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Glossary

Equilibrium

Equilibrium is a word denoting a static condition, the absence of macroscopic change with respect to time. In thermodynamics it is taken to mean not only the absence of change but also the absence of any tendency toward change on a macroscopic scale. Thus, a system at equilibrium is one that exists under such conditions that there is no tendency for a change in state to occur. Since any tendency toward change is caused by a driving force of one kind or another, the absence of such tendency indicates also the absence of any driving force.

The concept of equilibrium encompasses three varieties:

mechanical equilibrium (the pressure within a system is the same at all points),
thermal equilibrium (the temperature is uniform throughout a system), and
chemical equilibrium (the species composing a system no longer tend to react).

A system is in a state of complete equilibrium when it is in mechanical, thermal, and chemical equilibrium simultaneously. To say that a system is at equilibrium, thus, implies that the temperature of the system should be uniform throughout. (If the temperature of the system were non-uniform, then we would have at least two different temperatures, T1 and T2, in the system. A heat engine could conceivably be devised to operate between those two temperatures. We might also say, using the language of the mathematician, that two temperature levels in the system is the necessary and sufficient condition for the heat engine. Since this engine could produce reversible work, the system would not be in equilibrium. Ergo, the temperature of the system in equilibrium has to be uniform throughout.)

There are also systems whose properties are constant in time but that are not in equilibrium states. Consider, for example, a metal rod whose one end is placed in contact with a heat reservoir at a temperature T1, and the other in contact with a heat reservoir at a temperature T2 ≠ T1. The rod will eventually reach a state in which its properties remain constant in time. Although the properties of the rod in this state remain constant in time, the rod is not in thermodynamic equilibrium. The rod cannot be isolated from its surroundings without destruction of the state in which it is. Although the state of the rod is constant in time, the states of the reservoirs with which it is in contact are changing. Consequently, the entropy of the Universe is steadily increasing. (This state of system that remains constant in time, but which requires the production of entropy to maintain it, can be used to define a steady state.)

The natural tendency of a system is to proceed toward a state of equilibrium. This is the state in which the state variables, such as temperature, pressure, and volume, have values that are uniform and constant throughout the whole system. And, at equilibrium, any infinitesimal fluctuations away from equilibrium are opposed by the natural tendency to return to equilibrium. However, since thermodynamics is exceedingly general in its applicability that renders it incapable of answering the question of how fast a process (e.g., the process of attaining a state of equilibrium) will occur. In other words, thermodynamic considerations by themselves are not sufficient to allow calculation of the rates of chemical and physical processes. True, we know that the rate of change (i.e., the rate at which equilibrium is approached) is proportional to the difference in potential between the actual state and the equilibrium state. Therefore, the rate of change becomes very slow as equilibrium is approached.

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