Temperature is a measurable property of bodies. Measuring it means putting the body in thermal contact with an instrument — the thermometer — and reading the position of a physical variable calibrated on a scale. That variable might be the height of a column of liquid, the electrical resistance of a wire, or the wavelength of thermal emission: any quantity that responds reproducibly to the thermal state will do.
But why does a thermometer work? Because two bodies in contact reach, after some time, the same temperature. This is the fundamental observation on which all of thermology rests, formalised in the zeroth law of thermodynamics.
Principle — Thermal equilibrium (zeroth law)
Two bodies A and B placed in thermal contact reach, after some time, the same value of a certain quantity, which we call temperature. If A is in thermal equilibrium with B and B with C, then A is in thermal equilibrium with C (Atkins 2010).
The property of transitivity — if A matches B and B matches C, then A matches C — is what makes the use of the thermometer meaningful: by placing B (the thermometer) in equilibrium first with A and then with C, we can compare A and C without ever putting them directly in contact. Without this property, the very concept of temperature as a “label” shared by bodies in equilibrium would not make sense.
Historical context
The zeroth law (Carathéodory, 1909) is so called because it logically precedes the first and second laws of thermodynamics: without it, not even the concept of temperature would be defined. Its “zero” numbering was introduced when the first two laws had already been named. See Riferimenti bibliografici.
Links
Topics: Thermology Concepts: Temperature
Related exercises: Problem — Temperature and heat · Worked exercise — Fictitious gas of two balls · Worked exercise — Helium in a braking lorry