The laws of energy: conservation, entropy and efficiency: Heat and how it moves

4.1 Conduction, convection and radiation

Heat moves in three ways, and most real situations involve all of them at once.

Conduction is heat passing through a material from molecule to molecule, from the hot side to the cold side. Metals conduct heat well; still air, wool, foam and fibreglass conduct it poorly, which is why insulation works by trapping air in small pockets. The rate of conduction through a wall depends on its area, its thickness, the material and, crucially, the temperature difference across it. Double the difference and the heat flow roughly doubles.

Convection is heat carried by a moving fluid, air or water. Warm air rises from a heater and cooler air sinks to replace it, setting up a circulation. Wind blowing across a wall strips heat away faster than still air. Draughts through gaps around doors and windows are convection too, and in many buildings they account for a large share of heat loss or, in hot climates, heat gain.

Radiation is heat carried by electromagnetic waves, mostly infrared. It needs no material at all, which is how the Sun's energy crosses the vacuum of space. Every surface radiates, and the amount rises steeply with temperature, with the fourth power of absolute temperature. A sunlit roof in Rajasthan absorbs intense radiation and re-radiates heat into the rooms below. A white or reflective roof, which bounces back much of the sunlight, can keep the space underneath several degrees cooler.

For anyone looking at buildings, cold chains or industrial furnaces, the question is always the same: by which route is heat getting in or out, and which is cheapest to block?

• 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'

4.2 Water stores heat well and absorbs huge amounts when it evaporates

Materials differ in how much heat they can soak up per degree of temperature rise, a property called specific heat capacity. Water's is unusually high: about 4.18 kJ to warm one kilogram by one degree Celsius, four to five times that of dry soil or rock and more than four times that of air per kilogram. That is why oceans moderate coastal climates, why a hot-water bottle stays warm, why water is the standard fluid for moving heat in boilers, district heating and cooling towers, and why tanks of hot water are among the cheapest ways to store heat.

Phase changes involve far more energy still. Melting ice or boiling water absorbs heat without changing temperature, energy known as latent heat. Evaporating one kilogram of water at its boiling point takes about 2.26 MJ, more than five times the 0.42 MJ needed to heat it from freezing to boiling. At skin temperature it takes even a little more.

This single number explains a great deal. Sweating cools the body so well because each gram of sweat that evaporates carries away about 2.4 kJ. Evaporative coolers, the desert coolers common in north India, work the same way and use far less electricity than air conditioners, though they stop working in humid air. Power stations use cooling towers that evaporate water to dump their waste heat. And a steam boiler needs a lot of fuel mostly to supply that latent heat of evaporation.

Latent heat also explains condensing boilers. The water vapour in flue gas holds latent heat; cool the gas enough and the vapour condenses, giving that heat back. Smil highlights how condensing gas furnaces, by recovering it, raised home heating efficiency in a few decades from about 60% to 95% or more.

• 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'
• 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'

4.3 Buildings leak heat through their weakest parts

A building's envelope, its walls, roof, floor, windows and doors, sets how fast heat moves between inside and out. Insulation is rated by R-value, a measure of resistance to heat flow, or by its inverse, the U-value, which measures how much heat passes per square metre per degree of difference. A high R-value or a low U-value means less heat flow.

The weakest parts dominate. Smil devotes an essay to triple glazing because windows are almost always the worst-insulated part of a wall. A single pane of glass has an R-value of about 1 in American units, while a well-insulated wall reaches around 20. So a window loses heat many times faster per square metre than the wall around it. Double glazing roughly doubles the window's resistance. Triple glazing, with low-emissivity coatings that reflect infrared and argon gas between the panes, raises it several times more. Smil admires it because it has no moving parts, needs no fuel and keeps saving energy for decades.

The same logic applies in hot climates, with the direction reversed. In an Indian city, heat enters through a sun-baked roof, through west-facing glass in the afternoon and with warm air leaking in through gaps. Shading, reflective roofs, roof insulation and airtightness all cut the cooling load, which lowers both electricity bills and the evening peak on the grid.

Heat flow is proportional to the temperature difference. Setting an air conditioner to 26 degrees instead of 20 when it is 38 outside cuts the difference from 18 to 12 degrees, one third less. Since January 2020 the Bureau of Energy Efficiency has required star-labelled room air conditioners to come with a default setting of 24 degrees, an application of this simple proportionality.

• 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'
• 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

See it in the table

Check your understanding

Which route carries heat from the Sun to the Earth?

Why is sweating such an effective way to cool down?

If the indoor-outdoor temperature difference falls from 18 to 12 degrees, heat flow through a wall falls by about...