THE THERMODYNAMICAL TRIPLE POINT:

Implications for the Trinity

Michael J. Bozack

Surface Science Center

Department of Chemistry

University of Pittsburgh

Pittsburgh, PA 15260

From: PSCF 39 (March 1987): 39’Äì41.

There has been little progress in the doctrine of the trinity since the Athanasian Creed and the Westminster Confession of Faith. A large number of parallel concepts have been suggested, but the use of the thermodynamical triple point as an analogy to the trinity has not been previously discussed. In this study we show that the thermodynamical triple point possesses a number of elements in common with the trinity. The triple point contains (1) a singular nature shared by three coequal but distinct subsistences, (2) economical, and (3) ontological properties. It also preserves the distinction between the classical trinity and the (4) tritheistic and (5) trimodal formulations. These rigorous requirements have been difficult to satisfy in previous analogies. The triple point provides an epistemic counterpart for our thinking about the trinity and allows for development of new perspectives.

The triple point is defined as the point where the solid, liquid, and gaseous forms of a substance coexist in equilibrium. The concept is anticipated by the Gibbs’Äô phase rule, according to which the largest number of phases P which can coexist in a thermodynamical system plus the number of degrees of freedom F equals the sum of the components C of the system, plus 2. In algebraic terms,

P + F = C + 2

The phases P are the states of matter that make up the system, usually solid, liquid, and gas. Each phase is homogeneous and contains bounding surfaces which allow for mechanical separation (at least in principle). The degrees of freedom F refer to the number of independently variable parameters that completely specify the thermodynamic state of the system. Such parameters are normally temperature, pressure, and composition. The components C are the lowest number of substances of independently variable composition which comprise the system. In a solution such as salt water, possessing stable compounds, the number of components is two (NaCl and H₂O). In a metallic alloy, it is usually sufficient to count the elements involved. Most pure substances possess a three-phase equilibrium point.

Application of the phase rule to a substance results in a phase diagram showing the possible phases available to the substance at varying pressures, temperatures, and compositions. The simplest phase diagram is that for a one-component system whose composition is fixed at 100% of the material under consideration. The remaining degrees of freedom (temperature and pressure) are customarily plotted on a two-dimensional graph with appropriate regions representing solid, liquid, and gas. A common example is water, whose phase diagram is reproduced in Figure 1. Equilibrium between two phases occurs along the mutual boundary of the phase regions, and equilibrium among all three phases occurs at the intersection of the regions. This intersection is the triple point.

For the case of water, which has a fixed composition, C = 1; the maximum number of phases P of water that can coexist in equilibrium is three: ice, water, and steam. By Gibbs' phase rule,

P + F = C + 2

3 + 0 = 1 + 2

No degrees of freedom exist under these conditions. This means that coexistence of ice, steam, and water can occur only at one specific temperature and one specific pressure. Such a condition, indicated by a single point on the phase diagram, is called the triple point.

The phase rule governs a system in equilibrium, meaning that the thermodynamic system possesses properties that are independent of time. At the triple point, equilibrium requires that rigorous control of pressure, temperature, and composition results in maintenance of the triple point indefinitely. The equilibrium is dynamic, with transitions occurring continuously between the coexisting phases, but in a way such that no apparent change is evident with the naked eye. This means that, at the triple point, boiling and condensing, melting and freezing, and subliming and freezing of gas are all going on simultaneously. For the case of water, the necessary pressure (0.006 atm) is below 1 atmosphere and must be prepared in a special experimental setup.

Finally, it is noteworthy that the triple point is not equivalent to the mere existence of three forms of matter, but rather defines a unique relationship between the solid, liquid, and gaseous phases. Mere existence of three phases of matter is trimodal and therefore unsuitable for analogy to the trinity.

By analogy, we mean the extension of patterns of relationship drawn from one area of experience to coordinate other types of experience. This requires the establishment of a number of characteristics held in common by the objects of comparison. It is possible to identify at least seven important areas of comparison between the triple point and the trinity.

1. Both the triple point and the trinity possess a singular nature with three coequal but distinct subsistences.

The triple point and the trinity both have a singular essence and possess three subsistences which have real distinctions among them. For example, the three states of water at the triple point are conjoined by a common molecular structure, yet ice, steam, and water are quite different from one another macroscopically. The difference is manifested by the distinctive physical properties held by the states of matter, such as density, compressibility, electrical conductivity, et cetera. Because the coexisting phases at the triple point possess a distinctive set of physical properties, the union of one into three occurs without loss of identity of the phases. By comparison, the trinity is also a single essence containing three subsistences which are able to merge without loss of identity. There is an infusion of three-into-one in both models, the satisfaction of which constitutes a minimum requirement for establishment of an effective analogy to the trinity.

Fig. 1. Phase Diagram for Water.

The phase diagram of water, showing the possible phases available to H₂O at varying temperatures and pressures. Coexistence of two phases occurs along the lines marked S-L, L-G, and S-G, while coexistence of three phases exists at the intersection of the regions, defined as the triple point. Since the triple point of water occurs below atmospheric pressure, it must be put under vacuum to observe.

2. Both the triple point and the trinity are equilibrium states.

Equilibrium is that condition in a thermodynamic reaction beyond which no net change occurs in the concentration of any substance. It defines a state in which the properties of the system are independent of time. Dynamic equilibrium occurs when equilibrium is maintained by equal rates of forward and reverse reactions, as opposed to equilibrium maintained by the absence of reaction. In the case of the triple point, the equilibrium is dynamic. Transitions are continually occurring among the phases, and no net change in the relative amounts of liquid, solid, and gas are measurable. The existence of an equilibrium state is analogous to the immutability of the Godhead, meaning that the nature and attributes of the Godhead are invariant with respect to essence. The triple point is also invariant, since a given substance is composed of a distinct elemental composition and, by definition, an equilibrium state is independent of time.

3. The triple point is not a tritheism.

The triple point preserves the distinction between tritheistic and trinitarian viewpoints of the trinity. Tritheism holds that there are three Gods rather than three personal distinctions in one God. The persons of the triad refer to three deified beings and deny the unity of the essence of God. The triple point is incompatible with tritheism because, at the triple point, there are not three phases in the sense of taking steam, ice, and water from separate locations and combining them mechanically. There is unity of essence at the triple point, with the phases tied to each other at a particular set of thermodynamic conditions. Reversible transitions are occurring between the phases, while bounding surfaces separating the phases are maintained. The triple point of water does represent the existence of three "waters" united in a purpose. There is something more in the union of the phases at the triple point than merely the sum of the phases. The same is true of the conjoined persons of the trinity.

4. The triple point is not a trimodality.

Trimodalism holds that the Godhead is a trinity of revelation rather than a trinity of persons and denies the reality of the trinitarian persons. The postulate is that there are aspects or manifestations of one God, with no internal distinctions within the divine substance. It may be argued that the triple point is not modal because the thermodynamic phases possess distinct and unique properties and are merely different manifestations of the same thing. For example, although composed of identical molecules, ice is manifestly different from steam and water and exhibits different physical properties. Further, the phases of the triple point are locked together in a state of dynamic equilibrium which prohibits individual manifestation of the states of matter except by destruction of the triple point. This means that once the triple point is established, simultaneous exercise of the three coincident phases is guaranteed. No grounds exist for the action of one phase apart from another. In contrast, the trimodal God can manifest only a single aspect at a given time.

5. The phase relationships at the triple point are similar to the relationships in the trinity.

The interdependence of phases at the triple point is analogous to the sense of relationship found between members of the trinity. Thermodynamically, each phase at the triple point derives and sustains its character by mutual collaboration with the other two phases. In other words, thermodynamic phases at the triple point cannot exist independently of one another, but are interlocked in a state of thermodynamic equilibrium. This symphonic blending is similar to the relations between the persons of the Godhead.

The Godhead is sustained by a self-contained mutuality of relations, and no one person of the trinity is or can be without the others. There is a coequal sharing of the singular divine essence without intrinsic subordination of any person. The undivided essence belongs equally to each of the persons and each possesses all the substance and all the attributes of deity. The same could be said for the triple point phases, as no state of matter is more fundamental than another, nor is water any less itself because it exists in three coincident forms.

6. Both the trinity and the triple point have ontological properties.

There is a resemblance between the relationship of the phases at the triple point and the distinctions rendered by the ontological (’Äúin essence’Äù) trinity. Ontologically, the persons of the trinity have an internal numbering system whereby the Father as the first person neither proceeds nor is begotten; the Son as the second person is begotten by the Father; and the Spirit as the third person proceeds from both the Father and the Son. There is similarly a natural ordering of phase relations. It is a general law that reactions in nature tend to proceed in the direction of lowest energy and greatest disorder. The appropriate thermodynamic function which quantifies this tendency is the Gibbs free energy function. In order to minimize the free energy during a reaction, phase changes can occur and one phase may be considered to ’Äúbeget’Äù another or ’Äúproceed’Äù from another. The language is strained, however, and the true situation is more complicated. There is, however, a fundamental quantity which allows for phase ordering in a way that is suggestive of the trinitarian ordering.

7. Both the trinity and the triple point have economical properties.

The economical (’Äúin works’Äù) trinity expresses the view that the entire Godhead is involved in external divine acts, but usually one member of the triad is featured. This preeminence is ground for describing one person as distinct from another. Similar behavior is displayed by the states of matter of most substances. Take water as one example: steam is used to drive locomotives and heat buildings, ice is an effective coolant and friction reducer, and water provides power and sustains the human body. While such applications are normally carried out far from equilibrium and no necessity exists for maintaining three coexistent phases at the triple point, use of a substance at its triple point is not ruled out in principle for systems which operate at equilibrium. For example, in a ’Äútriple-point’Äù skating rink, the joint operation of all three phases contributes to the maintenance of lubrication while the solid (ice) phase is featured. Under idealized conditions, then, it is possible for the triple point to simulate a reaction which depends on the conjoined effort of all three phases but where only one phase is featured.

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