Thermodynamicshigh schoolundergraduate
Zeroth Law of Thermodynamics
Also known as: Law of thermal equilibrium · Transitivity of temperature
If two things each match a thermometer, they match each other.
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Bodies A and B each equilibrate with reference C; their thermometer readings converge, demonstrating A ~ C and B ~ C implies A ~ B.
Equivalent forms
The law that makes 'temperature' a well-defined, transferable number — the foundation every other thermometer reading rests on.
Unit systems
- SI:
- T in kelvin
- natural:
- T in energy units
- CGS:
- T in kelvin
Where it holds
Defines empirical temperature for systems in equilibrium; breaks down for systems never reaching equilibrium (active matter, steady-state driven systems).
Discovery
Ralph H. Fowler · 1935
Fowler named it the 'Zeroth Law' in the 1930s because it logically precedes the First and Second Laws — but those had already been numbered, so it got zero.
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Why does a thermometer work at all?
The fact that a thermometer reads the same number for two objects that are themselves in equilibrium is not obvious — it is a physical law so fundamental it had to be inserted before the First.
Research status: stable
Common misconceptions
It is not 'obvious' or trivial — it is an independent physical postulate that could conceivably fail; it is what guarantees temperature is a consistent single-valued property.
Derivation
Thermal equilibrium '~' is an empirical relation.
The Zeroth Law asserts it is transitive, hence an equivalence relation.
Equivalence classes are labelled by a single real parameter — the empirical temperature — which is what a thermometer measures.
Limiting cases
⟶ Global equilibrium; no net heat flows anywhere
Insulated bodies⟶ Each retains its own temperature; transitivity untested until contact