Heat & Thermodynamics

What this part of the map covers

Thermodynamics is the branch of physics that deals with the energy and work of a system.^[17] The US National Institute of Standards and Technology (NIST) describes it as the study of heat and how heat relates to other kinds of energy.^[2] The field was born in the 19th century, as scientists first worked out how to build and run steam engines.^[17]

Temperature and heat

Temperature is an absolute measure of the average internal energy of an object.^[1] In water, for example, it measures the average kinetic energy (energy of motion) of the molecules.^[5] At 25 °C, air molecules move at about 500 metres per second on average; some go 223 m/s, others 717 m/s.^[2]

Heat is thermal energy in transit: energy flowing from a hotter object to a colder one.^{[1, 5]} When heat stops flowing between two objects, they are in thermal equilibrium and are said to have the same temperature.^{[1, 18]}

Storing heat and changing state

Specific heat is the heat needed to raise the temperature of 1 gram of a substance by 1 °C.^[6] Water’s is high: the US Geological Survey (USGS) notes that warming a kilogram of water by 1 °C takes 4,184 joules, against 385 joules for a kilogram of copper.^[6]

Changing state takes energy too. One gram of ice needs 80 calories to melt (its latent heat of fusion), 100 more to reach boiling point and another 540 to turn into vapour.^[7]

How heat moves

Heat moves in three basic ways: conduction, convection and radiation.^{[5, 12]}

• Conduction passes thermal energy through direct contact.^[21]
• Convection carries heat through the movement of fluids; Earth’s oceans and atmosphere are heated this way.^[5]
• Radiation carries heat by electromagnetic waves, as when sunlight warms your skin.^{[5, 21]}

All matter warmer than absolute zero radiates energy, and the energy a surface radiates rises with the fourth power of its temperature.^[22]

The four laws

• Zeroth law. If two objects are each in thermal equilibrium with a third, they are in equilibrium with each other; equilibrium is what leads to the large-scale definition of temperature.^[18]
• First law. Energy is neither created nor destroyed: it can change form, but the total stays the same.^{[19, 12, 8]}
• Second law. Some processes would conserve energy yet never happen in nature, and the second law rules them out.^{[20, 13]} One version, given by Rudolf Clausius in 1850, says heat tends to flow from hot bodies to cold ones.^[25] Another says no engine working in a cycle can turn heat completely into work.^[13] In terms of a quantity called entropy, any irreversible process increases the total entropy of a system and its surroundings.^[20]
• Third law. The entropy of a perfect crystal approaches zero as its temperature approaches absolute zero.^{[15, 14]} Perfect crystals do not exist, and in practice absolute zero cannot be reached.^{[15, 14]}

Engines, fridges and heat pumps

A heat engine is a system that runs in a cycle and does net work on its surroundings.^[13] According to the US Energy Information Administration (EIA), steam turbines generate most of the world’s electricity, and in 2022 they produced about 42% of US electricity.^[9]

In 1824 Sadi Carnot (1796–1832) published Reflections on the Motive Power of Fire, one of the earliest attempts to explain heat engines.^{[23, 24]} He introduced an ideal engine, the Carnot engine, and showed that its efficiency depends only on the temperature difference within it, not on the substance, such as steam, that drives it.^{[24, 23]} The American Society of Mechanical Engineers (ASME) notes that engineers have used his ideas, working with bigger temperature differences, to make power plants, car engines and jet engines more efficient.^[23]

Refrigerators and heat pumps use electricity to move heat from a cool space to a warm one.^[10] Earth itself runs a heat engine: its atmosphere and ocean even out uneven heating by the Sun.^[22]

Measuring temperature

William Thomson proposed an absolute temperature scale in 1848, and the Kelvin scale is named after the title Baron Kelvin of Largs, which he received in 1892.^[26] Until 2019, the kelvin was defined from the triple point of water.^[3] Since May 2019, it has been defined by fixing the value of the Boltzmann constant at 1.380 649 × 10⁻²³ joules per kelvin.^[3]

The math (optional)

A degree Celsius is by definition the same size as a kelvin, and a Celsius temperature is the kelvin value minus 273.15:^[4]

t (in °C) = T (in K) − 273.15

Our own example: 0 K is −273.15 °C, and a room at 25 °C is at 298.15 K.^[4]

A short history

Lavoisier thought heat was a massless fluid, which he called “caloric”.^[16] James Joule showed that an electric current could generate heat, which went against the caloric theory.^[28] By heating water with a paddle wheel turned by a falling weight, he showed that mechanical work and heat are equivalent.^[16]

In 1850 Clausius declared the assumptions of the caloric theory false and replaced them with two laws of thermodynamics.^[25] In 1865 he summed them up for the whole universe: its energy is constant, and its entropy tends towards a maximum.^[25] Ludwig Boltzmann, famous for inventing statistical mechanics, argued that entropy increases almost always, rather than always.^[27]

Common misconceptions

“Entropy just means disorder.” Dan Styer of Oberlin College cautions that entropy doesn’t always mean disorder or uniformity.^[29]

Going further

Start with Energy & Work; Weather & Climate and Energy Technology show these ideas at work. Statistical mechanics and the gas laws are left for deeper pages.