The laws of energy: conservation, entropy and efficiency: The second law: entropy and the quality of energy

2.1 Heat flows downhill, and disorder only grows

Leave a cup of hot tea on a table and it cools to room temperature. It never spontaneously heats up by drawing warmth from the cooler room. Drop ink in water and it spreads; it never gathers itself back into a drop. These everyday observations express the second law of thermodynamics: in any spontaneous process, energy spreads out and the total entropy rises.

Entropy is a measure of how spread out, or dispersed, energy is among the possible arrangements of atoms and molecules. Concentrated energy, such as the chemical energy in a lump of coal, the electricity in a wire or steam at 600 degrees Celsius, has low entropy. The same amount of energy spread through a lake as slightly warmer water has high entropy. Processes run by themselves from the first state towards the second, never the reverse, unless something pays to push them back.

Rudolf Clausius put it simply in the 1850s: heat does not flow on its own from a colder body to a hotter one. William Thomson stated an equivalent version: no engine can take heat from a single source and turn all of it into work. Some heat must always be passed on to something colder.

The practical meaning is that energy has quality as well as quantity. A joule of electricity can run a motor, light a lamp, power a computer or heat a room. A joule of lukewarm bathwater can do almost nothing except keep you a little warm. Both are one joule by the first law. The second law says they are not worth the same. Engineers measure that worth as exergy, the share of energy that can still be turned into work, and Part 5 returns to it.

• Smil, Energy in Nature and Society: General Energetics of Complex Systems (2008) · via Smil Mastery Course, M1 'Entropy and the second law'
• Jaffe and Taylor, The Physics of Energy (2018) · via Smil Mastery Course, M1 'Entropy and the second law', 'Heat and how it moves'

2.2 Every conversion ends as low-grade heat

Follow any energy chain far enough and it finishes in the same place: as diffuse heat at close to the temperature of the surroundings, from which nothing more can be extracted. That is the second law's long-run verdict on everything we do with energy.

Consider a litre of diesel in a lorry. About a third becomes motion; the rest leaves at once as hot exhaust and warm radiator air. But the motion does not last either. Air resistance warms the air, tyres flex and warm up, brakes glow when the lorry stops. By the end of the journey every joule of the diesel has become heat spread through the atmosphere and the road.

The same is true of electricity. A data centre turns essentially all of its electricity into heat, which is why cooling is such a large part of its design. A phone's battery energy ends up warming your hand and pocket. Even the light from a lamp, once absorbed by walls and furniture, becomes warmth.

At the scale of the planet, the Earth receives high-quality energy as sunlight from a surface at about 5,500 degrees Celsius and sends the same amount back to space as infrared radiation from an effective temperature of about minus 18 degrees. Plants, weather and people all live off the difference in quality between what arrives and what leaves.

This is why waste heat is everywhere in industry, and why a whole stage of the Energy table is devoted to recovering it. Recovery cannot defeat the second law, but it can use heat that is still hot enough to be useful before it falls the rest of the way to ambient temperature.

• Smil, Energy: A Beginner's Guide (2006) · via Smil Mastery Course, M1 'Entropy and the second law'
• Smil, Energy in Nature and Society: General Energetics of Complex Systems (2008) · via Smil Mastery Course, M1 'Entropy and the second law'

2.3 Life and cities are dissipative structures

If disorder always increases, how can organisms, forests and cities be so highly organised? The answer is that the second law applies to the total. A local pocket of order is allowed, as long as it is paid for by a larger increase in disorder elsewhere.

Living things pay with energy. A plant captures low-entropy sunlight, uses a small part of it to build ordered sugars and cells, and radiates the rest as heat. An animal eats ordered food, builds and repairs its body, and gives off heat and simpler molecules such as CO₂ and water. Stop the inflow and the order decays: an organism that stops eating dies, and its body gradually returns to disorder.

Smil extends the same idea to human societies. Cities are dissipative structures in the language of the physicist Ilya Prigogine: patterns that can exist only while a steady stream of high-quality energy flows through them and leaves as waste heat. A modern city draws in fuel, electricity and food from far beyond its boundaries and exports heat, sewage, CO₂ and rubbish. Its buildings, roads and institutions persist only because that throughput continues.

Seen this way, energy is not just one input to an economy among many. It is the condition for any organised structure to exist at all. More complex economies, with more machines, materials and services, require larger flows of high-quality energy to keep themselves going, which is one reason energy use per person tracks economic development so closely.

This framing also clarifies what efficiency gains can and cannot do. They let a society maintain more order per unit of energy flow. They cannot remove the need for the flow.

• Smil, Energy in Nature and Society: General Energetics of Complex Systems (2008) · via Smil Mastery Course, M1 'Entropy and the second law'
• Smil, Energy: A Beginner's Guide (2006) · via Smil Mastery Course, M1 'Entropy and the second law'

See it in the table

Check your understanding

Which statement follows directly from the second law?

Why is a joule of electricity worth more than a joule of lukewarm water?

How can a city stay highly organised if total entropy always rises?