By Kent W. Mayhew

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:

Wlost=PatmdV (1)

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 explains 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*

Although
“negative work” conceptually feels counterintuitive, it is mathematically expressed by simply placing a negative sign in front of
the work term. To visualize negative work, all one needs to do is to take a syringe, and place 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 out on the syringe’s plunger). The volume inside the syringe expands, thus we are performing negative
work onto the volume of space that is now being created the inside of the syringe.

If the initial volume (*V _{i}*) of gas
within the expanding volume was zero, then our expansion of the hermetically sealed syringe to some final volume (

Wvol = -Patm(Vf-Vi) = -PatmVf = -Watm (2)

Where Patm is the atmosphere’s pressure, Watm is the work done onto the atmosphere

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 (ignoring the blackbody
radiation within), then the total energy of the atmosphere has not changed.

Importantly negative work tends to create
unstable volumes. In the case of the expanded syringe, once the plunger is released, the plunger will come crashing down into the
syringe removing the recently created volume within the syringe. One could rightfully argue that since the pressure inside of the
syringe was less then atmospheric, then the atmosphere’s pressure will drive the plunger into the syringe, and this would be the mechanical
answer.

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 displaces a mass in a gravitational field, then this is negative work to the volume that was previously occupied
by that mass.

Again how we consider 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 that a volume
of something replaces the volume that was once occupied by the syringe, as we bring the syringe out into Earth’s atmosphere’s surroundings,
i.e. outer space. 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 pulled. 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 vacuum 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 vacuum is a volume of nothingness. Adding or subtracting a volume of nothingness 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)

From the perspective of Earth and its surrounding atmosphere as a system, again the expansion of the syringe
did not represent a change to the system’s energy. Although 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.

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

*Understanding eqn 3) : Ideal Gas and Work*

A mathematical analogy
for this work is obtained by defining the process as isothermal (dT=0), thus the ideal gas law [PV=NkT] tells us that the pressure
multiplied by volume equals a constant (C’), i.e.:

PV=NkT=C’ (4)

When
the work required varies with the location at which the force is applied, the line integral is often used to calculate the work involved.
Now work is the integration of infinitesimal changes. Therefore, the total work (W) is defined by the integration of infinitesimal
work (dw), as follows:

W=integral (dw) = integral(Pdv) (6)

Notice that we transformed infinitesimal work (dw) into infinitesimal volume change (dv). Work now takes the more general form that
being the summation of all the work associated with each infinitesimal volume change. Substituting eqn 5 into eqn 6, gives:

W=integral (dw) = C’integral (dv/V) (7)

Performing
the integration gives:

W=C’In(Vf/Vi) (8)

which can be rewritten for the isothermal work as:

W=(NkT)In(Vf/Vi) (9)

Eqn 9 adheres to the traditional conceptualization for work. However, it possesses the following inherent ambiguity that
is not traditionally acknowledged. That being that it can equally be written in terms of pressure change,

W=(NkT)In(Pi/Pf) (10)

Although it is a moot point , a possible reason that traditional thermodynamics is always written in
eqn 9 rather than eqn 10 is the preference of volume over pressure as a parameter of relevance. In my previous blogs I gave a reason
for this oversight that being that volume increases are wrongly attributed to entropy increases, when entropy (S) is considered in
terms of Boltzmanns consideration [S=kIn(@)], where @ is the number of accessible states

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