The Concept of Lost Work
Sometimes the most obvious things elude us humans. Generally, when the obvious, yet unexpected happens, and not much damage is done, and we all 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.
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 cannot be downward into the solid Earth. Equally it cannot be sideways unless of course it results in pressure increase, which then can only result in an isobaric volume increase. Accordingly, we are left with one answer. Expanding systems tend to lift up our atmosphere upwards. And like lifting any mass, this requires work. There is no revelation here. Moreover, 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 expansion hence the upward displacement of our atmosphere.
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 upwardly displacement of our atmosphere's mass requires work!
At one atmosphere pressure (Patm), the work (Wlost) required to displace our atmosphere by a volume, dV, turns out to be:
It does not take a genius to show the validity of eqn (1) as is shown in my book.
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. Furthermore, our atmosphere is not homogeneous
in terms of either pressure, or molecular volume, therefore
Interestingly, an expanding system may result in a sudden localized pressure increase of the surrounding atmosphere. However, since the atmosphere is an open system, instantaneous localized pressure increases will generally revert into a volume increase due to mechanical equilibrium between molecules, in which case an isometric volume increases quickly transforms to an isobaric volume increase.
Moreover, the above said 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. In which case one e.g. man on the moon, would not be able to witness an atmosphere volume increase but should witness an atmosphereic temperature increase (assumming that his thermometer is accurate enough. In order for no volume increase to be witnessed then the increase in heat would need to be equilvalent to the potential energy gain that the atmosphere would recieve if it had experienced the isobaric volume increase defined by eqn 1.
Obviously no matter what the real outcome is, the equation of choice remains eqn 1 namely because it quantifies the work done onto the surrounding atmosphere! Moreover, it clearly explains where thsi lost work goes, it goes into the surrounding atmosphere!
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.
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, they formulated a series of beautiful eloquent mathematical solutions involving entropy and equated it to: 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.
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 became a complete complication of what should have been a simple science.
Rather than explaining lost work in terms energy given into the surrounding atmosphere, 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.
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
Copyright Kent W. Mayhew