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Temperature

As indicated before, thermal equilibrium, a thermodynamic system at an equilibrium state is characterized by the value of the thermodynamic coordinates. The following notation is used in this notes to represent the different thermodynamic coordinates for a given system, A: a1, a'1, a"1... where a, a', a" ... represent the different thermodynamic coordinates and the sub index 1 identified a particular value for these coordinates.
Thus, when two thermodynamic systems, A and B, are in thermal equilibrium with each other, the thermodynamic coordinates of the systems will have a well defined value such as a1, a'1, a"1... for system A and b1, b'1, b"1... for system B. After the systems have reached the equilibrium state, defined by the previous sets of thermodynamic coordinates, systems A and B can be insulated and separated from each other. When separated, suppose that system A is maintained unchanged; that is, it is surrounded by adiabatic walls and all its thermodynamic coordinates are kept fixed. On the other side, system B is also surrounded by adiabatic walls but some of the thermodynamic coordinates are changed to be a new set  b2, b'2, b"2.... Next, systems A and B are again placed in thermal contact with each other while both are insulated from the surroundings. At this point, their thermal evolution is studied experimentally.  Under the previous conditions, it is found that the two systems do not undergo further thermal exchange indicating that the two thermodynamic systems are still in thermal equilibrium.
 

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by Luis F. Sez, Ph. D.    Comments and Suggestions: LSaez@dallaswinwin.com