J. Willard Gibbs
Josiah Willard Gibbs earned the first American Ph.D. in Engineering from Yale in 1863. He went to France in 1869 where he studied with the great Joseph Liouville, who formulated the theorem that the phase-space volume of a system evolving under a conservative Hamiltonian function is a constant along the system's trajectory. The fluid inside the original phase-space volume is said to be incompressible. The Liouville theorem may not apply to gases if collisions are not time reversible, if the particle collisions do not preserve path information. Gibbs then travelled to Germany, where in Heidelberg he learned about the work of Rudolf Clausius, Hermann von Helmholtz, and Gustav Kirchhoff in physics, and Robert Bunsen in chemistry. Back in New Haven, Gibbs published several long monographs. Gibbs focused on five thermodynamical variables, volume, pressure, temperature, energy, and entropy. He showed that any three of these are independent variables, from which one can deduce the other two. In 1873, his first monograph introduced new diagrams relating thermodynamical quantities to one another. In Graphical Methods in the Thermodynamics of Fluids, Gibbs explored various two-dimensional planar graphs showing two of these independent variables to exhibit thermodynamic properties. He first cites the success of the pressure-volume graphs that are most often used to illustrate the thermodynamics of the Carnot Cycle. Émile Clapeyron had in 1934 first drawn such diagrams. Clausius had also used them in 1865. Since James Watt combined a pressure gauge with a volume indicator on his steam engine, engineers had graphed the relations between pressure and volume, whose product is the work done. Each point in the pressure-volume graph represents the state of the system, the integral around the curve is the work done by the system (the gray area in the figure), perfect for calculating the efficiency of steam engines or any heat engine. Gibbs argues that plotting entropy and temperature as the two coordinates is preferable to pressure-volume for many purposes. We believe it is the most intuitive graph as a teaching tool when explaining the relationship between energy and work available. One can look at this graph and visualize directly the maximum theoretical work that can be done by an engine working between a high temperature source and a low temperature sink. Gibbs wrote in 1873...
It is worthy of notice that the simplest form of a perfect thermodynamic engine, so often described in treatises on thermodynamics, is represented in the entropy-temperature diagram by a figure of extreme simplicity, viz: a rectangle of which the sides are parallel to the co-ordinate axes.Gibbs explains why an entropy-temperature graph is superior to pressure-volume. It is a "geometrical expression," a visualization of the second law of thermodynamics. Entropy, and "Negative Entropy" (cf., Information), are very difficult concepts to explain. He worries that entropy and the second law "may repel beginners as obscure and difficult of comprehension." They are usually presented with equations, which many non-scientists find difficult. After this first monograph, Gibbs fills his pages with dense equations. When the alternative is to use words, Gibbs says they are clumsy. It is sad that he did not continue his popularizing of this science with these simple diagrams...
The method in which the co-ordinates represent volume and pressure has a certain advantage in the simple and elementary character of the notions upon which it is based, and its analogy with Watt’s indicator has doubtless contributed to render it popular. On the other hand, a method involving the notion of entropy, the very existence of which depends upon the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension. This inconvenience is perhaps more than counter-balanced by the advantages of a method which makes the second law of thermodynamics so prominent, and gives it so clear and elementary an expression.The fact, that the different states of a fluid can be represented by the positions of a point in a plane, so that the ordinates shall represent the temperatures, and the heat received or given out by the fluid shall be represented by the area bounded by the line representing the states through which the body passes, the ordinates drawn through the extreme points of this line, and the axis of abscissas,—this fact, clumsy as its expression in words may be, is one which presents a clear image to the eye, and which the mind can readily grasp and retain. It is, however, nothing more nor less than a geometrical expression of the second law of thermodynamics in its application to fluids, in a form exceedingly convenient for use, and from which the analytical expression of the same law can, if desired, be at once obtained. If, then, it is more important for purposes of instruction and the like to familiarize the learner with the second law, than to defer its statement as long as possible, the use of the entropy-temperature diagram may serve a useful purpose in the popularizing of this science
Available Energy and InformationIn his second monograph, also published in 1873, Gibbs introduces two terms that have come to dominate modern discussions, "dissipated" and "available" energy. He writes...
For example, let it be required to find the greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition. This has been called the available energy of the body. The initial state of the body is supposed to be such that the body can be made to pass from it to states of dissipated energy by reversible processes.Gibbs does not give us another graphical representation of these kinds of energy, but we can broadly identify "available" energy with area ABCD, labelled W, the work done above, and "dissipated" energy with CDEF, the waste heat sent to the low temperate sink. Note that heat from the high temperature source is ABFE, the sum of ABCD and CDEF. In familiar modern terminology, the heat, or original energy content, is transformed into work and waste energy
dQ = dW + TdSToday we call the energy available to do work the Gibbs "Free Energy."
G = U - TS,where U is the total energy. So what is the connection between available "free" energy and information structures? Clearly, in a state of thermal equilibrium there is nothing of the "order" we associate with information. Equilibrium is the ultimate "disorder." In our explanation of the two-step cosmic creation process, the second step is exporting positive entropy away from the newly formed information structure. In the first step, available energy, or work, is essential for arranging the particles into a structure, usually one among many possible arrangements. In the early universe, the arrangement is controlled by quantum cooperative phenomena with electrostatic attractive and nuclear repulsive forces. In the subsequent billions of years, the formation of planets, star, and galaxies is controlled by gravitational forces. Work is done by these forces as structural components are pulled together. The new configurations cannot be stable entities unless positive entropy is radiated away to satisfy the second law. These information creation processes do not directly resemble the thermodynamic engines that Gibbs is discussing, with their obvious source of energy and heat sinks. But we can see the earliest universe as a cosmic source of high energy particles and radiation. We can locate the cold sink inside the universe, since there is no "outside." The sink for waste energy is the expanding space itself. Today we can see clearly across vast empty space to the uniform cosmic microwave background radiation at under three degrees Kelvin. The resemblance to a thermodynamic engine is easier to see for our Earth. The hot source is our Sun, whose radiation leaves the sun at a temperature of thousands of degrees. When it reaches Earth, its energy content temperature is only hundreds of degrees, and when it is thermalized by the planet, it is radiated away from the dark side of Earth into the night sky, Erwin Schrödinger described the Sun as the source of "negative entropy" on which "life feeds." He did not know how the Sun itself could get so far from equilibrium to be the source of available energy. That we explain by the expansion of the universe. The cosmological and astrophysical "engines" are doing work not by extracting available energy from a hot gas or liquid and dumping waste energy as a material stream. They are doing work with forces that are action-at-a-distance. They are exporting their positive entropy by radiating it away to the empty space appearing between the information structures. Gibbs' third monograph, in 1876, "On the Equilibrium of Heterogeneous Substances," began with Clausius' great first and second laws of thermodynamics in two simple sentences
"Die Energie der Welt ist constant. Die Entropie der Welt strebt einen Maximum zu."Gibbs' "great memoir," as Lewis and Randall called it in 1923, contains a brief but careful explanation of what later writers called the "Gibbs Paradox" (pp.163-165). E. T. Jaynes said in 1992 it came as a "shock" that Gibbs' explanation had been missed by textbook writers for 80 years? This passage also includes probably the most famous quote about the idea of spontaneous entropy decrease, one cited in hundreds of textbooks, starting with Boltzmann in 1898, and including Lewis and Randall's chapter 8, Entropy and Probability. Gibbs wrote...
we may easily calculate the increase of entropy which takes place when two different gases are mixed by diffusion, at a constant temperature and pressure. Let us suppose that the quantities of the gases are such that each occupies initially one half of the total volume. If we denote this volume by V, the increase of entropy will be...Ludwig Boltzmann must have thought this passage extremely important. He used the last line as the opening quotation for the second volume of his Lectures on Gas Theory, "the impossibility of an uncompensated decrease of entropy seems to be reduced to improbability." It was Gibbs' short text Principles in Statistical Mechanics published the year before his death in 1903 that brought him the most fame. In it, he coined the term phase space, phase volume, his phase rule and the name for his field - statistical mechanics. Earlier he named the chemical potential and the statistical ensemble. He showed how his graph planes can become the surfaces of three-dimensional objects that identify "phase changes," between gases and liquids, and between liquids and solids.
ReferencesGraphical Methods in the Thermodynamics of Fluids Gibbs "Paradox" Gibbs paradox and its resolutions (a great list of references, but links are all dead) Wikipedia Stanford Encyclopedia of Philosophy Normal | Teacher | Scholar