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Beverley John C. Beverley IE 500/PHI 598: Ontological Engineering 30 November 2013 Thermodynamic Equilibrium Ontology I. Introduction Thermodynamics is the study of energy, state systems, work, and path systems. This physical science branch is often bifurcated into classical and statistical fields of study where the former focuses on macroscopic behavior, while the latter focuses on microscopic behavior. While both of these branches deserve the attention of an ontologist, for the purpose of this project only the macroscopic tree will be considered in what follows. The field of thermodynamics is rife with terminological confusion and antiquated definitions. This observation is supported by cursory glance in any introductory textbook concerning the field.1 A prime example of antiquated use is the term latent heat that is sometimes considered synonymous with enthalpy and other times not (Cengel & Boles). While it is not the job of the ontologist to clarify these uses and abuses, awareness of these issues might bring needed terminological clarity to the field. Moreover, it is clear that a well-developed ontology must begin with the foundations of the field of inquiry. It is with that in mind, and the lofty goals of terminological clarity, appropriate characterization of thermodynamic systems, and potential extensions into For instance, the phrase ‘reversible’ has a precise definition in the literature: a microscopic change of energy state, which can be restored by infinitesimal alterations. Yet it is often used interchangeably with the meaning, ‘able to be reversed,’ even by physicists! Consider the typical example of a reversible piston under constant pressure. Here the use of reversible is applied to a macroscopic object. This misuse is even more apparent when it is noted that on a microscopic scale, all chemical reactions in a thermodynamic system are considered reversible. 1 1 Beverley existing chemical ontologies, on the distant horizon, that the following Thermodynamic Equilibrium Ontology was designed. As indicated above, Thermodynamics is the study of energy, but more specifically, it is the study of energy inhering in a Thermodynamic System. Such systems will be formally defined below in the Classes section, but the intuition underlying the concept is easily grasped: they are arbitrary regions of space. Systems have accompanying properties, and it is from consideration of properties in a system, some held constant while others vary, that the famous Thermodynamic Laws are derived.2 Indeed, when certain properties are assumed constant then various thermodynamic equilibria can be established in a thermodynamic state. From these latter considerations derive chemical, thermal, and mechanical equilibria, as well as the broader, inclusive, thermodynamic equilibrium, which is the focus of this ontology. These aspects of thermodynamic systems are the foundation of thermodynamics as practiced. While several features of thermodynamic systems were not included in the current ontology, every attempt was made to create a baseline thermodynamic ontology amenable to additions. That is, while certain, perhaps more complicated, aspects of thermodynamic systems were not included in the present ontology, additions can be made to accommodate greater breadth. Areas for extension will be noted when applicable in what follows. II. Scope and Methodology The Thermodynamic Equilibrium Ontology focuses on Thermodynamic Systems for various Thermodynamic Properties and Thermodynamic States. The Buffalo Formal Ontology 1.0 was 2 Zeroth Law: If two systems have the same temperature as a third, then they have the same temperature as each other; First Law: the total energy of an isolated system is constant; Second Law: an isolated system spontaneously evolves towards a state of higher entropy; Third law: establishment of absolute zero. 2 Beverley employed as the framework for this ontology following similar use by other chemical ontologies.3 Properties and States inhere in Thermodynamic Systems. Thermodynamic Reactions are included as well for comprehensiveness, as processes inhering in Thermodynamic Systems. The goal of this ontology is to design, in Protégé, an appropriate ontology that brings these concepts together while specifying relations among the classes and subclasses. Before turning to the definitions of each class and subclass, and taking a cue from thermodynamics textbooks, a few diagrams will help solidify the meanings of these terms. Consider the following: Figure 1.1 Figure 1.1 represents a Thermodynamic System with associated Thermodynamic System Boundary and Thermodynamic Surroundings. A system is simply an area under investigation and is demarcated by the boundary, which shields it from the surroundings. On the right hand side of the above photo, we have a raging fire demarcated as the system, with the boundary arbitrarily chosen encompassing the flames and the surroundings represented by everything else in the photo. The Thermodynamic System Boundary was included in the Thermodynamic Dumontier Labs, for instance, employs BFO in several of its ontologies. Dumontier’s Complex Chemical Composition Ontology will be discussed in depth below. 3 3 Beverley Equilibrium Ontology, the Thermodynamic Surroundings not included in the final version. This is due to the lack of specification of the System boundary in various textbooks considered. For instance, some defined the Surroundings as merely the adjacent environment of the System Boundary, while others included the entire universe (Cengel & Boles). To be sure, Thermodynamic Surroundings should be included in the ontology, but at present, it is unclear precisely what the phrase means. The following diagram specifies the focus of the Thermodynamic System further into Open Systems, Closed Systems, and Isolated Systems: Figure 1.2 Open Systems are those that allow Free Energy or Mass to flow through the Thermodynamic Boundaries. A Closed System has a Thermodynamic Boundary that is impermeable to Mass transfer, while an Isolated System is impermeable to Free Energy and Mass transfer. Thermodynamics texts often focus on Isolated Systems since they are more amenable to idealization. This ontology has included Thermodynamic Reactions as inhering in Thermodynamic Systems in general, however, rather than simply in Isolated Systems. This is 4 Beverley due to the fact that the Systems considered above may undergo chemical, mechanical, and thermal reactions, as well as may reach chemical, mechanical, and thermal equilibrium. The focus on Isolated Systems, while helpful in calculation, can be treated as any other System in this ontology, as long as the transfer restrictions are maintained. One final note must be made before moving to the Classes section. While the above Systems involve Free Energy and Mass transfers, the transfer of energy and mass is not included in this ontology. Physicists studying thermodynamics typically use these concepts while Chemists tend to focus on the Mass and Energy inhering in a system. Energy transfer and Mass transfer can be included, however, in later designs, to better approximate the Physicist’s understanding of thermodynamic processes. 4 Classes As mentioned above, the Basic Formal Ontology was chosen as the skeleton for this project. Thus, basic classes included Thing, entity, continuant, occurrent, independent continuant, spatial region, processural entity, etc. Most classes were not pertinent for the purpose of this ontology. The major division in BFO, between occurrent and continuant, was the first major obstacle however. Thermodynamic Equilibrium, and its component equilibria, are continuants. That is, when such equilibrium occurs it is wholly present at that time. Moreover, Thermodynamic Equilibrium is a dependent continuant since it inheres in other entities, namely, Thermodynamic States. Thermodynamic Properties and Thermodynamic Disposition States inhere in Thermodynamic States as well. The upper-level classes of the Thermodynamic Equilibrium Ontology follow: Class Genus Description 4 The Helmholtz Free Energy was included for just this purpose. Thermochemistry tends to use Gibbs Free Energy (also included) as a measure of Thermodynamic System’s capacity to do work while Helmholtz Free Energy is the bread and butter of Thermal Physics. 5 Beverley Quality Dependent continuant Thermodynamic System Quality Quality Thermodynamic Property Thermodynamic System Quality Extensive Property Thermodynamic Property Intensive Property Thermodynamic Property Thermodynamic System Disposition disposition Object Independent_continuant Thermodynamic System Object Object_boundary Independent_continuant Thermodynamic System Boundary Object_boundary Thermodynamic Reaction Process Chemical Reaction Thermodynamic Reaction 6 Exhibited if it inheres in an entity at all A dependent_continuant quality that inheres in a Thermodynamic System. A Thermodynamic System Quality inhering in a thermodynamic system that does not solely determine the global properties of the system. Properties of a thermodynamic system that are dependent on the size of the system Properties of a thermodynamic system that are independent of the size of the system. A Thermodynamic System has the disposition to reach equilibrium under various constant conditions. Spatially extended independent continuant Any arbitrary region of space currently under inspection. Surface of some sort (whether inside or outside of a thing) Object that is the real or imagined surface that separates a Thermodynamic System from its surroundings. Process inhering in a Thermodynamic System in which equilibrium is not sustained and Free Energy, Pressure, Temperature, and Enthalpy are dynamic. Thermodynamic Reaction Process of varying chemical movements in Thermodynamic System leading to transformations in Free Energy. Beverley Mechanical Reaction Thermodynamic Reaction Thermal Reaction Thermodynamic Reaction Thermodynamic Reaction Process of varying Pressure in Thermodynamic System leading to transformations in Free Energy. Thermodynamic Reaction Process of varying Enthalpy, Temperature, and Entropy in Thermodynamic System leading to transformations in Free Energy The largest class, Extensive Property, is listed below, as it comprises a significant portion of the ontology, and almost all of the Thermodynamic Properties superclass. Class Enthalpy Genus Thermodynamic Property Entropy Thermodynamic Property Free Energy Thermodynamic Property Gibbs Free Energy Free Energy Helmholtz Free Energy Free Energy Internal Energy Thermodynamic Property Thermodynamic System Mass Thermodynamic Property Volume Thermodynamic Property 7 Description An extensive thermodynamic property that is energy supplied to a thermodynamic system as heat under constant pressure. Measure of molecular disorder or randomness in a thermodynamic system. Energy of a Thermodynamic System under specific constant conditions. . Energy of a Thermodynamic System under constant pressure. Energy of a Thermodynamic System under constant temperature. Sum of all microscopic forms of energy in a thermodynamic system. Extensive Thermodynamic Property that gives rise to the phenomenon of resistance to force by the system. Measure of space occurrent occupies in three dimensions Beverley The following section will detail the Object Properties used in this ontology, as well as several relevant relations among the above classes. Object Properties The following table outlines the object properties associated with the Thermodynamic Equilibrium classes described. Domain Relation Range Thermodynamic System Bearer of Thermodynamic Property Thermodynamic Reaction Depends on Thermodynamic Equilibrium Has proper part Thermodynamic Disposition State Chemical Equilibrium Thermodynamic Property Inheres in Thermodynamic System Mechanical Equilibrium Is proper part of Thermodynamic Equilibrium This is a relatively small number of examples, but they should be adequate to explain the role these Object Properties play in the ontology. The goal, to reiterate, is to connect the various properties and states to the Thermodynamic System. Thus, relations such as ‘bearer of’ were crucial, as well as inverses such as ‘inheres in.’ The ‘is proper part of’ relation was also important in describing the complicated combination of equilibria which result in Thermodynamic Equilibrium. That is, Thermodynamic Equilibrium is composed of various other equilibria, which must obtain. With that in mind, the relation seemed to require Asymmetry, as well as an Irreflexive restriction. This followed since X ‘is proper part of’ Y does not mean either that Y ‘is proper part of X’ or that X ‘is proper part of’ X. Indeed, the typical definition of proper part precludes this, as nothing can be a proper part of itself. 8 Beverley Data Properties Thermodynamic as practiced by the chemist is a predominantly numerical enterprise. It should be no surprise then that there are a large number of Data Properties in this ontology. These serve the purpose of relating numerical quantities to Thermodynamic States, Properties, and Reactions, as well as the Thermodynamic System in general. The following section will outline the various Data Properties by giving examples of their respective use within the ontology. Domain Chemical Reaction Internal Energy Non-Spontaneous Reaction Mechanical Reaction Spontaneous Reaction Enthalpy Open System Mechanical Reaction Thermal Equilibrium Enthalpy Volume Relation Has Enthalpy value Has Kinetic Energy value has Entropy value Has Gibbs value Has Helmholtz value Has Internal Energy value Has Mass value Has Pressure value Has Temperature value Has Thermodynamic Potential value Has Volume value Range Real number Integer Real number Real number Real number Integer Positive Integer Real number Positive Integer Integer Real number The calculations resulting from assessment of a Thermodynamic System allow values to be associated with Properties of the system. Unfortunately, BFO 1.0 does not seem to have a framework into which generically_dependent_continuants can be placed, though later versions of BFO allow for the inclusion of Information Artifacts of this nature. Moreover, since later versions of BFO are backward compatible, it should be able to accommodate actual calculations resulting in values for the Data Properties given above. It should be noted that Professor Rudnicki who noted that, for instance, the Gibbs Free Energy is measurement of the Thermodynamic System rather than a genuine part of the system itself brought this to the author’s attention. 9 Beverley III. Thermodynamic Equilibrium Ontology With the classes specified, it is now time to turn to the Thermodynamic Equilibrium Ontology itself. Features of the Ontology Several features of the Thermodynamic Equilibrium Ontology have already been mentioned. In the following section, the heart of the ontology will be discussed in detail. Figure 3.1 10 Beverley Figure 3.1 is a snippet of the Class hierarchy with Thermodynamic Property highlighted. This property is composed of Intensive and Extensive properties, which are themselves divided into several subclasses. Figure 3.2 below elaborates on one of the Extensive properties: Enthalpy. As indicated below, Enthalpy takes Internal Energy and Thermodynamic Potential values and is disjoint with the other Extensive properties. Figure 3.3 further indicates that Enthalpy inheres in Thermodynamic System and is a subclass of Thermodynamic Property. Figure 3.2 Figure 3.3 These class relations represent how chemists employ enthalpy in calculations. Enthalpy is a feature of Thermodynamic Systems, which relies on the Internal Energy and Thermodynamic Potential of the system. Indeed, it is a rather interesting property in that it is often determined by holding temperature constant. That is, when temperature is held constant and energy enters a 11 Beverley system, there is a measurable increase in Internal Energy that cannot be accounted for by common means, i.e. via temperature. This is enthalpy. Figure 3.4 below highlights the Thermodynamic System class. As shown in Figure 3.5, this class has three subclasses: Closed, Open, and Isolated. Figure 3.4 12 Beverley Figure 3.4 Figure 3.5 Figure 3.5 presents several interesting features of the Thermodynamic System class. For instance, a Thermodynamic System has a Thermodynamic System Boundary as a proper part. Moreover, a Thermodynamic System is the bearer of some Thermodynamic Property and some Thermodynamic System Disposition. This latter feature is perhaps the most important as it includes Thermodynamic Equilibrium to which we now turn. A final feature, which we will consider in this section, is the Thermodynamic Equilibrium class. Figure 3.6 indicates its place in the Class hierarchy as a subclass of Thermodynamic Disposition State. It should be noted that Thermodynamic Equilibrium has several sibling classes: Chemical Equilibrium, Mechanical Equilibrium, and Thermal Equilibrium. Figure 3.7 shows the interesting relationship which Thermodynamic Equilibrium 13 Beverley has with its siblings. Each of the siblings is a proper part of Thermodynamic Equilibrium. That is, when a Thermodynamic System has reached a state in which Chemical Equilibrium, Mechanical Equilibrium, and Thermal Equilibrium obtain, then it is in a state of Thermodynamic Equilibrium. Figure 3.6 14 Beverley Figure 3.7 Figure 3.8 Moreover, though not indicated in Figure 3.8, the fact that Thermodynamic Equilibrium inheres in some Thermodynamic System while each of the Chemical, Mechanical, and Thermal Equilibrium’s are related to Thermodynamic Equilibrium as proper parts of should be reiterated. True Path Testing Any ontology worthy of BFO should follow the basic True Path Rule. Several examples of true path tests follow. Italicized classes were added to the BFO frame: I. II. III. Gibbs Free Energy is_a Free Energy is_a Extensive Property is_ a Thermodynamic Property is_a Thermodynamic System Quality is_a quality is_a dependent_quality is_a continuant is_a entity is_a Thing Temperature is_a Intensive Property is_a Thermodynamic Property is_a Thermodynamic System Quality Closed System is_a Thermodynamic System is_a object is_a independent_continuant 15 Beverley IV. Spontaneous Reaction is_a Thermal Reaction is_a Thermodynamic Reaction is_a process is_a processural_entity is_a occurrent Each of these entities follows a true path from the bottom of the class hierarchy to the upper level ontology. IV. Comparison with Existing Ontology Relatively few chemistry ontologies account for the thermodynamic properties developed in this ontology. The extensive labor involved in relating classes associated with specific variables to thermodynamic systems is perhaps a deterring aspect of these ontologies. Nevertheless, there have been attempts to characterize the upper-level domain of the field of chemistry, which have included aspects of Thermodynamic Equilibrium. The following is an example of just this sort from Dumontier Labs. Pertinent differences with the Dumontier ontology will be discussed as they arise in the discussion. Dumontier Labs An Ontology was located that attempts to accommodate thermodynamic systems by an alternative method. The Dumontier Labs chemistry ontology varies in significant detail from the ontology developed above. In the following section, several relevant differences will be examined. Differences include: While the Dumontier Complex Chemistry Ontology includes classes describing various reactions it has no Thermodynamic System Class. States are characterized by various thermodynamic systems, and are incompletely described without them. This ontology includes Thermodynamic System as a subclass of object, which is a continuant. Moreover, Thermodynamic System has subclasses: Isolated System, Closed System, and Open System. Again, without an appropriate way to describe the underlying thermodynamic system, descriptions of chemical processes are moot. Dumontier Labs does not boundaries for their represented reactions. Thermodynamic Equilibria are boundary states for reactions and so create the starting and finish lines necessary for said reactions. The Thermodynamic Equilibrium Ontology obviously includes this framework. Dumontier includes separate classes for Group Elements. These classes are defined with disjunction. For instance, the Group 10 Elements are defined by extension with: Darmstadtium, Nickel, Palladium, or Platinum. None of the Group Element classes, 16 Beverley however, includes Hydrogen. Hydrogen is typically included in either the Group 1 Elements or the Group 17 Elements due to its unique properties. The Dumontier Labs ontology, however excludes the element. Thus, a disjoint union of the Group Element classes would be not be exhaustive of the periodic table, though this is precisely what one should expect from such a union. For comprehensiveness, the Thermodynamic Equilibrium Ontology includes up-to-date Atoms, Elements, Compounds, and Molecules. Regardless, Group designations are unnecessary for the Thermodynamic Equilibrium, and so this ontology avoided having to make a choice as to where Hydrogen should be placed. Dumontier Labs has the element with atomic number114 incorrectly listed as Ununquadium. IUPAC adopted the name Flerovium for this element in 2012. A similar oversight was made with Ununhexium, which was named Livermorium in 2012. There is also no Copernicum element listed in the ontology. These have been corrected in the present ontology. Finally, Dumontier Labs includes 18 Group Element classes corresponding to ‘group element’ extension classes. This appears to be a redundancy in the ontology, as deletion of any of the separate Group Elements, or all of the seemingly redundant classes, seems to effect no relevant alteration in the ontology. Indeed, the 18 Group Elements are sibling classes of the continuant and occurrent class though they are clearly continuant entities. The major issues with the Dumontier Labs chemistry ontology have been avoided in the construction of the current ontology. The major complaint with Dumontier is the absence of a framework within which thermochemical reactions, or any reaction, could take place. If the Dumontier ontology were employed, for instance, to account for the various calculated data acquired from thermodynamic research it would be unable to do so without significant overhaul. Indeed, several of the classes seem haphazardly organized with island classes unrelated to the rest of the ontology prevailing. This is rather surprising as Dumontier Labs hosts several rather impressive ontologies on its website. These range from various aspects of the Biological Sciences to Physics and Metric measurement ontologies. Again, many of these ontologies are well designed and capable of handling quantitative development. This cannot be said, however, for the Complex Chemical Ontology. V. Areas for Further Research 17 Beverley The next step in the development of this ontology is to update it to BFO 2.0 and include the generically dependent continuant class to allow for information artifact definitions. Following this step, the inclusion of physics related thermodynamic information would expand the ontology exponentially. This would include classes that covered Work, Heat transfer, various phase transitions, and associated values. Again, this includes a great deal of data as can be seen from Figure 5.1 and Figure 5.2 below. Figure 5.1 Figure 5.2 Figure 5.1 and Figure 5.2 are the beginning and ending of a Saturated Water Table at varying Temperature. Saturation in this table indicates that water is midway between a gas and liquid, or liquid and solid. Given increasing temperature in such a state associated properties of the molecule change. Thus, specific volume (volume divided by mass), Internal energy, 18 Beverley Enthalpy, and Entropy change according to the amount of temperature change. It is hoped that in the future this information can be accessed via an appropriate ontological framework. It should be noted, however, that this is a rather tall order due to the number of molecules available for study, and the number of variables, which can be held constant when obtaining such information. Nevertheless, the water table above relies on a Thermodynamic System with Thermodynamic Properties already defined. Thus, significant ground has been broken in the development of an ontology that can accommodate substantial data in this field. 19 Beverley Work Cited Cengel, Y., Boles, M. (2010). Thermodynamics: An Engineering Approach. Fifth Edition. Prentice Hall Publishing. 20