Heat and Thermodynamics

Every material is made of particles that are always moving. In a solid they vibrate in place; in a liquid they slide past each other; in a gas they fly around and collide. Temperature tracks how fast they move on average. Add energy and they speed up, and the temperature rises.

Three scales are in common use. Celsius puts water's freezing point at 0 °C and its boiling point at 100 °C (at sea-level pressure). Fahrenheit puts them at 32 °F and 212 °F. Scientists use the Kelvin scale, which starts at absolute zero, the lowest possible temperature, where particles have the least energy they can have. Absolute zero is 0 K = −273.15 °C. A kelvin is the same size as a Celsius degree, so:

T(K) = T(°C) + 273.15     T(°F) = 1.8 × T(°C) + 32

Note: we write "300 K", not "300 °K". In any gas-law calculation, always use kelvins.

Heat flows on its own from hotter to colder, until both reach the same temperature: thermal equilibrium. It travels in three ways.

• Conduction: fast-moving particles bump their neighbors and pass energy along, through a solid or between things touching. Metals are good conductors because their free electrons carry energy quickly. Wood, air, foam and wool are insulators. That railing feels colder than the bench because metal conducts heat away from your hand much faster.
• Convection: in a liquid or gas, warm fluid expands, becomes less dense and rises, while cooler, denser fluid sinks to take its place. The loop that forms, a convection current, heats a pot of soup, a room and drives sea breezes.
• Radiation: every object gives off electromagnetic waves, mostly infrared at everyday temperatures. Radiation needs no material, which is how the Sun's energy crosses 150 million kilometers of space. Dark, dull surfaces absorb and emit it well; shiny ones reflect it.

How much heat does it take to warm something up? It depends on three things: how much there is (mass m), what it's made of (specific heat c), and how big a temperature change you want (ΔT):

Q = m c ΔT

Here Q is in joules, m in kilograms, c in J/(kg·°C) and ΔT = T_final − T_initial. If ΔT is negative, Q is negative: the object gave heat away.

Water's specific heat is unusually high, about five times that of sand or rock. That's why the sea stays cool on a hot afternoon while the beach scorches, why coastal places have milder climates, and why water is used to cool car engines.

Heat a block of ice and something odd happens at 0 °C: the temperature stops rising until all the ice has melted. The energy goes into breaking the bonds that hold the particles in place, not into making them move faster. The same happens at 100 °C while water boils. This hidden energy is called latent heat:

Q = m L

For water, the latent heat of fusion (melting) is L_f = 334 kJ/kg, and the latent heat of vaporization (boiling) is L_v ≈ 2,260 kJ/kg. Boiling 1 kg of water away takes more than five times the energy needed to heat it from 0 °C to 100 °C. The same energy comes back out when steam condenses, which is why a steam burn is worse than a burn from boiling water, and why sweating cools you: evaporating sweat carries heat away from your skin.

Most materials expand when heated, because faster particles push each other farther apart. A solid rod of length L grows by ΔL = αLΔT, where α is its coefficient of linear expansion (about 12 × 10⁻⁶ per °C for steel). That's tiny, but over a 100 m bridge a 40 °C swing adds about 5 cm, so bridges have expansion joints. Water is a famous exception: ice is less dense than liquid water, so it floats, and between 0 °C and 4 °C liquid water shrinks as it warms, so lakes freeze from the top down.

Gases expand much more, and simply. For a fixed amount of an ideal gas, pressure P, volume V and kelvin temperature T are linked by the ideal gas law:

PV = nRT     or     P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂

where n is the number of moles and R = 8.314 J/(mol·K). Hold one quantity fixed and you get the older laws: Boyle's law (PV stays constant at fixed T), Charles's law (V ∝ T at fixed P) and Gay-Lussac's law (P ∝ T at fixed V). That's why tire pressure drops on a cold morning.

• Zeroth law: if A and B are each in thermal equilibrium with C, they're in equilibrium with each other. That's what lets a thermometer work.
• First law: energy is conserved. The change in a system's internal energy equals the heat added to it minus the work it does: ΔU = Q − W. Pump up a bike tire and the pump gets warm: you do work on the gas, and its internal energy rises.
• Second law: heat flows on its own only from hot to cold, never the reverse. Put another way, the total entropy of an isolated system never decreases. A refrigerator can move heat from cold to hot, but only by using work, and it dumps even more heat out the back.
• Third law: you can get closer and closer to absolute zero, but never reach it in a finite number of steps.

A heat engine, like a car engine or a power-station turbine, takes heat Q_H from something hot, turns part of it into work W, and must release the rest, Q_C, to something colder. Its efficiency is the fraction that becomes work:

e = W ÷ Q_H = 1 − Q_C ÷ Q_H

In 1824 Sadi Carnot showed that no engine working between two temperatures can beat the ideal Carnot efficiency, with temperatures in kelvins:

e_max = 1 − T_C ÷ T_H

Because T_C can never be 0 K, no heat engine can be 100% efficient. Real car engines typically turn only about a quarter to a third of their fuel's energy into work.

For most of the 1700s, heat was thought to be an invisible fluid, later called caloric. In Glasgow in the early 1760s, the chemist Joseph Black (1728–1799) noticed that melting ice soaks up heat without getting warmer. He called this latent heat, and also saw that different materials need different amounts of heat to warm by the same amount: the idea behind specific heat.

In 1798 Count Rumford (Benjamin Thompson) reported that boring cannon barrels seemed to make heat without limit, a problem for the caloric theory. In 1824 the French engineer Sadi Carnot published Reflections on the Motive Power of Fire, showing that an engine's best efficiency depends only on the temperatures it works between.

In the 1840s the English brewer and physicist James Prescott Joule measured how much mechanical work makes a given amount of heat, most famously by letting falling weights turn a paddle wheel in water. Heat, he showed, is a form of energy, and the SI unit of energy is named after him. William Thomson, later Lord Kelvin, proposed an absolute temperature scale in 1848, and Rudolf Clausius stated the first and second laws in 1850 and coined the word entropy in 1865.