Abstract
It is shown that Steenbeck's principle of minimum power, or voltage, for discharges with fixed current is not a corollary of the principle of minimum entropy production, in contrast to what is frequently assumed; besides, the latter principle itself does not provide a reasonable approximation in gas discharge physics. Similarly, Steenbeck's principle is not a corollary of mathematical models of gas discharges. Hence, this principle contradicts the mathematical models. A methodically correct evaluation of the error caused by the use of Steenbeck's principle requires a comparison of a solution obtained with the use of this principle with an exact solution to the same problem, rather than with experimental results or results deemed reasonable from the point of view of common sense. Such a comparison is performed for two examples from the theory of a cylindrical arc column. The examples show that the error incurred by the usage of Steenbeck's principle is uncontrollable and may be unacceptably high.
Highlights
In 1932, Max Steenbeck proposed [1] that parameters of a current-controlled cylindrical arc discharge, such as the arc temperature, vary in a way that the axial electric field in the arc attains a minimum value
There is a serious problem concerning the principle of minimum entropy production itself: for continuous systems, this principle may be derived from laws of thermodynamics only in certain very special cases [21], and a question arises whether this principle provides a reasonable approximation in gas discharge physics
Application of Steenbeck’s principle to the arc channel model is equivalent to finding a state with a minimum entropy production among stationary states of different systems, in contrast to the principle of minimum entropy production in non-equilibrium thermodynamics where a minimum is sought among all possible states of the same system, including states that are not stationary
Summary
In 1932, Max Steenbeck proposed [1] that parameters of a current-controlled cylindrical arc discharge, such as the arc temperature, vary in a way that the axial electric field in the arc attains a minimum value. Steenbeck’s principle of minimum power, or voltage, is broadly understood as follows: states that are realized in gas discharges with fixed current are those that require minimal power (voltage) for their maintenance. This principle has been extensively invoked in investigations of many gas discharge phenomena, in particular cylindrical arcs [4], effect of normal current density on glow cathodes [5], cathode spots in arc discharges [6]. The question whether the principle of minimum entropy production provides a reasonable approximation in discharge physics is analyzed in Appendix B for the example of a cylindrical arc
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