edition, the Statistical Review of World Energy used the substitution method. It counted non-fossil electricity as the fossil fuel that would have been needed to make it in a typical thermal plant of about 40% efficiency. A kilowatt-hour of solar was recorded as about 2.5 kilowatt-hours of primary energy. That method treats electricity from any source as equally valuable, but inflates the totals and the shares of wind, solar, hydro and nuclear.

The 2025 edition switched to the physical energy content method, in line with the United Nations' International Recommendations for Energy Statistics. Wind, solar photovoltaics, hydro and tidal power are counted at their electricity output, so one kilowatt-hour is one kilowatt-hour. Nuclear, concentrating solar and biomass power are counted by the heat they produce, assuming 33% conversion efficiency, so one nuclear kilowatt-hour counts as about three. Geothermal power is counted at 10% efficiency, so one kilowatt-hour counts as ten.

The effect is substantial. The world total for 2023 was about 620 EJ under the old method and about 580 EJ under the new. For 2024, Our World in Data's series on the old basis gives about 635 EJ (calculated from 176,700 TWh), against 592 EJ. The Energy Institute describes the 2024 system as effectively 7% more efficient as a result. Nothing physical changed. Under the new method, fossil fuels' share rises and the share of wind and solar falls by more than half.

Neither method is wrong. Each answers a different question. Whenever you see a renewable share of primary energy, check which convention was used, and remember that useful energy, the real target of the transition, is better measured in other ways.

• Energy Institute, Statistical Review of World Energy 2025: Methodology, 2025 web ↗ · Efficiency factors under the physical energy content method (wind, solar, hydro 100%; nuclear and CSP 33%; geothermal 10%). https://www.energyinst.org/__data/assets/pdf_file/0003/1658154/Methodology-2025.pdf
• Ritchie, H. and Rosado, P., 'How primary energy is measured has changed across our charts', Our World in Data, 2026 · Substitution versus physical energy content methods, worked examples for coal, gas, solar and nuclear. https://ourworldindata.org/primary-energy-measurement-change
• Energy Institute, Statistical Review of World Energy 2025 (74th edition), Energy Institute with KPMG and Kearney, 2025 web ↗ · Methodology change p. 8; 'effectively 7% more efficient' p. 9; total energy supply 2023 and 2024 p. 13. https://www.energyinst.org/statistical-review (copy at https://assets.kpmg.com/content/dam/kpmg/tr/pdf/2025/07/Statistical_Review_of_World_Energy.pdf)
• IPCC, 2014: Annex II: Metrics and Methodology (Krey, V. et al.), in Climate Change 2014: Mitigation of Climate Change, Working Group III contribution to AR5, Cambridge University Press · Section A.II.4 Primary energy accounting: the report adopts the direct-equivalent method. https://www.ipcc.ch/site/assets/uploads/2018/02/ipcc_wg3_ar5_annex-ii.pdf
• Our World in Data, energy dataset (owid-energy-data.csv), 2026 · World primary energy 2024 on the substitution basis, 176,737 TWh (about 636 EJ). https://github.com/owid/energy-data

See it in the table

Check your understanding

A gas boiler delivers 90% of its fuel energy as hot water at 60 C. Why is its exergy efficiency only about 10%?

Under the physical energy content method, how is 1 kWh of nuclear electricity counted?

What is the difference between final and useful energy?