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20  Ambiguous Terminology

20.1  Background

As always, ideas are primary and fundamental. Terminology is important only insofar as it helps us formulate and communicate the ideas.

By way of analogy, consider the relationship between organic vegetables and organic chemistry. There is nothing wrong with either of those two ideas. Neither one – by itself – is a misconception. However, we have a problem with the terminology. The word “organic” is being used with two different definitions. You can create a misconception by using one definition in a situation where the other is appropriate, but that is a secondary, artificial, and needless problem. The primary problem is the terminology.

Sometimes a word has two definitions that are so different that no confusion arises, for example “dove” (the past-tense verb) and “dove” (the bird). In contrast, you can easily get into trouble if a word has two meanings are similar enough to be deceptive, yet not so similar that the difference can be ignored.

Many of the most-important terms in thermodynamic can be highly deceptive if you’re not careful.

In such a situation, good learning and good critical thinking demand that you learn each concept in its proper context, and then learn to reconcile them all. That requires learning how to distinguish one context from the other, so that each concept can be used appropriately. The goal should be to understand the whole situation. To say the same thing the other way: You’ll never really understand the subject if you learn one concept and ignore the other. Studying one part of the elephant in great detail will not make the rest of the elephant go away.

I don’t mind struggling with something if it is intrinsically hard and complicated. In contrast, it’s painful to see people struggling with things that are complicated for no good reason, for instance because the terminology is messed up. That’s a wanton waste of resources. We should be able to fix the terminology, so that nobody has to struggle with it!

20.2  Overview

In physics, there is only meaning of “energy”, but the physics meaning conflicts with the plebeian meaning, as discussed in section 1.8.1 and section 20.3.

In physics, there is almost only one meaning of “conservation”, but the physics meaning conflicts with the plebeian meaning, as discussed in section 1.8.2 and section 20.4.

There are multiple inconsistent technical meanings for “heat”, not to mention innumerable nontechnical meanings, as discussed in chapter 17.

There are multiple inconsistent technical meanings for “work” as discussed in chapter 18.

There are multiple inconsistent technical meanings for “adiabatic” as discussed in chapter 16.

In the literature, the term “state” is used inconsistently. It can either mean microstate or macrostate, as discussed in section 2.7 and section 12.1.

Similarly, “phase space” is ambiguous:

Phase-space means one thing in classical canonical mechanics; it corresponds to what we have been calling state-space, as discussed in section 12.3.   Phase space means something else in classical thermodynamics; it has to do with macroscopic phases such as the liquid phase and the solid phase.

(Ironically, Gibbs has his name associated with both of these notions.)

I’m not even talking about quantum mechanical phase φ, as in exp(i φ); that’s a third notion, which is not terribly troublesome because you can usually figure out the meaning based on context.

Given how messed-up our language is, it’s a miracle anybody ever communicates anything.

20.3  Energy

As mentioned in section 1.8.1, the plebeian notion of energy corresponds roughly to “available” energy or “useful” energy. This is important, but very hard to quantify.

The “available energy” is not equal to the physics energy E, and also not equal to the Helmholtz free energy F or the Gibbs free enthalpy G (as defined in chapter 15). The simple way to understand this is to realize that E, F, and G are functions of state, whereas the plebeian notion of “useful energy” is not. The physics energy of a particular parcel depends only on the properties of the parcel itself, whereas the usefulness of that energy depends on properties of the parcel and properties of the surrounding world.

By way of analogy: A grocery store in Iowa sells a lot more bags of ice in mid-summer than it does in mid-winter. The thermodynamic state of the ice is the same in either case, but its usefulness is wildly different.

In relative terms, F and G are “closer” to capturing the idea of “available” energy, but in absolute terms they are not close enough. They are not viable contenders for quantifying the “useful" or “available" energy.

Any proper theory of “useful energy” would involve a great deal of microeconomics, not just physics. There is an elaborate theory of microeconomic utility.

20.4  Conservation

  1. In physics, the main meaning of conservation refers to continuity of flow, as expressed in equation 1.1.
  2. Unfortunately, even within physics the word “conservative” has been given a second meaning, as we now discuss. Sometimes a vector field is the gradient of some scalar potential, in which case we say the vector field is grady. Mathematicians would call it an exact differential, or an exact one-form. This math terminology is not recommended, because it conflicts too strongly with the common-sense concept of “exact” as in strictly true, not an approximation. Also, to my way of thinking, there is no such thing as an inexact differential; if it’s not exact, it’s not a differential at all. You could call it an inexact non-differential, or an inexact one-form, or (preferably) a non-grady one-form.

    Sometimes in physics, a grady force-field is called a “conservative” force, and by the same token a non-grady force-field is called a “non-conservative” force. This terminology is emphatically not recommended, because it conflicts with the definition of conservative flow as expressed in equation 1.1.

    Whenever you want to describe a force field that is not the gradient of any potential, I strongly recommend calling it a non-grady force field. Similarly, if you ever see the term “non-conservative force”, cross it out and substitute “non-grady force”. A non-grady force, such as you find in a transformer or in a betatron, does not violate any conservation laws.

  3. We now consider a third definition of “conservation”, namely the plebeian definition, i.e. the non-physics definition. The key idea here has to do with saving, preserving, not wasting, not dissipating. For example, we speak of conservation of endangered wildlife.

    This is an important concept, but very difficult to quantify.

    Wasting something, almost by definition, is irreversible, which suggests that the plebeian notion of conservation is loosely related to the idea of entropy – but only loosely.

20.5  Other Ambiguities

Numerous other conflicts are discussed in reference 45. This includes a great many basic terms used in math, physics, and thermodynamics ... including force, acceleration, gravity, closed system, et cetera.


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