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The Scientific Papers of J. Willard Gibbs, Vol. 2 epub ebook

by J. Willard Gibbs,Josiah W. Gibbs

The Scientific Papers of J. Willard Gibbs, Vol. 2 epub ebook

Author: J. Willard Gibbs,Josiah W. Gibbs
Category: Physics
Language: English
Publisher: Ox Bow Pr (February 1, 1994)
Pages: 284 pages
ISBN: 188198706X
ISBN13: 978-1881987062
Rating: 4.9
Votes: 687
Other formats: doc mobi mbr txt


Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics.

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous inductive science

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made important theoretical .

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made important theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous deductive science. In 1901 Gibbs received what was then considered the highest honor awarded by the international scientific community, the Copley Medal of the Royal Society of London, "for his contributions to mathematical physics".

Willard Gibbs, why did you do to this to us? . Let us start with the specific picture. In Paper I, Gibbs showed that the thermodynamics of a pure substance is entirely specified by a relation between three variables: energy, volume, and entropy

5 people found this helpful. In Paper I, Gibbs showed that the thermodynamics of a pure substance is entirely specified by a relation between three variables: energy, volume, and entropy. He called the relation the fundamental thermodynamic equation of the substance. The equation is specific to each individual substance.

FORMERLY PROFESSOR OF MATHEMATICAL PHYSICS IN YALE UNIVERSITY. VECTOR ANALYSIS AND MULTIPLE ALGEBRA. ELECTROMAGNETIC THEORY OF LIGHT. ETC. LONGMANS, GREEN, AND CO. 39 PATERNOSTER ROW, LONDON. The present volume contains all the published papers of Professor J. Willard Gibbs except those upon Thermodynamics, which are placed in Volume I. of this collection.

Josiah Willard Gibbs. Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Josiah Willard Gibbs You can read Scientific Papers of J. Willard Gibbs. by Josiah Willard Gibbs in our library for absolutely free. Read various fiction books with us in our e-reader.

Gibbs, J. Willard, Gibbs, Josiah W. Published by Ox Bow Pr (1994). ISBN 10: 188198706X ISBN 13: 9781881987062. Longmans, Green and Company, 1906. Electromagnetic theory of light, etc Volume 2 van Scientific Papers of J. Willard Gibbs, Henry Andrews Bumstead. Josiah Willard Gibbs. Henry Andrews Bumstead, Ralph Gibbs Van Name.

JjuJKM.. A Permission for the preserU reprvni of the different papers contained in these volumes has in every case been obtained from the proper authorities.(Typographical errors above are due to OCR software and don't occur in the book.)About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text. Read books online for free at www.forgottenbooks.org
Reviews (4)
Kinashand
As other reviewers of Gibbs have said this work is the origin of physical chemistry. It is challenging to read his material but worth the effort to see how thermodynamics developed.

Gianni_Giant
This research in this monograph is among the greatest theoretical physics of the 19'th century. It's impact has been tremendous, even outside physics and chemistry. Gibbs approach to equilibrium --maximize S and minimize E,H,A, and G and is now the cornerstone of field of Chemical Thermodynamics, a field which he created in this book. He also invented A and G and greatly expanded the interpretations of H and E, yielding the general structure of thermodynamics. Gibbs' chemical potential is now a household word. He generalized thermodynamics to processes for which mole numbers change (the main motivation for his work). This opened the way to systematic and unified treatments(based on Gibbs chemical potential balance equations)of,for example, major phenomena in chemistry like chemical, phase, and solubility equilibria. Gibbs ensemble concept, which is an extension of his formulation of thermodynamics, is now the foundation of the more advanced field of statistical mechanics. And there is so so much more. l

However the book reminds me of Dr. Jekyl and Mr. Hyde. Namely, it is the most awfully written and incomprehensible scientific work I have ever encountered. If you don't believe me just give it a try. For example, it features such "treats" as 100 word sentences. But its verbosity gives anything but detailed clarifying explanations. It is just horrible writing which only enhances the obscurity of an otherwise incomprehensible text.

I have been working on it off and on for two years. I still only understand ~ 25% in detail,and even for this small part there are still aspects of some derivations which I don't understand completely.

Willard Gibbs, why did you do to this to us?

Ramsey`s
I bought this reprint from Ox Bow Press in 1990s. The quality of print is excellent. The book collects all papers written by Gibbs on thermodynamics. Over the years I have returned to the book many times, and will continue to do so in coming years. I'll keep updating this review. Gibbs is timely and timeless. No need to read him in rush.

Gibbs wrote three main papers on thermodynamics. Paper I (pp. 1-32) introduced the fundamental thermodynamic equation that relates energy, volume and entropy. Gibbs showed that the fundamental equation generates all relations among all functions of state. Paper II (pp. 33-54) represented the fundamental thermodynamic equation as a surface in the three-dimensional space of energy, volume and entropy. Gibbs introduced a geometrical approach to equilibrium, stability, metastability, phases, critical point, and available energy. The first two papers were limited to thermodynamics of a pure substance, capable of two independent variations. Paper III (pp. 55-371) extended the basic approach to systems of more independent variables, and studied a large number of phenomena, a list of which appeared in the Synopsis (pp. 350-353).

Paper I. GRAPHICAL METHODS IN THE THERMODYNAMICS OF FLUIDS, 1873

The title of the paper does not do justice to the scope of the paper, which goes beyond the graphical methods. Specifically, Gibbs introduced the “fundamental thermodynamic equation”, and showed that it generates all other thermodynamic relations. The paper introduced his approach to thermodynamics, the approach that we use today.

This paper focusses on states of equilibrium. Like Clausius and others, Gibbs limited himself to a system whose state is capable of two and only two independent variations. Why two? Carnot seemed to have a firm grip over the early developers of thermodynamics. His devotion to steam engines had made the fluid of a pure substance the system of choice. A pure substance is capable of two independent variations. For example, once the volume and temperature are fixed, so are all other functions of state (e.g., pressure, energy, entropy).

From beginning Gibbs disentangled himself from the mythical origin of thermodynamics, and listed three basic equations:

energy is the sum of heat and work, du = dq + dw,
work equals the pressure times the increment of volume, dw = - Pdv, and
heat equals the temperature times the increment of entropy, dq = Tds.

Gibbs took these equations from Clausius, and did not re-derive them. The result was a crisp synopsis of thermodynamics. In effect, Gibbs took the existence of energy and entropy for granted, and developed their consequences. This approach has been made into a set of postulates (e.g., Tisza, 1966; Callen, 1960, 1985). Clausius discovered entropy, and Gibbs made it useful.

Clausius’s three equations involve seven quantities: entropy, energy, volume, temperature, pressure, work and heat. Of the seven quantities, energy, entropy, volume, temperature and pressure are functions of state, but work and heat depend on path. Starting with Clausius’s three equations, Gibbs eliminated work and heat, and obtained an equation involving only the five functions of state:

du = Tds - Pdv.

This equation is now known as the Gibbs equation.

Gibbs noted a remarkable fact. The function u(s,v) constitutes the thermodynamic model of the substance. This single function generates all thermodynamic relations of the substance. Because the state of a pure substance is capable of two and only two independent variations, we can use two of the five functions of state as independent variables to specify the state, and express the other three as functions of the two independent variables. Say we use entropy and volume as two independent variables, and use energy, temperature and pressure as independent variables. If the energy is expressed as a function of entropy and volume, u(s,v), the partial derivatives of this function give the temperature and pressure as functions of entropy and volume, T = du(s,v)/ds and P = - du(s,v)/dv. Gibbs called the relation between energy, entropy and volume, u(s,v), the fundamental thermodynamic equation.

Gibbs illustrated his method using ideal gases. Again his presentation was crisp. Centuries of prior work on ideal gases reduced to two equations: Pv = RT and u = cT. From these two equations, he obtained the fundamental thermodynamic equation of ideal gases, u(s,v).

We now know that for an ideal gas the specific heat c varies with temperature. That is, the energy is a function of temperature independent of volume, but the function u(T) is not necessarily linear in T. Indeed, this statement is readily shown if we combine Pv = RT and du = Tds - Pdv. Recall that R is a constant, and the other variables are functions of state.

Instead of entropy and volume, other pairs of functions of state can also serve as independent variables. When the two independent variables are chosen, one can then express all other functions of state as dependent variables. From the five functions of state, TvPus, we can make ten choices of three functions of state, and thus have ten distinct thermodynamic relations (i.e., equations of state).

Gibbs did not name other functions of state beyond the five. One can of course add to the list the enthalpy, heat capacity (at either constant volume or constant pressure), coefficient of thermal expansion, compressibility, Gibbs function, Helmholtz function, etc. Every one of these properties is a function of state, and the function can be derived from the fundamental thermodynamic equation, u(s,v).

For Gibbs, the number two is also significant for another reason. He said, “the state of the body, like the position of a point in a plane, is capable of two and only two independent variations.” Consequently, one can associate a state of the body to a point in the plane. Gibbs left the method of association completely arbitrary, except requiring that neighboring states of the body be associated with the neighboring points in the plane. That is, the two coordinates of the plane should be continuous functions of, say, the entropy and volume. Let x and y be the coordinates of the plane. Gibbs associated the states of the body to points in the plane by two arbitrary functions s(x,y) and v(x,y). On the plane, a constant value of a function of state forms a line. We can draw five sets of lines: lines of equal pressure, of equal temperature, of equal volume, of equal energy, and of equal entropy.

This general method requires three functions: u(s,v), which is intrinsic to the substance, and s(x,y) and v(x,y), which are arbitrary. In effect, x and y are two functions of state, because any function of two functions of state is yet another function of state. One can define an arbitrary number of functions of state, but one might wish to focus on those having practical significance. Gibbs's method is perhaps too general. Most of his discussions about this general graphic method do not enter the modern practice of thermodynamics.

What do enter, however, are his specific examples. In addition to the volume-pressure diagram introduced for this purpose by Clapeyron (1834), Gibbs advised us to use the entropy-temperature diagram and the volume-entropy diagram. From the five functions of state, TvPus, we have a total of ten choices of pairs. Many of these pairs are in use today as axes of the diagrams.

Gibbs offered tips for the uses of the diagrams of various kinds. Pv diagram and Ts diagram display work done and heat received for cycles. The Carnot cycle is a rectangle on the Ts diagram. When gas, liquid and solid phases are in equilibrium, the state of the body corresponds to a point in a triangle in the vs diagram, but to a point in a line on the Pv or Ts diagram. “This,” Gibbs remarked, “must be regarded as a defect in these diagrams, as essentially different states are represented by the same point.”

Curiously, Gibbs did not mention the temperature-pressure diagram. What would he say about the pervasive use of the PT diagram today? On the PT diagrams, different states of three-phase mixture collapse to a single point, which we call triple point. Meanwhile his beloved volume-entropy diagram is unmentioned in nearly all modern textbooks. Will the volume-entropy diagram make a comeback?

The science is clear. We can draw diagrams of three types. Type A: both axes are intensive variables (PT). Type B: both axes are extensive variables (vs and many other choices). Type C: one axis is an extensive variable and the other axis is an intensive variable (Pv and many other choices). The psychological effects on people are not so clear. The defect to Gibbs might be beauty to others. The PT diagram collapses three-phase states into a single point, collapses two-phase states to curves, and represent single-phase states by regions. The diagram may be easier to look at than a vs diagram.

Why two independent variations, again? A system capable of two independent variations is amenable to graphical representation: a state of the system corresponds to a point in a plane. But the analytical method developed in this paper is suitable for any system of any number of independent variations.

Gibbs was timely. He did not discover energy and entropy. Nor did he discover the fundamental laws that govern them. He did, however, turn Clausius's thermodynamics into a procedure of everyday mathematics: functions, partial derivatives, and diagrams. He freed thermodynamics from its initial narrow concern over the heat and work of an engine, and made thermodynamics ready for prime time, for phases, for reactions, for mixtures, and for everything else under the sun and above. He moved forward with a massive number of applications during a period of commotion, after Clausius set up the basic laws, when many people were confused, Maxwell among them. He prepared himself for his Paper II and Paper III.

Gibbs is timeless. Thermodynamics after him has remained unchanged in its aim and method. Today we use thermodynamics in the way as he taught us. We are all Gibbsians.

A few years before Gibbs published his Paper I, Massieu (1869) had also discussed relations between functions of state, and showed that certain such relations are capable of generating all other thermodynamic relations. See Bordoni, The European Physical Journal H 38, 617 (2013). for the development of thermodynamics in the late nineteenth century.

Paper II. A METHOD OF GEOMETRICAL REPRESENTATION OF THE THERMODYNAMIC PROPERTIES OF SUBSTANCES BY MEANS OF SURFACES, 1873

Gibbs discovered a picture of extraordinary beauty and importance. He devoted Paper II to describing this picture in words, with few equations. The specific picture did not appear in the paper, did appear in a later textbook by Maxwell, and has been purged from nearly all modern textbooks. But Gibbs’s ideas have prospered. They constitute the thermodynamic theory of equilibrium, stability, metastability, phases, critical points, and exergy. He described all essentials in this remarkable paper of twenty-some pages.

Let us start with the specific picture. In Paper I, Gibbs showed that the thermodynamics of a pure substance is entirely specified by a relation between three variables: energy, volume, and entropy. He called the relation the fundamental thermodynamic equation of the substance. The equation is specific to each individual substance. Mathematically, an equation between three variables corresponds to a surface in a three-dimensional space, with the three variables as axes. Thus, the thermodynamics of a pure substance is fully specified by a surface in the three-dimensional space of energy, volume, and entropy. Gibbs called the surface the thermodynamic surface of the substance. Now we call the energy-volume-entropy space the Gibbs space, and the substance-specific surface the Gibbs surface. How does this surface look like?

Energy, volume and entropy are extensive variables. That is, each of them is proportional to the amount of the substance. Consequently, the shape of the surface is independent of the amount of the substance, and the size of the surface is linear in the amount of the substance. To be definite, let u, v and s be the energy, volume and entropy of a piece of the substance divided by the number of molecules in the piece. We use (u,v,s) as the three axes for the Gibbs space.

Gibbs knew the following empirical facts. A pure substance has three phases: solid, liquid, and gas. Prescribed with a fixed energy and a fixed volume, the substance can equilibrate in a homogenous state of one phase, or an inhomogeneous state of two phases, or an inhomogeneous state of three phases.

For the time being, let us represent each phase by its own fundamental thermodynamic equation. The three phases correspond to three surfaces in the Gibbs space. Gibbs called them the primitive surfaces. When the substance equilibrates in an inhomogeneous state, with several parts, each part is in a homogeneous state, corresponding to a point on one of the primitive surfaces.

Consider a piece of a pure substance equilibrated in an inhomogeneous state of two parts. The piece has a total of N molecules, of which N’ molecules are in one homogeneous state, and N’’ molecules are in another homogeneous state. The number of molecules in the piece is conserved, N = N’ + N’’. Denote the fractions by y’ = N’/N and y’’ = N’’/N. Thus, y’ + y’’ = 1, and y’ and y’’ are both non-negative.

Energy is an extensive variable, so that the energy of the piece of the substance is the sum of the energies of the two parts. The same is true for volume and for entropy. Denote the energies, volumes and entropies of the two homogeneous states by (u’,v’,s’) and (u’’,v’’,s’’). Denote the energy, volume and energy of the substance in the inhomogeneous state by (u,v,s). Write

u = y’u’ + y’’u’’
v = y’v’ + y’’v’’
s = y’s’ + y’’s’’

These equations are known as the rules of mixture, or the lever rules. They have a simple geometrical interpretation. The two homogeneous states, (u’,v’,s’) and (u’’,v’’,s’’), correspond to two points on the primitive surfaces. The inhomogeneous state (u,v,s) corresponds to a point on the straight-line segment joining the two points (u’,v’,s’) and (u’’,v’’,s’’), located at the center of gravity on the segment, depending on the fraction of molecules y’ and y’’ allocated to the two homogeneous states at the two ends of the segment.

In general, the point (u,v,s) is not on any of the primitive surfaces. Given the primitive surfaces of individual phases, the rules of mixture create a set of points, which constitute a solid figure in the Gibbs space. In general, each point in the solid figure represents an inhomogeneous state of the substance. In the modern mathematics of convex analysis, the solid figure is called the convex hull, which is a convex set generated from all the points on the primitive surfaces using the rules of mixture.

The solid figure (i.e., the convex set) is unbounded in some directions, but bounded in others by a surface, which Gibbs called the derived surface. The derived surface is generated from the primitive surfaces as follows.

If a plane tangent to one point on a primary surface does not cut any primary surfaces, this point of the primary surface belongs to the derived surface. Gibbs called the set of all such points the surface of absolute stability. The tangent plane can roll on the primary surface to change the two slopes of the tangent plane independently. Thus, the surface of absolute stability has two independent variations.

If a plane tangent to two points on the primary surfaces does not cut any primary surfaces, the straight-line segment connecting the two points belongs to the derived surface. The straight-line segment is now known as the tie line. The common tangent plane can roll on the two primary surfaces to change its slope by a single degree of freedom. As the common tangent plane rolls, the tie lines form a developable surface, and the two tangent points trace out two curves on the primary surfaces. Gibbs called the two curves the limits of absolute stability.

If a plane tangent to three points on the primary surfaces and does not cut any primary surfaces, the triangle connecting these three points belongs to the derived surface. The tangent plane has no degree of freedom to roll, and the triangle is fixed in the Gibbs space. Say the piece of the pure substance has a total of N molecules, of which, N’ molecules are in one state, N’’ molecules are in another state, and N’’’ molecules are in yet another state. Denote number fractions by y’ = N’/N, y’’ = N’’/N, and y’’’ = N’’’/N. Denote the energies, volumes and entropies of the three states by (u’,v’,s’), (u’’,v’’,s’’) and (u’’’,v’’’,s’’’). Denote the energy, volume and energy of the substance in the inhomogeneous state by (u,v,s). Write

u = y’u’ + y’’u’’ + y’’’u’’’
v = y’v’ + y’’v’’ + y’’’v’’’
s = y’s’ + y’’s’’ + y’’’s’’’

The inhomogeneous state (u,v,s) corresponds to a point, located at the center of gravity in the triangle, depending on the fraction of molecules y’, y’’ and y’’’ allocated to the three homogeneous states at the vertices of the triangle.

How does the derived surface look like? The derived surface contains a flat triangle tangent to the primitive surfaces at three points. From each edge of the triangle we roll out a developable surface, consisting of ties lines, each contacting the primitive surfaces at two points. From each vertex of the triangle we retain a convex part of a primitive surface. The derived surface has a single sheet, and is a convex surface.

So far the three variables (energy, volume and entropy) play symmetric roles. All Gibbs invoked was that energy, volume and entropy are extensive variables. What breaks the symmetry is Clausius’s statement of thermodynamics: An isolated system conserves energy (and volume), but maximizes entropy. This statement singles out entropy to play a special role, but leaves energy and volume to play symmetric roles. If we isolate a quantity of a pure substance, its energy and volume will be fixed, but its entropy will increase in time, and the substance attains a state of equilibrium when its entropy maximizes.

To maximize the entropy we need variables. We can divide the given quantity of substance into many parts, each part being in a homogeneous state of thermodynamic equilibrium, corresponding to a point on one of the primitive surfaces. We now have a large number of variables: the number of such homogeneous states, the location of each homogeneous state on a primitive surface, and the proportion of the substance allocated to each homogeneous state. Because the energy, volume and entropy are each an extensive variable, their values of the quantity of the substance, (u,v,s), correspond to a point, located at the center of gravity of all the substance allocated to all the points. In the language of convex analysis, the point (u,v,s) is a convex combination of all the points on primitive surfaces.

We choose the entropy as the vertical axis of the Gibbs space, and the energy and volume as the two horizontal axes. (Gibbs chose energy as the vertical axis, which complicated his presentation.) The derived surface is a convex surface bounding the solid figure (the convex set) from above. When a substance is isolated with a fixed energy and a fixed volume, the substance in general is in an inhomogeneous state, corresponding to a point on a vertical line in the solid figure, below the derived surface.

Such an inhomogeneous state in general is not in a state of thermodynamic equilibrium. The isolated system reaches a state of thermodynamic equilibrium at the point where the vertical straight line intersects the derived surface. The derived surface represents all stable states of equilibrium of the substance. A point on a primary surface represents the substance in a homogeneous state of a single phase. A point on a tie line represents the substance in an inhomogeneous state of two phases. A point in the triangle represents the substance in an inhomogeneous state of three phases. Thus, the Gibbs surface accounts for the empirical facts of phases.

The Gibbs surface also suggests a theory of metastability. A primitive surface may contain a convex part and a non-convex part. Gibbs called the curve separating the two parts the limit of essential instability. If a convex part of the primitive surface lies below a tangent plane of the derived surface, the part of the primitive surface is beyond the limit of absolute stability. Each point of this part of the primitive surface is now known as a metastable state. Gibbs noted that such a state is stable in regard to continuous changes of state, but is unstable in regard to unstable changes of state.

Gibbs introduced the theory of critical point. He cited a paper by Andrews (1869), which reported the experimental observation of a substance can change continuously from liquid states to gaseous state. Gibbs then wrote, “...the derived surface which represents a compound of liquid and vapor is terminated as follows: as the tangent plane rolls upon the primitive surface, the two points of contact approach one another and finally fall together. The rolling of the double tangent plane necessarily come to an end. the point where the two points of contact fall together is the critical point.”

Thus, we may model a pure substance with two primitive surfaces: a convex surface for the solid phase, and a non-convex surface for the liquid and gaseous phases. Maxwell constructed the Gibbs surface with great care, and sent Gibbs a cast. You can find photos of Maxwell’s cast online.

Gibbs projected the derived surface onto the volume-entropy plane (Figure 2). He drew the triangle for the states of coexistence three phases, limits of absolute stability, limits of essential instability, and critical point. He did not, however, draw the primitive surfaces and the derived surface in the three-dimensional energy-volume-entropy space. But Maxwell drew the surface in three dimensions in a later edition of his textbook, Theory of Heat. Planck projected the derived surface on the energy-volume plane (Figure 4) in his textbook, Treatise on Thermodynamics. Planck made a mistake of adding a critical point for the solid-liquid transition.

In the above, we have developed the entire theory using only three functions of state: energy, volume and entropy. We next discuss the roles of temperature and pressure.

In Paper I Gibbs showed that the slopes of the tangent plane define the temperature and pressure. Thus, rolling the tangent plane represents changing temperature and pressure. For a substance equilibrating in states of one, two and three phases, the temperature and pressure are capable of two, one and zero degrees of freedom. In Paper III, Gibbs would generalize this result to the Gibbs phase rule.

We can arbitrarily set the reference value for energy to be zero. Volume is positive, but can be made very small under high pressure. Entropy is zero at absolute zero temperature. Energy, volume and entropy have no upper bound. Because temperature is positive, entropy is a monotonically increasing function of energy. Assuming a positive vapor pressure, entropy is also a monotonically increasing function of volume. We can write the derived surface as a function s(u,v), and can also invert the function to write two other functions u(s,v) and v(s,u).

If we adopt function s(u,v), the Gibbs equation in Paper I takes the form

ds = (1/T)du + (P/T)dv

The slopes of the function s(u,v) are

1/T = ds(u,v)/du
P/T = ds(u,v)/dv

When the substance equilibrates in an inhomogeneous state of two phases, a tangent plane contacts the primary surfaces at two points, (u',v',s') and (u'',v'',s''). The common tangent plane has the same slopes at the two points, so that the two coexistent states have the same temperature and pressure:

T' = T''
P' = P''

The common tangent plane cuts the vertical axis s at some point. The intercept can be calculated using the quantities at either state (u',v',s') or (u'',v'',s''), so that

s' - (1/T')u' - (P'/T')v' = s'' - (1/T'')u'' - (P''/T'')v''

The above three equations transcribe the geometrical expressions of the condition of equilibrium into analytical expressions. One can similarly write the condition of equilibrium of three phases.

Gibbs also introduced what is known today as the Gibbs function, u - Ts + Pv. He elaborated the idea in terms of the available energy (now known as exergy). This needless complication muddled his presentation of the essentials of this paper, and has left a permanent scar in thermodynamics. Gibbs seemed to prefer energy to entropy. Instead of maximizing Clausius’s entropy, Gibbs asked us to minimize this different function.

Planck, in his Treatise on Thermodynamics, used the function s - (u + Pv)/T, which was introduced by Massieu (1869), prior to Gibbs's paper. This function serves the identical purpose as the Gibbs function, but makes it clear that, in dealing with a system subject to constant temperature and constant pressure, we should follow the same principle given by Clausius: an isolated system conserves energy and maximizes entropy. In this case, the isolated system consists of three subsystems: a system of interest, a thermal reservoir of constant temperature T, and a weight that applies a constant pressure P. The function s - (u + Pv)/T, up to an additive constant, is the entropy of the isolated system.

To see this, let a quantity of heat q goes from the reservoir to the system of interest. The reservoir changes its energy by - q, and changes its entropy by - q/T. The system of interest changes its entropy from s0 to s, changes its energy from u0 to u, and changes its volume from v0 to v. The weight changes its potential energy from Pv0 to Pv, but does not change its entropy. The isolated system conserves energy, so that q = (u - u0) + P(v-v0). Consequently, the entropy of the isolated system is s - (u + Pv)/T + constant. This function should be maximized for the isolated system to equilibrate.

It might be too late for future textbooks to switch the Gibbs function back to the Massieu function, but let us hope that they will bring back the Gibbs space, the Gibbs surface, and Maxwell’s cast.

Xanzay
This is a reprint of his original papers which cement the mathematical foundations of thermodynamics. Gibbs's work is a work of genius, but this book is an extremely challenging read. Writing in viscous 19th century prose, Gibbs is never one to use a sentence where a paragraph will do. Very few non-native English speakers who are experts in thermodynamics have the ability in English to read this from cover-to-cover. The questions one is left asking are 'Has the difficulty of this text slowed the further development of thermodynamics? Would any errors in Gibbs's work be spotted swiftly?' My answers to these questions are 'Yes,' and 'No,' respectively. Anyone who hopes to make advances in the fundamental theory or interpretation of thermodynamics (assuming, contrary to current dogma, that such advances can be made) needs to read the majority of this book.
Some of my views on thermodynamics are given in: D. J. Bottomley, Jpn. J. Appl. Phys. Part 2, vol. 36, L1464 (1997).

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