# The Zeroth Law of Thermodynamics

**Zeroth Law of Thermodynamics: **If object A is in thermal equilibrium with object B, and object B is in thermal equilibrium with object C, then object C is in thermal equilibrium with object A.

Establishing and defining the fundamental basics of thermodynamics is important in order to reference exactly why you came to one conclusion over another. The laws of thermodynamics contain working logic of physical quantities in equilibrium in order to prevent technically impossible conclusions from being reached.

The zeroth law of thermodynamics was established after the first and second laws were already in place, but was determined to be more fundamental than the first two. Therefore, the term “zeroth” was coined.

Let’s assume we are in an isolated system in a perfect vacuum with no heat transfer except for between the physical objects inside the system.

We know in geometry and mathematics that if the volume of a ball is equal to the volume of a box, and the volume of the box is equal to the volume of a cylinder, then the volume of the cylinder is equal to the volume of the ball. This is basic logic and seems like it should be applied to anything. So, why not temperature?

If the same ball was in thermal contact with the box, heat will flow from the warmer object to the cooler object until there is no net heat able to be transferred. At this point, the two objects are in thermal equilibrium.

If we then move the box to be in contact with the cylinder and there just so happens to be no heat transfer between the two objects, then the box and the cylinder are in thermal equilibrium.

Therefore, the cylinder is in thermal equilibrium with the ball.

This is the basis of temperature measurement. If we know that object A is in thermal equilibrium with object B, and object B is in thermal equilibrium with object C, it is conceivable that object C may not be in thermal equilibrium with object A.

Because there is an equivalence relationship thermally (similarly with the volume example), then we know there can be a standardized method of labeling the thermal “level”. In the case of thermodynamics, it is called temperature and it has been standardized based on easily repeatable points such as the freezing and boiling point of water at 1 atm pressure.

*Jarrett Linowes**Mechanical Engineeromniamfg@gmail.com*

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