Zeroth Law of Thermodynamics: Definition, Formula & Examples

Thermodynamics is an area of physics concerning transfers of heat energy. It is often understood in terms of a set of laws.

The zeroth law helps to define the ​concept of temperature​, as it has to do with thermal equilibrium between objects. Heat flows from hotter matter to colder matter, and thermal equilibrium, sometimes called thermodynamic equilibrium, occurs when there is no net flow of heat. This occurs when the objects are at the same temperature.

What Is the Zeroth Law of Thermodynamics?

There were originally three central laws of thermodynamics. However, scientists in the early 1900s realized that another, more basic law was necessary for their theories to be complete and correct. Because this law was considered more fundamental than the others, calling it the fourth law of thermodynamics didn't seem appropriate, so it was made the zeroth law to show that it supersedes all the others.

The zeroth law of thermodynamics states that if thermal system A is in thermal equilibrium with thermal system B, and thermal system B is in thermal equilibrium with thermal system C, then A must be in thermal equilibrium with C.

This is called a ​transitive relation​, and is also commonly seen in algebra: If A = B and B = C, then A = C. The zeroth law of thermodynamics represents this concept with temperature.

Significance of The Zeroth Law of Thermodynamics

Mathematical theories often necessitate a relation called an equivalence relation: A way of saying whether two things are the same or not. The zeroth law is the equivalence relation of thermodynamics because it provides for the mathematical concept of temperature and allows for the existence of physical thermometers.

A key concept is the difference between energy and temperature. Knowing how much energy two individual objects have is not enough to know which way heat will flow when they are put in contact. It is the relative temperatures of the two systems that determine the direction of heat flow.

But how can temperature be measured? Typically, a thermometer is an object that exhibits known and calibrated properties depending on its temperature. For example, mercury expands in volume in a well-defined way as it heats up. Putting the thermometer in thermal equilibrium with an object and then observing those properties, such as how much the mercury has expanded, is a way to measure the temperature of an object.

The importance of the zeroth law can be seen when trying to compare the temperatures of two objects. If a thermometer is placed in liquid A, it becomes in thermal equilibrium with that liquid and reads a certain temperature.

If that thermometer is then placed in liquid B, reaches thermal equilibrium and reads the exact same temperature as it did when it was in thermal equilibrium with liquid A, the zeroth law is what allows us to say that liquid A and liquid B are the same temperature.

Other Laws of Thermodynamics

The first law of thermodynamics states that the total energy of an isolated system is ​constant​. The change in the internal energy of the system will always exactly equal the difference between the heat put into the system and the work the system does on its environment.

The second law of thermodynamics states that the ​total entropy​ of an isolated system can never decrease over time. The total entropy of the isolated system ​and​ its surroundings can remain constant in some ideal cases, but it can never decrease.

The third law of thermodynamics states that the entropy of an isolated system becomes constant as its temperature approaches absolute zero. This constant value of entropy cannot depend on any other parameters of the system, like its volume or pressure.


About the Author

Meredith is a science writer and physicist based in Seattle. She received her Bachelor of Science degree in physics from the University of Illinois at Urbana-Champaign and her Master of Science degree in physics from the University of Washington. She has written for Live Science, Physics, Symmetry, and WIRED, and was an AAAS Mass Media Fellow in 2019.