Zeroth Law of Thermodynamics
The zeroth law of thermodynamics states that if system A is in thermal equilibrium with system C, and system B is in thermal equilibrium with C, then A and B are in thermal equilibrium with each other. Thermal equilibrium is therefore transitive, which guarantees the existence of a single property, temperature, that is equal for all systems in mutual equilibrium and can be measured by a thermometer.
Curious
When two objects touch and are left alone, heat flows between them until it stops; they are then in thermal equilibrium. The zeroth law says this relationship passes along: if A matches C and B matches C, then A matches B. That sounds obvious, but it is an experimental fact about nature, not a logical necessity, and without it there would be no consistent way to assign a single number, the temperature, to each object.
The law was named last. The first and second laws were already established when physicists, notably Ralph Fowler in the 1930s, realised that this more basic statement was needed underneath them, so it was called the “zeroth” law.
Exploring
| Thermometer | Property that changes | Typical range |
|---|---|---|
| Liquid-in-glass | Thermal expansion | ~−100 to 600 °C |
| Constant-volume gas | Pressure | ~3 K to ~1,300 K |
| Thermocouple | Voltage at junction of two metals | ~−270 to 2,300 °C |
| Platinum resistance | Electrical resistance | ~14 K to ~960 °C |
| Pyrometer | Thermal radiation spectrum | above ~600 °C |
Deep Dive
Logical role. Formally, the zeroth law states that thermal equilibrium is an equivalence relation (reflexive, symmetric and transitive). It follows that the states of all systems can be sorted into classes of mutual equilibrium, each labelled by an empirical temperature θ. The specific scale is then fixed by choosing a thermometric property; the absolute thermodynamic temperature is defined independently of any substance through the efficiency of reversible engines (see Second Law).
Statistical view. In statistical mechanics, two systems exchanging energy reach equilibrium when the derivative of entropy with respect to energy is equal in both, 1/T = ∂S/∂U (see Entropy). Transitivity then follows because this derivative is a single number for each system. The zeroth law can fail, or needs care, for systems with long-range interactions (such as self-gravitating star clusters, which have negative heat capacity; see Stellar Structure) and for small systems far from the thermodynamic limit.
Practice. The International Temperature Scale of 1990 (ITS-90) defines a set of fixed points and interpolating instruments that realise thermodynamic temperature in practice. The 2019 SI redefinition fixed kB = 1.380649×10−23 J/K exactly, tying the kelvin to energy (see Constants).
Concept Relationship Map
Requires: thermal contact and equilibrium (no prior law)
Enables: temperature, thermometry, first law
Commonly confused with: equal heat content
Sources
- Fowler, R.H., Guggenheim, E.A. (1939). Statistical Thermodynamics. Cambridge University Press.
- Callen, H.B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd ed.). Wiley.
- Bureau International des Poids et Mesures (2019). The International System of Units (SI), 9th ed.