Zeroth Law of Thermodynamics
If two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. This foundational principle defines temperature.
The Foundation of Temperature
The zeroth law is the most fundamental of the four laws of thermodynamics — so fundamental that it was only formally stated after the first and second laws had already been established, which is why it received the number zero.
In plain language: if system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then systems A and B are in thermal equilibrium with each other. This may seem obvious, but it establishes something profound — it provides a rigorous physical definition of temperature.
Why It Matters
The zeroth law justifies the existence of thermometers. A thermometer (system C) is placed in contact with system A and reaches equilibrium — the mercury settles. Then it is placed in contact with system B and reaches the same reading. The zeroth law guarantees that A and B are also in equilibrium with each other, even though they never touched.
Without this law, temperature would not be a well-defined, transitive property. Two objects could each be in equilibrium with a thermometer but not with each other — a situation that would make the concept of temperature meaningless.
Thermal Equilibrium
Two systems are in thermal equilibrium when there is no net flow of heat between them. When objects at different temperatures are brought into contact, heat flows from the hotter object to the cooler one until both reach the same temperature — equilibrium. This process is irreversible in practice: the system moves toward the state of maximum entropy.
The rate of heat transfer depends on the temperature difference, the thermal conductivity of the materials, and the contact area. But the direction is always the same: from hot to cold. This directionality is described by the second law.
Mathematical Formulation
If T(A) = T(C) and T(B) = T(C), then T(A) = T(B) where T denotes temperature — a transitive equivalence relation.
The transitivity of thermal equilibrium is what allows temperature to be represented as a single number on a scale (Celsius, Fahrenheit, Kelvin). The Kelvin scale, based on absolute zero and the triple point of water, is the SI unit of temperature and the natural scale for thermodynamics.
Historical Context
The zeroth law was first explicitly stated by Ralph Fowler in the 1930s, long after the first law (1850s) and second law (1850s–1860s) were established. Physicists realised that the concept of temperature — which both the first and second laws rely on — required its own formal foundation. Because it was logically prior to the other laws, it was given the number zero.
Key Takeaways
- The zeroth law establishes temperature as a well-defined, transitive physical property
- It justifies the use of thermometers — if two objects are in equilibrium with the same thermometer, they are in equilibrium with each other
- Thermal equilibrium means no net heat flow between systems
- The law was named "zeroth" because it is logically prior to the first and second laws
Frequently Asked Questions
Why is it called the "zeroth" law?
Because it was formulated after the first and second laws but is logically more fundamental. Since the first and second laws assume the concept of temperature, which the zeroth law defines, it was given a number that precedes them.
Is the zeroth law trivially obvious?
It seems obvious intuitively, but it is not mathematically trivial. Transitivity is a specific property of equivalence relations that must be stated as an axiom. There are physical quantities for which transitivity does not hold. The zeroth law asserts that thermal equilibrium is transitive — a fact about nature, not logic.