Temperature
Temperature is the physical quantity that takes the same value for all systems in mutual thermal equilibrium (zeroth law) and determines the direction of spontaneous heat flow, from higher to lower temperature. Thermodynamically, absolute temperature is defined by 1/T = (∂S/∂U) at fixed volume and particle number; for a classical ideal gas it is proportional to the mean translational kinetic energy per particle, ⟨Ek⟩ = (3/2)kBT. Its SI unit is the kelvin (K).
Curious
Everyday temperature is about hot and cold, but physics defines it precisely. When two objects touch, heat flows from the one with the higher temperature to the one with the lower until they match (see Zeroth Law). Zoom in, and the molecules of a hotter gas move faster on average: at room temperature, nitrogen molecules in the air move at roughly 500 metres per second.
Scientists use the kelvin scale, which starts at absolute zero, the lowest possible temperature (see Third Law). A change of 1 K equals a change of 1 °C, and 0 °C is 273.15 K.
Exploring
| Scale | Zero point | Water freezes / boils (1 atm) |
|---|---|---|
| Kelvin (K) | Absolute zero | 273.15 / 373.12 (ITS-90 value; ~373.15 nominal) |
| Celsius (°C) | 273.15 K | 0 / ~99.97 |
| Fahrenheit (°F) | 255.37 K (absolute zero is −459.67 °F) | 32 / ~212 |
| Rankine (°R) | Absolute zero | 491.67 / ~671.6 |
Deep Dive
Definitions. Kelvin used the second law to define an absolute scale independent of any substance: for a reversible engine between two reservoirs, Qh/Qc = Th/Tc (see Second Law). Statistical mechanics gives 1/T = ∂S/∂U (see Entropy), and equipartition gives (1/2)kBT per quadratic degree of freedom in classical systems. Since 20 May 2019, the kelvin is defined by fixing kB = 1.380649×10−23 J/K exactly, rather than by the triple point of water.
Negative absolute temperature. In systems whose energy is bounded above, such as nuclear spins in a magnetic field, a population inversion makes ∂S/∂U negative, giving T < 0 K; such states are hotter than any positive temperature, since heat flows from them to any positive-temperature system. Purcell and Pound demonstrated this in 1951 and it has since been realised with ultracold atoms (2013). Whether the Boltzmann or the alternative Gibbs definition of entropy should be used, the latter forbidding negative temperatures, was debated in 2014 and later; most physicists accept the Boltzmann treatment for these systems, but the debate is recorded here as unresolved in detail.
Extremes. The cosmic microwave background is at 2.7255 K (see Cosmic Microwave Background); the Sun's core is about 15 million K (see Stellar Structure); heavy-ion collisions have produced quark–gluon plasma at trillions of kelvin.
Concept Relationship Map
Requires: zeroth law
Enables: heat, ideal gas law, second law
Commonly confused with: heat; internal energy
Sources
- Bureau International des Poids et Mesures (2019). The International System of Units (SI), 9th ed.
- Purcell, E.M., Pound, R.V. (1951). “A Nuclear Spin System at Negative Temperature.” Physical Review, 81, 279–280.
- Preston-Thomas, H. (1990). “The International Temperature Scale of 1990 (ITS-90).” Metrologia, 27, 3–10.