# The Zeroth Law of Thermodynamics

The Three Laws of Thermodynamics are well known, and are listed here. However, after the three laws were explained practically and theoretically, a more fundamental law was noticed. In science, sometimes the blindingly obvious is missed, and this is a good example of such an occurrence. So, instead of calling this new law the Fourth Law, it was decided to call it the 'Zeroth' Law1, as it was more fundamental and should be listed first.

#### The Zeroth Law

The Zeroth Law states:

If object A is in thermal equilibrium with object B, and object B is in thermal equilibrium with object C, then object C is also in thermal equilibrium with object A.

This Law allows, among other things, the creation and calibration of thermometers.

#### Who Came up with the Idea?

Like many laws of physics, the Zeroth Law wasn't discovered in a sudden, dramatic flash of inspiration. Its significance was initially overlooked because it was something that the scientific community knew was true and took mostly for granted. It was only when scientists tried to make thermodynamics systematically logical that they realised that the Zeroth Law was a necessary fundamental principle upon which the rest of thermodynamics was based. Without it, one can't be sure that temperature means anything, and temperature (and heat) are fundamental to thermodynamics.

#### What Does it all Mean?

It is observed that when an object is in contact with another object whose temperature is lower than its own, the former will transfer heat to the latter. The two objects will approach the same temperature, and - in the absence of loss to other objects - they will then maintain a constant temperature. The objects are then said to be in 'thermal equilibrium'.

To put it even simpler, thermodynamics is the science of the movement of heat. The Zeroth Law, rather appropriately, is about when heat doesn't move. It says that there is a state that two objects can share in which heat will not flow between them when they are touching. In addition, it is a general state that can be shared by any number of objects. When they are all in this state, then any two of them can be touched together and heat will not flow between them. This state is called 'being at the same temperature'.

#### How Do We Use It?

Well, by using this law we can make thermometers. In thermodynamics, there are a number of variables that affect each other. For example, at the melting point of water, liquid water and ice coexist, and the temperature will remain constant (at a constant pressure). The ice and water are in thermal equilibrium with each other, and if one puts a thermometer in the mixture it will reach equilibrium with both and show that the temperature is exactly 0°C. Similarly, at the boiling point, water and steam co-exist at exactly 100°C. By noting the material properties over the range between freezing and boiling, one can calibrate a thermometer.

The Zeroth Law also allows us to define temperature. The definition is based around what is known as a 'triple point'. In terms of melting and boiling, two states (solid, liquid or gas) can exist simultaneously at different temperatures depending on the pressure of the system2. There is only one distinct pressure and temperature at which all three can co-exist: the triple point. Thermodynamic temperature is defined according to the absolute, or Kelvin, scale. One kelvin3 is defined as 1/273.16 of the temperature of the triple point of water, making absolute zero -273.15° Celsius since the triple point is at 0.01° Celsius.

1As in 0th, 1st, 2nd...2This is why you can't make a decent cup of tea at the top of a mountain. The pressure is lower, so the water boils at a lower temperature, so making tea becomes an impossibility. This Researcher's advice is to take a thermos.3Kelvin does not have a degree sign associated with it. You use kelvin, not degrees kelvin.