Zeroth Law of Thermodynamics
Two systems in thermal equilibrium with a third are in equilibrium with each other.
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Example
If two cups of coffee each match a thermometer’s reading, they are the same temperature.
How it works
The zeroth law says that if system A is in thermal equilibrium with system B, and system B is also in thermal equilibrium with system C, then A and C must be at the same temperature and will not exchange heat when brought together. This is what makes temperature a consistent, measurable property rather than just a vague feeling of hot or cold. It works because thermal equilibrium means there is no net heat flow, so a third system can act as a reliable reference for comparing temperatures.
When to use it
Use this law whenever you want to justify why thermometers work or why equal temperature readings imply thermal balance. It is especially useful in problems about temperature measurement, calibration, and comparing different objects or systems without direct contact.
Worked example, step by step
A thermometer is placed in contact with a metal block and reaches thermal equilibrium at 18°C. The same thermometer is then placed in contact with a liquid sample and again reaches thermal equilibrium at 18°C. Because the thermometer is in equilibrium with both systems, the metal block and the liquid sample are in thermal equilibrium with each other. Therefore, the metal block and the liquid sample have the same temperature: 18°C.
Common mistakes to avoid
- Thinking the law says all three objects must be physically touching each other
- Confusing thermal equilibrium with having the same amount of heat energy
- Assuming equal temperature always means the objects contain the same internal energy
Did You Know?
The zeroth law was named last but is so fundamental it had to come "before" the first — it defines temperature.
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