I will be writing about the work of J. Willard Gibbs (1839-1903) in the next several posts and wanted to provide the following context before doing so.

Mirco-to-macro and the 1st Law of Thermodynamics

In the world of classical thermodynamics, we are concerned with the macroscopic properties of matter and how they change in various processes.  We know that whatever atomic interactions happen in the microscopic world of the system of interest, they obey the fundamental conservation laws, especially the one in which we’re most interested right now, the conservation of energy.  If a certain amount of energy disappears here, it must re-appear somewhere else in the exact same amount.  Not the same approximate amount.  The same exact amount.  This law is applicable to individual atoms and thus to systems comprised of billions of these atoms and all of their collisions, interactions and reactions.  The system follows this law because each and every one of the billions of atoms follows this law.  Nothing is lost in scale-up.  This discovery became embedded inside the 1^st Law of Thermodynamics.  Internal energy is conserved and constant in an isolated system, only changing in response to external influences such as heat and work.

Micro-to-macro and the 2nd Law of Thermodynamics

We also know that at the core of this macroscopic world exists a fundamental law: nature resides in its most probable state.  There is no driving force involved here.  It is purely probabilistic.  Not the probability involved with Heisenberg Uncertainty but the probability of large numbers.  A system of atoms and molecules consistently spreads itself over space and energy in a very repeatable way, the same way every time.  This tendency of nature to follow probabilistic laws is neatly summarized in the concept of entropy.  If you leave a system alone, it will move towards its most probable state and reside there forever.  This is the law of large numbers in action.  This discovery became the retroactive core basis of the 2^nd Law of Thermodynamics.

Connecting the fundamental properties

That the two laws of thermodynamics could be tied together in a single equation—dU = TdS – PdV—is simply amazing.  Clausius created the 1^st Law of Thermodynamics for a system:  dU = δQ – δW.  The conversion of δW to PdV was not a huge step, for it had been discovered well prior.  It works for fluids (pressure is equal throughout the system), and, since much of chemistry deals with liquids and gases, it was an acceptable substitution to make.  The conversion of δQ, on the other hand, to TdS was a huge step and still boggles the mind to this day.  That such a property as entropy exists is fascinating in and of itself.  That such a property changes exactly as the ratio of the heat absorbed divided by absolute temperature (δQ/T) is beyond fascinating, not only from a fundamental physics point of view—why exactly does entropy change in this way? —but also from the viewpoint of enabling Clausius to create an equation based solely on the properties of nature:  dU = TdS – PdV.  The absolute icing on the cake, as we’ll soon see, was that the structure of the equation differentiates the extensive but not the intensive properties, and that the non-differentiated intensive properties T and P also serve as the criteria for thermal and mechanical equilibrium.

The starting point for classical thermodynamics: dU = TdS – PdV

The equation, dU = TdS – PdV, which arguably became the starting point for classical thermodynamics, and many others that were derived from it all demonstrate that nature is not random.  At its core, the physical world is comprised of atoms that move and behave in ways that we can codify as law.  These movements and behaviors result in macroscopic properties that we can directly measure (T, P, V, N, m_i, x_i) and those we can’t, such as energy and entropy.  While each property quantifies something different than the others, they are not totally independent.  If you tell me the temperature, pressure, and number of moles of an ideal gas, I’ll tell you the volume.  The properties are interconnected because they are measuring the same system of moving atoms, just from different angles.  It’s as if each property were a lever on a large mechanical device, with each lever connected to all the other levers inside the device.  If you move one lever, another lever moves in response.  In nature, if you move one property, another property moves in response.  You cannot simply change the temperature of an ideal gas without changing some other property.  The ideal gas equation spells this out.  This equation and all the many others tell you how the levers are connected inside the machine called nature.

The fact that the properties of matter are connected is a prelude to our next section on J. Willard Gibbs.  It was Gibbs who not only told us this but who also showed us these exact connections.  In the true spirit of the scientific method, Gibbs deduced the consequences of Clausius’ induced hypothesis, dU = TdS – PdV, by bringing an advanced level of calculus together with a relentlessly deductive mind to bear on the subject. In one fell swoop, he put the capstone on the development of classical thermodynamics, creating the field of physical chemistry in so doing.

Get to know the work of J. Willard Gibbs!

I spent 5 of 43 chapters in my book, Block by Block – The Historical and Theoretical Foundations of Thermodynamics, on J. Willard Gibbs. Find out why by reading the book : )

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