Material Insights · Understanding the Material World

The laws of energy: conservation, entropy and efficiency: Key terms, quiz and sources

Understanding Energy / Module 2: The laws of energy: conservation, entropy and efficiency Wrap-up

The laws of energy: conservation, entropy and efficiency: review

Key terms

First law of thermodynamics
Energy cannot be created or destroyed; in any process the total stays the same.
Second law of thermodynamics
In any spontaneous process total entropy increases, so heat flows on its own only from hot to cold.
Entropy
A measure of how dispersed energy is; concentrated energy has low entropy, diffuse heat has high entropy.
Efficiency
Useful energy output divided by energy input for a device or chain.
Rebound effect
The tendency for cheaper energy services to be used more, offsetting part of an efficiency saving.
Jevons paradox
The extreme case of rebound, observed in 1865, where efficiency gains raise total fuel use.
Heat engine
A device that turns part of a flow of heat from a hot source to a cold sink into work.
Carnot limit
The maximum efficiency of any heat engine, 1 minus T_cold divided by T_hot in kelvin.
Kelvin
The absolute temperature scale, equal to degrees Celsius plus 273.
Combined cycle
A power plant that uses a gas turbine's hot exhaust to raise steam for a second turbine, reaching about 60% efficiency.
Coefficient of performance (COP)
Heat moved by a heat pump or air conditioner per unit of work used, typically 3 to 4.
Specific heat capacity
Energy needed to warm one kilogram of a material by one degree; 4.18 kJ for water.
Latent heat
Energy absorbed or released when a substance melts, freezes, evaporates or condenses, without a change in temperature.
R-value and U-value
Measures of a building element's resistance to heat flow (R) and of the heat it lets through (U).
Exergy
The maximum work obtainable from energy as it comes into balance with its surroundings; a measure of energy quality.
Primary energy (total energy supply)
Energy as first taken from nature and counted, before any conversion by the energy industry.
Final energy
Energy delivered to end users, such as electricity at the meter or fuel at the pump.
Useful energy
Energy provided by the end-use device as the service wanted: heat, light, motion.
Substitution and physical energy content methods
Two conventions for counting non-fossil electricity as primary energy: as the fossil fuel it replaces, or by its output or heat.

Try it in the table

  • Open the Steam turbines and thermal power plants tile and find the steam temperatures and efficiencies it gives. Apply the Carnot formula with cooling water at 30 C and compare the limit with the real figure.
  • Open the Gas turbines and combined cycle tile. Using the flow in this module, work out how much of the plant's output comes from the steam turbine and why that part needs no extra fuel.
  • Open the Heat pumps, air conditioning and refrigeration tile and note the COP values it reports. Calculate how much electricity a heat pump with that COP would need to supply 10 kWh of hot water, compared with an Electric heating element.
  • Open the Combined heat and power tile and the Waste-heat power (steam Rankine) tile. Compare their typical efficiencies and explain, using exergy, why using heat directly often beats turning it into electricity.
  • Open the Industrial heat pumps and vapour recompression tile and find the temperature lifts it describes. Explain why the COP falls as the delivery temperature rises.
  • Open the Geothermal power plants tile and compare its electrical efficiency with the 10% factor the Statistical Review uses for geothermal. Then compare with the Geothermal direct use and ground-source heat pumps tile.

Final quiz

A device claims to deliver more electricity than the fuel energy it receives, with no other input. Which law does it break?

Getting more energy out than in, with no other input, violates conservation of energy, the first law.

A coal plant runs steam at 600 C and rejects heat at 30 C. What is its Carnot limit?

1 - 303/873 is about 0.65. Real plants reach about 38 to 45% because of practical losses.

Why does a combined-cycle gas plant reach about 60% when a gas turbine alone reaches about 40%?

The exhaust leaves the gas turbine at around 600 C, hot enough to drive a steam cycle with no extra fuel.

A heat pump has a COP of 4. How can it deliver 4 kWh of heat from 1 kWh of electricity without breaking the first law?

The extra heat is taken from the outside air or ground; energy is conserved.

Which of these has the lowest exergy per joule?

Heat only slightly above ambient temperature can do almost no work; its exergy share is under 2%.

Evaporating 1 kg of water at 100 C takes about how much energy compared with heating it from 0 to 100 C?

About 2.26 MJ for evaporation versus 0.42 MJ for heating: a ratio of over five.

According to the 2024 Brockway study, roughly what share of the world's final exergy became useful exergy in 2020?

Final-to-useful efficiency was about 65% in energy terms but only about 23% in exergy terms, because much useful energy is low-temperature heat.

Why did the Statistical Review's world energy total fall when it adopted the physical energy content method?

The substitution method inflated non-thermal renewables to their fossil equivalent; the new method counts them at output, cutting the 2023 total from about 620 to 580 EJ.
Next module: Earth's energy flows: sun, wind, water, heat and life →

Sources for this module

  • Smil, Energy: A Beginner's Guide (2006) · via Smil Mastery Course, M1 'Conservation and efficiency', 'Entropy and the second law'
  • Smil, Energy and Civilization: A History (2017) · via Smil Mastery Course, M1 'Conservation and efficiency'
  • Smil, Energy in Nature and Society: General Energetics of Complex Systems (2008) · via Smil Mastery Course, M1 'Entropy and the second law'
  • Smil, Numbers Don't Lie: 71 Stories to Help Us Understand the Modern World (2020) · via Smil Mastery Course, M1 'Heat and how it moves'
  • Smil, How the World Really Works: A Scientist's Guide to Our Past, Present and Future (2022) · via Smil Mastery Course, M1 'Heat and how it moves'
  • Jaffe and Taylor, The Physics of Energy (2018) · via Smil Mastery Course, M1 'Entropy and the second law', 'Heat and how it moves'
  • 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/
  • 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)
  • 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
  • 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
  • Mercom India, 'To promote energy efficiency, BEE sets new standards for air conditioners', 13 January 2020 · Default temperature of 24 C for star-labelled room ACs from 1 January 2020. https://mercomindia.com/energy-efficiency-bee-standards-air-conditioners
  • 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