### Thermodynamic System

The study of thermodynamics considers the basic subject of the analysis what is called a system. In general, a system can be defined solely as the part of the universe that the research or study focus the attention. The previous understanding of system divides the universe into two parts, the system and the surroundings. Thus, the surroundings is everything in the universe outside of the system.

#### Macroscopic Point of View

The thermodynamics study of a system can be described in terms of general quantities such as the system composition (chemical composition in many cases), volume, pressure, and temperature. This is the macroscopic point of view of a thermodynamic system. Thus, the macroscopic point of view of a thermodynamic system refers to the large scale properties of the system.

#### Microscopic Point of View

The microscopic study of thermodynamic system is based on the formulations of statistical mechanics. Under this formalism, the thermodynamic system is considered to be formed by a very large number of molecules, N, where the individual molecules are characterized by six independent parameters. Of the six independent parameters, three are the position coordinates of the molecule at any instant of time; and, the remaining three parameters are the velocity coordinates of the molecule. The molecules of the thermodynamic system can interact with each other through simple collisions or through forces produced by their particular fields. These forces are especially important when they are of the magnetic or electric nature. The thermodynamic system is analyzed in terms of the possible energy states accessible to the individual molecules.  After measuring macroscopic quantities associated to the thermodynamic system, the value of the macroscopic parameters are a reflection of the equilibrium state of the thermodynamic system as obtained from the probabilistic analysis of the possible microscopic individual energy states of the molecules.  The probabilistic analysis of the possible states of the individual molecules of the system determines all the possible states of the thermodynamic system; from those, the state with the highest probability is called the equilibrium state. In the study of thermodynamic systems, the population (number of molecules) of the different molecular energy states is the foremost problem to be solved.

In many cases, to validate the probabilistic approach to the study of thermodynamic systems the system is considered part of an ensemble of systems. An ensemble  of system is a large number of similar system where the system under study is a part.

 The drawing above represents an ensemble of similar molecular system. The system of interest is embedded in this ensemble.

#### Mechanical and Thermodynamic Coordinates

Mechanical coordinates are associated to the external analysis of the position and velocity of a complete system such as a rigid body. Based on the mechanical coordinates of the system, the potential and kinetic energies of the system can be calculated. The potential and kinetic energies are called the mechanical or external energy of the system, On the other side, macroscopic quantities determining the internal state of the system are called thermodynamic coordinates. The thermodynamic quantities are used to establish the internal energy of the system.

A system is a thermodynamic system, if it can be described in terms of the thermodynamic coordinates.

#### Thermal Equilibrium

If for a given state of a thermodynamic system, the set of thermodynamic coordinates have a definite constant value for unchanged external conditions, the state of the system is an equilibrium state. An individual system reaches the equilibrium state when under unchanged external conditions the thermodynamic coordinates describing the system have a defined constant value. On a multiple systems case, when two systems are in contact with each other,  they can be in contact by way of a wall that can be perfectly adiabatic all the way through a wall that is perfectly diathermic.

A wall is called adiabatic if the wall does not permit the transfer of energy (heat) (add link to heat) between the systems. Under this conditions, the two systems can maintain their own equilibrium state without interfering with each other. Thus, the thermodynamics coordinates associated with each other are unchanged because of the contact between the two systems. Therefore, the two systems can coexist for any value of the thermodynamics variables associated to the equilibrium state of the individual systems. Materials such as concrete, asbestos, and styrofoam represent a good approximation of adiabatic walls.

Diathermic Walls

A diathermic wall allows the exchange of energy between the two systems (thermal interaction). This exchange of energy produces a change in the thermodynamic coordinates of the two systems until an equilibrium state between the two systems is obtained. When the two systems have reached an equilibrium state, the two systems are in thermal equilibrium. Thus, thermal equilibrium is achieved by two or more systems when in contact through diathermic walls, if all the thermodynamic coordinates of the systems reach determined constant values characteristic of the individual system equilibrium states.

#### Zero Law

Experimentally, it can be seen that thermodynamic systems in equilibrium satisfies the fallowing transitivity rule:

If the thermodynamic system A is in thermal equilibrium with the thermodynamic system B, and the thermodynamic system B is in thermal equilibrium with the thermodynamic system C; then, the thermodynamic system A is in thermal equilibrium with the thermodynamic system C.

The previous statement is called the zero law of thermodynamic. The name is originated from the fact that after the first and second law of thermodynamic were established, it was concluded that the previous statement was implicitly assumed to be valid without a formal foundation.

A simple experiment that illustrate the scope of the Zero Law of Thermodynamic is described as follow:

 In the schematic drawing on the left, between systems A and B there is an adiabatic wall that prevent the thermal exchange between the two systems. At the same time, both systems are in contact with a third system, C, through diathermic walls that allow the thermal exchange. Thus, the thermal exchanges are possible between systems A and C, or between systems B and C. Nevertheless, the thermal exchange between systems A and B is still prevented by the adiabatic wall. In order to prevent the thermal exchange between the systems and the surroundings, the three systems are enclosed by adiabatic walls.  After maintaining the experimental configuration described above for sufficient time, it is encountered that systems A and B reach thermal equilibrium with system C. That is, there is not more thermal exchange between systems A and C or between systems B and C. Remember that the adiabatic wall is preventing the thermal exchange between systems A and B. At this point, system C can be removed from contacting systems A and B. In addition, the adiabatic wall between systems A and B is replaced by a diathermic wall. As mentioned before, this kind of wall allows the thermal exchange between the systems in contact. However, the experimental result is that there is not thermal exchange between the two systems, A and B. There is not net thermal exchange when the systems in contact have reached thermal equilibrium. Therefore, systems A and B reached equilibrium between them when they reached equilibrium with system C. Thus, if system A is in thermal equilibrium with system C and system C is in thermal equilibrium with system B; then, system A is in thermal equilibrium with system B which is exactly the postulated of the Zero Law of thermodynamics.
 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com