In my previous blogs I have discussed that lost work (Wlost) involved the displacement of Earth’s atmosphere against gravity. And that it is equal to:
Where Patm is the atmosphere’s pressure and dV is the atmosphere’s displacement volume or if you prefer the volume increase of the expanding system. See blog on "Lost Work"
The above helps to explain why useful processes are not reversible. It also implies that the second law should not be applied the way it is traditionally applied to useful processes. In other words both entropy and the second law need reconsideration and thermodynamics as a science is in dire need of an overhaul.
“Negative work” conceptually feels counterintuitive! It is mathematically expressed by simply placing a negative sign in front of the work term. Negative work can be visualized by taking a syringe, placing the plunger all the way to the bottom, as is illustrated in the top of Fig. 1.7.9. Now hermetically seal the syringe’s opening with your finger and finally apply a volume expanding force (pull the syringe’s plunger outwards). We are now performing negative work onto the volume of space that is being created inside of the syringe!
If the initial volume (Vi) of the gas within the expanding volume was zero, then our expansion of the hermetically sealed syringe to some final volume (Vf) means that our final pressure (Pf) is that of a vacuum (zero pressure). Therefore, ignoring any blackbody radiation within the syringe, then our final energy state within that created volume is zero. Accordingly, the work done onto the volume within the syringe (Wvol) in creating the vacuum is:
Wvol = -Patm(Vf-Vi) = -PatmVf = -Watm (2)
Where Patm is the atmosphere’s pressure, Watm is the work done onto the atmosphere (exact differential)
Now ask, has the energy of the atmosphere changed? Since the atmosphere’s upward displacement was due to the introduction of a volume of nothingness (VON) , then the total energy of the atmosphere really has not changed. Of course this ignores any increase in the blackbody radiation within. see Equilibrium
Important: Negative work tends to create unstable volumes. In the case of the expanded syringe, once the plunger is released, the plunger will go crashing down into the syringe, thus removing the recently created volume. One could rightfully argue that since the pressure inside of the syringe was less then atmospheric, then the atmosphere’s pressure drove the plunger into the syringe, and this would be the mechanical answer. However, from an energy perspective, we could say that that the plunger went crashing down into the syringe because the interior of the syringe signified negative work, when compared to its surroundings! Hence was an inherently unstable volume. Ultimately, when a volume of nothingness (VON) displaces a mass in a gravitational field, then this is negative work onto the volume, which was previously occupied by that mass. Note: In this case its the mass of the displaced atmospheric gas molecules.
Again how one considers the work maybe a matter of perspective. From a thermodynamics perspective, the expansion of the syringe does not mean much. We could take the syringe full of nothing, bring it into outer space, then release the plunger and nothing will happen. However, claiming that nothing happens is from the perspective of inside the syringe. The reality is that a volume of something quickly replaces the VON, as we bring the syringe out into outer space i.e. Earth’s atmosphere’s surroundings. Okay are now verging upon metaphysics.
Consider what man on the moon sees. Although it was not noticed on Earth, the man on the moon clearly saw the Earth’s atmosphere’s volume increase, as the syringe was expanded. He then looks at his extraordinary accurate instrumentation and notes the Earth’s temperature remained constant. Did the actual energy of the Earth and its atmosphere isothermally increase? He ponders, perhaps it was due to cosmic rays, adding energy onto the system, Earth. So the man on the moon checks and no cosmic rays struck the Earth at that instant of time. He then recalibrates his equipment, and no errors are found. Facing a conundrum, the man on the moon turns blue.
If only the man on the moon knew all the intricacies going on in the system Earth, he would then understand that there were no real changes, due to the syringe’s expansion. We must emphasize that the created VON is not exactly a volume of nothing because it does contain blackbody radiation, but the point is in terms of mass in a gravitational field, the VON is a volume of nothingness. Adding or subtracting a VON to a system does not necessarily change the system’s total energy.
Now ponder that the syringe starts at a specified non-zero value, and then negative work is done onto that volume of gas within the syringe. Now the pressure inside of the syringe decreases as its volume increases. Herein we shall consider that the gas inside of the syringe is an ideal gas hence the ideal gas law: PV=NkT=C’ = constant, applies. Therefore the negative work done onto the volume of gas within the syringe becomes:
Wvol = -(NkT)In(Pi/Pf) = -(NkT)In(Vf/Vi) (3)
Eqn (3) is based upon a path independent differential as expressed in terms of the parameters within the piston-cylinder as a system. However the total energy of the gas within the piston remains constant i.e for a monatomic ideal gas the gas's constant energy =3PV/2 i.e. dEsys=0. This is another example of using the wrong parameters to express the work that is done!
Specifically, eqn (1) still determines the actual irreversible work (AKA lost work) done onto the surrounding atmosphere! see expanding. And from the perspective of Earth and its surrounding atmosphere as a system, the expansion of the syringe did not represent a change to its energy. Specifically, although the Earth’s atmosphere was upwardly displaced, the magnitude of the potential energy increase equals the magnitude for the negative work associated with the expanded volume, as defined by eqn (2).
To see work done on a vacuum [eqn (2)] vs work done onto a gas [eqn (3)]: see
Graph 1.7.1 vs 1.7.2. To repeat this represents the work done in terms of the expander system's parameter, which is really due to
the applied expanding force. But this does not necessarily equate to the lost work that is done onto the atmosphere!
To see work done on a vacuum [eqn (2)] vs work done onto a gas [eqn (3)]: see Graph 1.7.1 vs 1.7.2. To repeat this represents the work done in terms of the expander system's parameter, which is really due to the applied expanding force. But this does not necessarily equate to the lost work that is done onto the atmosphere!
Potential into Kinetic Energy
If the addition of a VON requires work hence represents an increase in potential energy of the atmosphere but not an actual witnessed energy increase into our atmosphere. Then what happens to this potential energy when the VON collapses? When the VON collapses then the additional potential energy within our atmosphere transforms into an kinetic energy increase within our atmosphere.
Reconsider the expanded piston-cylinder. As it expands then:
1) our atmosphere's potential energy increases
2) the magnitude of negative work increases at the same rate
Hence it appears that the energy of our Earth and atmosphere as a system remains constant.
Now consider its collapse: As the expanded volume inside the piston-cylinder decreases the above potential energy transforms into kinetic energy, while the VON collapses. This holds true for both the expanded vacuum and for the expanded gas. And this is all defined by eqn (1) and eqn (2) BUT NOT eqn (3)!!
Stability of Negative Work
We have discussed that negative work is unstable. If one wanted you could equally argue that negative work is reversible. If anyone is interested I could expand this into cavitations and how they correlate to negative work. Just let me know
Thanks for reading what I write.
I am still looking for help in rewriting the science. It is mostly done but I need to throw ideas of some people to see if they understand and more brains involved the better the final product and hopefully outcome will be. If it interest anyone with an open mind scientific mind who also has thick skin and a want to actually accomplish something.
Copyright Kent Mayhew