The zero law of thermodynamics allows us to use thermometers to compare the temperature of two objects we like. The zero law of thermodynamics states that if two bodies are individually in equilibrium with a third separate body, then the first two bodies are also in thermal equilibrium with each other. This statement states that thermal equilibrium is a left Euclidean relationship between thermodynamic systems. If we also define that any thermodynamic system is in thermal equilibrium with itself, then thermal equilibrium is also a reflexive relationship. Binary relations that are both reflexive and Euclidean are equivalence relations. Therefore, again implicitly assuming reflexivity, the zero distribution is often expressed as a right Euclidean statement: the entropy of an irreversible process can be measured and expressed in terms of external and internal properties, regardless of the energy content of the system. We can obtain the same distribution of internal parameters imposed by a set of external parameters, both reversibly and irreversibly. These different pathways lead to different changes in work and energy in the system. However, it is thought that a set of local parameters determines entropy, and so we can set up an ideal process that would reversibly bring the system to any configuration of the irreversible process. For example, the diffusion of a substance is an unbalanced process and the local concentration profile is necessary to define the system. We can reversibly apply a centrifugal field to the system to maintain the same concentration profile in a steady state.

The energy reversibly applied to the centrifugal field differs from that of the system in an irreversible diffusion process. Thus, the thermodynamic states of an irreversible diffusion process and the corresponding equilibrium system are different. However, entropy is the same in both systems and is defined by steady-state properties. Entropy can be computed as the corresponding entropy of the real system. The first law expresses the qualitative equivalence of heat and work as well as the conservation of energy. The second law is a qualitative statement about accessibility and direction of progress of actual processes. For example, the efficiency of a reversible motor is only a function of temperature and cannot exceed the unit. These statements are the results of the first and second laws and can be used to define an absolute temperature scale independent of the material properties used to measure them. A quantitative description of the second law results from the use of entropy and entropy generation. In other words, the zero law means that all three bodies have the same temperature, according to NASA (opens in a new window).

James Clerk Maxwell (opens in a new window) put it perhaps more simply when he said, «All heat is the same.» (Longmans, Green et Cie, 1875). Most importantly, the zero law states that temperature is a fundamental and measurable property of matter. First, the energy equipartition for granular materials is violated. In other words, the prediction of the «zero law» of steady-state thermodynamics, which applies to molecular gases, does not apply to granular materials. These are the Euclidean relations that apply directly to thermometry. An ideal thermometer is one that does not measurably change the state of the system it is measuring. Assuming that the fixed reading of an ideal thermometer is a valid marking system for equivalence classes of a set of synchronized thermodynamic systems, then the systems are in thermal equilibrium if a thermometer provides the same reading for each system. If the systems are thermally connected, no subsequent state changes can occur. If the measured values are different, the thermal connection of the two systems causes a change in the states of the two systems.

The zero law does not provide any information on this final reading. The internal energy of a system is defined as the sum of the kinetic energies of the constituent particles of the system. A system that is well suited for today`s purposes is so-called ideal gas. It has been known for more than three centuries that gases approaching this type of behavior obey the relation PV = constant (Boyle`s law) if the gas is kept at a constant empirical temperature well above the conditions under which it can be liquefied. This allows us to adopt the PV product as a function that is a direct measure of τ. This has the advantage of providing a linear relationship, as briefly shown. Over the years, He-Gas, with its boiling point and very low inertia, has been chosen as the medium par excellence for such measurements; The devices used for this purpose are called gas thermometers. It is concluded that equilibrium corresponds to the temperature equality between the subsystem and the reservoir, which is essentially the zero law of thermodynamics. This is an implicit equation for the equilibrium energy of the subsystem, Ē = E(N, V, T).

Nevertheless, the most common application of the zero law of thermodynamics can be seen in thermometers. We can observe the zero law in action by taking a very ordinary thermometer with mercury in a tube. When the temperature rises, this mercury expands because the surface of the tube is constant. This extension increases the height. Now, increasing the height of the mercury label shows the temperature changes and basically helps us measure them. The zero law of thermodynamics is one of the four main laws of thermodynamics. It provides an independent definition of temperature without reference to the entropy defined in the second law. The law was introduced by Ralph H. Fowler in the 1930s, long after the first, second, and third laws were widely recognized. Fowler & Guggenheim (1936/1965) wrote about the zero law as follows: Thermodynamics has its own unique vocabulary associated with it. A good understanding of the basic concepts forms a good understanding of the different topics covered in thermodynamics to avoid possible misunderstandings. Two systems in thermal contact eventually reach a state of thermal equilibrium.

This state is clearly defined by temperature, which is a universal function of state properties and internal energy. If system 1 is in equilibrium with system 2 and if system 2 is in equilibrium with system 3, then system 1 is in equilibrium with system 3. This is called the zero law of thermodynamics and involves the construction of a universal temperature scale (first given by Joseph Black in the 18th century and named much later by Guggenheim). If a system is in thermal equilibrium, it is assumed that the energy is clearly distributed over the volume.