Second Law and Missing the Obvious

Sometimes the most obvious things elude us humans. Generally, when the obvious, yet unexpected happens, and not much damage is done, we laugh. Often we mumble to ourselves when no one is watching things like; I can be such an idiot or if your friends are watching, you may okay guys I just had a brain fart, then move on, trusting that we have learned something, and we all are no worse for wear.

Now if I was to ask you:

1) Does our atmosphere have mass?

2) Does an expanding system generally have to displace this mass?

If you answer yes to the above two questions. Then we must ask; what direction is this displacement? Certainly, it can be downward into the solid Earth. Equally it cannot be sideways unless of course it results in pressure increase, which then this can only result in an isobaric volume increase. Accordingly, we are left with one answer. Expanding systems tend to lift up our atmosphere. And like lifting any mass, this must require work. There is no revelation here. It certainly becomes obvious once stated.

Now consider a useful system that being a system that can move man and/or machine.

Certainly the vast majority of such systems involve the displacement of our atmosphere,. Just consider your standard combustion engine. Certainly one or more steps in its cycle involves the displacement of our atmosphere.

Consider that idealized Carnot engine/cycle. Such heat engines all had a step that includes expansion, hence the displacement of our atmosphere. Certainly such an upwardly displacement of a mass requires work! At one atmosphere pressure, the work (W) required to displace our atmosphere by a volume, dV, turns out to be: W=PdV. It does not take a genius to do the calculation as is shown in book.

So what else can we say about this work? If our atmosphere is being displaced upwardly, then any upwardly displaced gas molecules must experience an increase in potential energy. This is no different than lifting any other mass with one exception: Unlike a solid object, we cannot harness this potential energy increase. Think about it. I can tie a rope to a rock, elevate the rock and then upon letting the rock fall, harness its potential energy gain. Now try doing that to uncontained gas molecules.

Ultimately in general a potential energy of a gas in our atmosphere cannot be harnessed.

According the work that increases the atmosphere’s potential energy must become lost. That being: “lost work”.

Now realize that in the 19th century greats, such as Clausius, Maxwell, Boltzmann, and Lord Kelvin formulated entropy, and its accomplice, the second law, in order to explain why work that was lost by cyclic heat engines, i.e. the Carnot engine. Moreover they measured this lost work and accurately determined that: W=PdV.

So rather than seeing the obvious, they did as humans too often do; they looked for the complicated. Specifically, they formulated some beautiful eloquent mathematical solutions involving entropy and equated it: PdV. And from this the Second law, and the entropy based modern (now traditional) thermodynamics was born.

It is amazing how many of us (me included) adhered to the very conscripts of what has become modern thermodynamics. I never questioned the sanity of shuffling all those partial differentials around until I had something that equated to the empirical data before me. I never even considered that the act of equating relations to: PdV and then exclaiming that since these very equations equate (or approximately so) then the theory based upon these very equations must be based upon circular logic.

It was so simple. It had been staring me in the face the whole time, yet I remained oblivious to it. I think of the decades I spent pondering what is wrong with thermodynamics and all the various complex rationals I tried to ensvision, and then write down. So although it took me decades to realize, and years to accept, I still could not laugh. I just couldn’t get Eddington’s words out of my head: The law that entropy always increases holds, I think, the supreme position among the laws of Nature. 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 sometimes. 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. (Taken from: http://physics.stackexchange.com/questions/91017/why-are-the-laws-of-thermodynamics-supreme-among-the-laws-of-nature)

One of my favorite quotes: I know that most men — not only those considered clever, but even those who are very clever and capable of understanding most difficult scientific, mathematical, or philosophic, problems — can seldom discern even the simplest and most obvious truth if it be such as obliges them to admit the falsity of conclusions they have formed, perhaps with much difficulty — conclusions of which they are proud, which they have taught to others, and on which they have built their lives.

(Taken from: http://en.wikiquote.org/wiki/Leo_Tolstoy)