Important Energy/Mass-System Concepts
and the Essence of Thermodynamics

A draft by M. Kostic ( www.kostic.niu.edu ); more at www.kostic.niu.edu/energy

 

·   Thermodynamics is a funny subject. The first time you go through it, you don’t understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don’t understand it, but by that time you are so used to it, it doesn’t bother you anymore.”-- Arnold Sommerfeld:

·   "Thermodynamics is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown."Albert Einstein

·    “Every mathematician knows it is impossible to understand an elementary course in thermodynamics.” Arnold (1990)

·   Truesdell describes the present state of the theory of thermodynamics as a "dismal swamp of obscurity."

·   "The law that entropy always increases - the Second Law of Thermodynamics - holds, I think, the supreme position among the laws of physics. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things from time to time. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." — Sir Arthur Eddington

·   “Isn’t thermodynamics considered a fine intellectual structure, bequeathed by past decades, whose every subtlety only experts in the art of handling Hamiltonians would be able to appreciate?” Pierre Perrot, author: “A to Z Dictionary of Thermodynamics”

 

The above quotes are interesting. Thermodynamics deals with very basic natural/physical concepts and one need to think through and make some sense and logic out of these concepts, which are very essential. Thus, Thermodynamics require a lot of thinking and focusing, it will challenge you intellectually, but it does not require o lot of math at all. We will try to understand different explanations of the same basic concepts, i.e. to generalize and simplify.

 

What is the study of Thermodynamics and what are its governing principles or laws? The Thermodynamics studies the physical and chemical systems’ changes, thus the physical and chemical processes, caused by energy exchanges. If it is expended to all natural processes in the universe, the original concepts will be applied on biological (live) processes, including information and the human behavior, thus becoming very complex study of all existence and changes. For simplicity, we will focus on physical and chemical processes only.

 

We’ll begin by looking in a portion of the real world by calling it a system,” and try to define it and its interaction with all other portions of the real world, if any, which we will call the “surroundings.” If there are no any interactions (influences) between our system and the surroundings, i.e. the system “left alone in every and all respects” it is called an “isolated system.” If our isolated system is “isolated” in every and all respects from its surrounding (limiting ideal case), it is observed (experienced) that any preexisting system’s non-uniformity and activity if present will, given enough time, equalize and cease, thus the system will spontaneously come to a permanent and stable equilibrium, i.e. in a state which could be described by that system properties. One need to conceptualize and “visualize” the above in order to start comprehending and defining important terminology for precise description of fundamental principles which are empirical (never experienced otherwise) but logical (could be reasoned and should make sense!).

 

What makes up the isolated system described above? It is made up of one or more substances in equilibrium. And we know that any substance has its microscopic structure, i.e., it is made up of atoms, molecules, etc., which are microscopically active and if influenced have a potential for changing its equilibrium state into another one. We distinguish between the mass of the substance and its activity (or its structure) and potential for change or (re)structure, calling that activity and potential to (re)structure the system’s energy. Thus, the mass and energy are property of a system. We even know that mass may transfer in energy in nuclear reactions, as described by the famous Einstein’s law, E=mc2, and we do not know whether the mass is originally made up of energy, i.e. a “condensed energy.” If in fact the mass and energy are uniquely interrelated, and they are all there is in the universe, we may logically conclude that a system (and thus the universe), is made up of mass and energy (which are furthermore interrelated, thus fundamentally the same). Thus, the mass and energy must be conserved, i.e. stay in the universe or in an isolated system, with a possibility to transfer from one form to another. If the interchange of mass and energy does not exist or is negligible, we may account for mass and energy conservation separately. Since the activity of a system structure and its potential to (re)structure through an activity are diverse, we have many forms/types of energy. Energy could be classified as kinetic (active) or potential, and each class could belong to the system as a whole (macroscopic or external) or to its microstructure (microscopic or internal). Energy could be more specifically classified as (a) mechanical kinetic energy if the whole system is in motion with reference to the surroundings, (b) mechanical potential energy of the whole system mass in a gravitational force field; (c) internal thermal energy representing internal activity of the system structure (molecules and atoms), (d) chemical potential energy related to binding or (re)structure of atoms from one type of molecules to the others; (e) nuclear potential energy related to binding or (re)structure of atom particles from one type of atoms to the others; (f) electromagnetic energy related to electromagnetic radiation, due to subatomic activity of photons and other particles, etc. All those energy types are related to the system properties and represent total system energy, which is also the system property itself in its own right, like mass, and other properties. The system is separated from its surrounding with its own boundary, or interface between the system and the surrounding, called the system boundary. The system activity (energy) may influence the other surrounding systems (i.e. the surroundings) and vice versa if the energy is allowed to cross the system boundary, which is the surface around the volume occupied by the system. Then we are talking about energy transfer (through the boundary surface) which may occur in three fundamentally different ways: (a) in random, disorganized way via micromolecular activity of the system structure which is known as heat transfer; (b) in focused, directional and organized, force-like way, known as work transfer; and (c) as electromagnetic radiation due to subatomic activity of the system structure. We have to notice that internal structure, its form, potential and activity make up the system and define its state, and its resulting surface manifestation provides for boundary energy transfer, i.e. energy exchange with the surroundings. Due to internal activity and structure of the system, the surroundings may influence the system, not only through the boundary, but also remotely via gravity and or electromagnetic field forces. Gravity is a mysterious phenomenon and may be consequence/manifestation force of the “condensed energy” into matter (mass), thus holding the mass/energy and the universe together, since the mass and energy are interrelated. Opposite mysterious phenomenon to the gravity would be radiation, which tends to “dissipate” energy off any mass according to the thermal radiation law (E/Ae= sT4). The whole universe (and any substance for that matter) holds its form/structure in gravitational field and exchange energy via radiation. Could we claim that the whole universe is thus made up of energy only (activity which in turn is organized/focused in different structures/forms/forces)?

 

A system in equilibrium is macroscopically stable (does not changes, i.e. microscopically reversible) and have fixed properties which define the state of the system. Furthermore, there is a minimum number of independent intensive properties which define a system and its all other properties which are dependent of such set of minimum number of properties. The system will undergo change (will change its state and some or all properties) if influenced by its surroundings, i.e. if energy is exchanged with the surroundings. Such system is NOT isolated. Interestingly, the numbers of independent properties, which define a system state, are equal to the number of energy transfer types. So, for so-called simple (only heat transfer, Q, and one type of work transfer, W, allowed or relevant) and compressible substance (the work type is compression ‘pV’ work), the two independent intensive properties define the state of the simple compressible system, like p&v, or T&v, or p&T, or similar.

 

The p-v-T phase diagram represents the value of one property as a function of other two independent properties, and is illustrated as a surface above the plane defined with the two independent properties, for example, p=p(v,T)=function(v,T), Such surface will have different regions corresponding to different phases (solid, liquid and gas) and mixtures of those the system may take form of. This 3-D (dimensional) surface may be projected in 2-D views on any two pairs of property axes with the remaining third axis as the parameter lines, representing the cut-off of that constant-parameter planes and the 3-D surface. Often, the table values with the characteristic properties of the phase changes and single phases are given. Of the most practical interest are saturated liquid-vapor and so-called superheated tables of water, refrigerants and other technical fluids. To utilize those tables, one needs to understand what those tables represent, relative to the property surfaces and characteristic lines. The saturation pressure and temperature are dependent on each other and are uniquely related as seen from the p-T diagram. For example, with heating (energy increase) at the constant pressure (isobaric process) the temperature of a solid will increase until it starts to melt, the temperature will stay constant during ‘quasi-equilibrium’ melting, then the melted liquid if further heated will increase its temperature until it starts to boil (saturated liquid, ‘f’), the temperature will stay constant during boiling until all liquid just evaporates (saturated vapor, ‘g’), and finally the temperature of the vapor will further increase after boiling is completed (superheated vapor, where T>Tsat and/or p<psat), see the corresponding diagram. You should know and be familiar with characteristic points (critical, ‘C’; triple, ‘TP’), characteristic regions and lines (sublimation, melting, saturation) and characteristic regions (solid, liquid, superheated vapor (gas) and supercritical). You should also be familiar with iso-property lines (isobaric, p=const; isometric/isochoric, v-const, isothermic, T=cons, etc.); and their trends (slopes and relative values). Then you should compare your given properties and compare them with corresponding saturation properties and determine whether your system state is in the saturation region [for which any property y=(1-x)yf+ xyg=yf+ x(yg- yf); where x=g_quality-ratio] or outside of it [for liquid use subcooled/compressed liquid tables or approximate with saturated liquid values, y(p,T)=yf(T), or superheated/depressed vapor tables if appropriate, y= y(p,T)].

 

In addition to the isolated system (no mass and energy exchange with the surroundings, thus will come to an equilibrium state if not already, a non-isolated, closed-mass system may exchange energy with the surroundings (in form of work and/or heat). The conservation of energy will imply that any net energy transfer into the system will stay and increase the energy of the system:

, where

or per unit of time, the energy rate must be conserved:

                         , where

 

If a system allows, not only the energy transfer, but also mass transfer with the surroundings, then for such, so-called open (or control volume) system, both, the mass and the energy of the system, together with the surroundings, must be conserved. The concept is the same as for the case of a closed system, except that accounting details are more complicated.