# The laws of energy: conservation, entropy and efficiency: The second law: entropy and the quality of energy Source page: https://www.materialinsights.org/learn/energy/laws-of-energy/p2/ [Understanding Energy](https://www.materialinsights.org/learn/energy/) / [Module 2: The laws of energy: conservation, entropy and efficiency](https://www.materialinsights.org/learn/energy/laws-of-energy/) Part 2 of 5 ## The second law: entropy and the quality of energy The first law says the quantity of energy is fixed. The second law says its quality only goes one way: down. Heat flows from hot to cold, concentrated energy spreads out, and no conversion can be reversed for free. That single direction explains why every machine ends by warming its surroundings, and why living things and cities need a constant inflow of high-quality 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. Worked example #### A refrigerator does not break the law A refrigerator moves heat from its cold interior to the warmer kitchen, which looks like heat flowing uphill. It is allowed because the fridge is not doing it spontaneously. It spends electricity to drive a compressor, and the kitchen ends up receiving both the heat taken from inside and the electrical energy used. Put your hand behind a running fridge and you can feel it. The total entropy of fridge, kitchen and power station still rises, as the second law demands. - 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. Process flowchart A litre of diesel in a lorry, all the way to heat Inputs **Diesel**1 litre, about 36 MJ Process steps 1 **Engine** about 12 MJ becomes shaft work; about 24 MJ leaves at once as exhaust and coolant heat 2 **Drivetrain and tyres** friction and flexing turn some of the work into heat 3 **Air resistance and braking** the remaining motion becomes heat in the air and brakes Outputs **Diffuse heat in air and road**36 MJ, all of it **Useful service**goods moved a few kilometres The energy is conserved (first law), but it ends at ambient temperature where it can do no more work (second law). Source: Smil, Energy: A Beginner's Guide (2006), via Smil Mastery Course, M1 'Entropy and the second law' In the data #### How much heat do power stations throw away? Thermal power stations worldwide reject roughly as much energy as heat as the electricity they produce, often more. A 1 GW coal unit at 37% efficiency rejects about 1.7 GW of heat (calculated), most of it into cooling water or towers, which is why plants sit near rivers or the sea and why Indian plants consume so much water. Where a town or factory can use that heat, Combined heat and power plants capture it, raising total efficiency to 75 to 90%. - 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. Value chain Order maintained by energy throughput - **Inflow of high-quality energy** sunlight, food, fuels, electricity - **Plants** sunlight → sugars and tissue; heat radiated - **Animals and people** food → body, movement, warmth; heat and CO2 out - **Cities and economies** fuels, electricity, food → buildings, transport, services; waste heat, CO2 and waste out Source: Smil, Energy in Nature and Society: General Energetics of Complex Systems (2008), via Smil Mastery Course, M1 'Entropy and the second law' Worked example #### A body as a dissipative structure An adult eating 2,200 kilocalories a day takes in about 9.2 MJ of ordered chemical energy. Over the day, nearly all of it leaves as heat, at an average of about 100 W, plus a little mechanical work that also ends as heat. Body temperature stays near 37 degrees Celsius only because this flow is continuous. In a hot, humid Indian summer, when the body struggles to shed that heat, the strain shows how tightly life depends on getting rid of low-grade energy as well as taking in high-grade energy. - 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 [H₂O Water](https://www.materialinsights.org/commodities/water/)[Tea Tea](https://www.materialinsights.org/commodities/tea/)[CHP Combined heat and power](https://www.materialinsights.org/energy/e_chp/) ### Check your understanding Which statement follows directly from the second law? Some heat must always be passed to a colder sink, so no heat engine can be 100% efficient. Why is a joule of electricity worth more than a joule of lukewarm water? Both are one joule in quantity, but electricity is almost pure exergy while warm water near room temperature can do almost no work. How can a city stay highly organised if total entropy always rises? Local order is allowed if it is paid for by a larger increase in entropy elsewhere, through continuous energy throughput. [← Part 1: The first law: energy is conserved](https://www.materialinsights.org/learn/energy/laws-of-energy/p1/)[Mark read · Part 3: The limits to efficiency: Carnot and beyond →](https://www.materialinsights.org/learn/energy/laws-of-energy/p3/) ## Other sections - [Module overview](https://www.materialinsights.org/learn/energy/laws-of-energy/index.md) - [The first law: energy is conserved](https://www.materialinsights.org/learn/energy/laws-of-energy/p1/index.md) - [The limits to efficiency: Carnot and beyond](https://www.materialinsights.org/learn/energy/laws-of-energy/p3/index.md) - [Heat and how it moves](https://www.materialinsights.org/learn/energy/laws-of-energy/p4/index.md) - [Exergy and the three stages of energy accounting](https://www.materialinsights.org/learn/energy/laws-of-energy/p5/index.md) - [Key terms, quiz and sources](https://www.materialinsights.org/learn/energy/laws-of-energy/review/index.md)