The Concept of Lost Work and Entropy’s demise
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 is not downward into the solid Earth. Equally it cannot be sideways unless of course it simply results in a regional pressure increase. Okay we will discuss this shortly.
Seemingly we are left with one answer. Expanding systems tend to lift our atmosphere upwards. And like lifting any mass, this requires work. There is no revelation as it seemingly 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 expansion hence involve the upward displacement of our atmosphere. At one atmosphere pressure (Patm), the work (Wlost) required to displace our atmosphere by a volume, dV, turns out to be:
Okay dV is the volume increase of the expanding system, which to someone (i.e. man on the moon) observing our Earth, appears as a volume increase to the atmosphere. For discussion of expanding piston-cylinder click here. You can cosnider that the expanding system is actually a system within a system that being the Earth's atmosphere.
What else can we say about the above lost work? If our atmosphere is being displaced upwardly, then any upwardly displaced gas molecules must experience an increase in potential energy. Furthermore, our atmosphere is not homogeneous in terms of either pressure, or molecular volume, therefore it must be the atmosphere’s pressure at the location/elevation that the system’s expansion occurs, and that is in general 1 atm for those of us standing upon Earth’s surface.
It does not take a genius to understand the validity of eqn (1) which can be simply derived from first principles concerning work, force, mass, pressure etc., as is done in my book. We can elaborate upon eqn 1) and say that this is the work done by an expanding system onto the surrounding atmosphere but it does not necessarily mean that the atmosphere’s volume increases.
Interestingly, an expanding system may also result in a sudden localized pressure increase of the surrounding atmosphere. However, since the atmosphere is an open system confined only by gravity, instantaneous localized pressure increases often revert into a volume increase due to mechanical equilibrium between molecules. In which case a isometric pressure increases often quickly transforms to an isobaric volume increase.
Even so our reality maybe a tad more complex than we just made it seem because the above assertions assume that the intermolecular collisions are elastic. In my Apr 2018 paper (and its sister paper July 2017) in the Journal Progress in Physics, I clearly showed that what is witnessed in the laboratories concerning kinetic theory is better explained in terms ofinelastic collisions. Accordingly, collisions between atmosphereic gases are inelastic!
Furthermore, the previously stated localized pressure increase may also result in an increase to intermolecular friction, which in turn results in an increase in heat i.e. thermal energy, or if you prefer molecular dissipation. In which case the atmosphere experiences a infinitesimal temperature increase. In order for no volume increase to actually be witnessed then the increase in heat would need to be equivalent to the potential energy gain that the atmosphere would receive if it had experienced the isobaric volume increase defined by eqn (1) i.e. W=PdV.
Obviously no matter what the real outcome is, eqn (1) quantifies the work done onto the surrounding atmosphere! Moreover, it clearly explains where this work goes, it goes into the surrounding atmosphere! And this is work does not increase the atmosphere's pressure by an real measureable value. And since the atmosphere would need to be at a higher pressure than the system it surrounds in order for the atmosphere to actually do any work onto that system. Hence the work is lost work i.e. irreversible work.
This all fits with this author’s assertion that inelastic collisions also means that thermodynamics must also consider a system’s thermal radiation as part of that system’s thermal equilibrium i.e. a new understanding of both thermal equilibrium and what temperatures measures.
Of interest is traditional thermodynmics illusionary reversible work, which is wrongly defined in terms of the expanding system's parameters. It is also of interest that many discuss W=PdV is work done onto the surroundings but all fail to realize that this exact differential is lost work.
Let us concern ourselves with lost work in this blog. Lost work goes by many names such as lost heat, lost energy, dissipated energy and non-sensible energy. In its broadest context, it is energy that is lost by a system/machine thus preventing 100% efficiency in machines and reversibility in processes. Lost work by expanding systems is pertinent too most engines and other useful processes, because at some point in their cycle, there is system expansion that upwardly displaces the Earth’s atmosphere’s mass against gravity, thus adding to our atmosphere’s energy.
Lost work is different than the reversible work of lifting a rock up into the air wherein energy is transformed into the rock’s potential energy increase. Importantly, a rope can be tied to that rock, enabling us to harness its increased potential energy when the rock falls back to the ground. Unlike the reversible work of the rock, an increase to Earth’s atmosphere’s potential energy is not so readily harnessed. Specifically, if the expanded system collapses back to its original state, then the gained potential energy is transformed into atmospheric molecular kinetic energy, which eventually generally results in an atmospheric temperature increase, which may or may not radiate away. Or perhaps the expanding volume results in a localized pressure increase which results in heat due to increased molecular friction.
Furthermore, the thermal energy (heat, potential, kinetic etc) will be small compared to the total energy contained within the atmosphere. So like any heat bath/sink the atmospheres temperature increase will be infinitesimally small i.e. too small to measure, hence the atmosphere will be considered isothermal. And without a temperature difference or pressure difference between the atmosphere and the system that it surrounds, then no work can be extracted from the atmosphere.
Moreover, because the atmosphere is such a massive heat bath/sink, then the energy added into the atmosphere (lost work) by the expanding system does not measurably change our atmosphere. Hence the atmosphere remains both isobaric and isothermal hence it cannot do work onto other 1 atmosphere pressure systems nor can it provide energy to other isothermal systems that it surrounds.
Remember for System 1 to do work onto System 2 then System 1’s mechanical parameter pressure must be greater than System 2’s. And for System 1 to give thermal energy into System 2 then System 1’s temperature (thermal parameter) must be greater than System 2’s.
Just consider your standard combustion engine. Certainly one or more steps in its cycle involve the displacement of our atmosphere. Ditto for the steam engine, where expanding steam continuously powers locomotives all by switching of valves. Consider the idealized Carnot engine/cycle. Such heat engines all had a step that includes expansion, hence the displacement of our atmosphere. Certainly such an upward displacement of our atmosphere's mass requires work!
According based upon our new understanding of lost work, we can now understand why useful processes are generally not reversible. And we no longer require the second law in any of its forms to explain why?
Consider Lord Kelvin’s (Thomson) statement “It is impossible to transform an amount of heat completely into work in a cyclic process in the absence of other effects” (reference: “Entropy, Reversibility, Irreversibility And Thermodynamic Cycles” by D.Sands and J. Dunning-Davis)
Obviously expanding systems are systems that most often do work. Or if you prefer mechanical work is generally done by allowing the expansion of higher pressure systems. And from a mechanical perspective such systems can be deemed useful systems. Since such systems must lose work onto the atmosphere we now begin to understand Lord Kelvin’s statement. But there is more to this see second law.
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 it is: W=PatmdV
So rather than observing the obvious, they did as humans too often do; they searched for the complicated. Specifically, beautiful eloquent mathematical solutions were formulated based upon probabilities and statistical math which involved entropy and was equated it to: PdV. And from this the Second law in the form of isothermal entropy never decreases, 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.
The story goes further as you will find out in my other blogs/discussions. It carries on into the 20th century with our wrongful acceptance of Boltzmann’s conceptualization of randomness, and from there entropy, the second law, internal energy all becoming parts in the complication of what should have been a simple science.
Rather than explaining irreversibility in terms lost work, the traditional interpretation is that the expanding system experienced an increase in randomness. An association with randomness and entropy ensues with the lost work being wrongly explained in terms of isothermal entropy change. One well versed in traditional thermodynamics may also realize that this lends itself to the dreadfully misunderstood misapplied erroneous second law.
Does the above mean thatstatistical thermodynamics is absolutely useless? No it still has its place although our understanding of statistical sciences will require a rethink. However, it does now mean that statistical thermodynamics is no longer the only way of fully understanding irreversibility.
Wow: It is amazing how when we make a simple gross oversight early in the game, then how everything that follows can become a disaster. So now what, 150 yrs of indoctrination may be next to impossible to overcome.
See Law of work vs Thermal Energy in order
to help understand why lost work onto the atmosphere is not reversible
See Law of work vs Thermal Energy in order to help understand why lost work onto the atmosphere is not reversible
Sorry but we are all only human
Sorry but we are all only human
Sometimes the most obvious things elude us humans. Generally when the obvious, yet unexpected happens, and not much damage is done, and we all have a good laugh. Often we mumble to ourselves when no one is watching things like; I can be such an ID-10-T or if your friends are watching, you may say: “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. Accordingly to error is simply to be human. Too often we men/women of science forget the fragility of our humanity.
If you have taken whatever is said here personally; please don't. Just lighten up and hold your chin high. Life is to short to behave otherwise. Too many have already foolishly commited suicide over the subject of thermodynamics. The simpler you make life, the more enjoyable it becomes.
Copyright Kent W. Mayhew