The following was taken from this book: It is given to show the style of writing and provides some of the conclusions and insights attained in this unique thermodynamic perspective. Certainly some people's indoctrination may prevent them from appreciating what is written. All I ask for is that you maintain an open mind.

 

  Please note the equations did not post over, hence have been rewritten herein. Which is to say that in the book the delta signs, arrow, internal energy, and other symbols are correct in book but  herein they may not be or have been replaced with words. I do apologize for this, but I am not the one who has rendered writing scientific papers and publishing them on the net such a horrible messy task. Luckily this, Section 1.16 has very little in the way of mathematical deductions and certainly does not provide any unique previously unseen equations,  in the way that the rest of this book does.  Note the books equations were done using the microsoft word equation editor, and do look surprsisingly  good in the book.

 

  Chapter 1 Section 16:  Defying the Laws     

 

  Perspectives do change! In the 18th century, heat was considered to be a substance called phlogiston, which was considered to be part of combustible bodies with the conservation of phlogiston being an early thermodynamic law. Our comprehension changed, starting in 1798, when Count Rumford (1753-1814) professed, “heat is merely a form of motion of the particles in a body” 27pg 134. The count’s radical statement did not have an immediate impact, as it was not accepted until well into the 19th century.  It remains the basis of thermodynamics into the 21st century whereby temperature is wrongly limited to molecular motion, wherein Clausius’s entropy and its accomplice, the second law reign supreme.

Interestingly, Robert Mayer argued against expressing heat/energy in terms of the increased motions of the smallest parts of matter.(28) Max Planck agreed with Mayer. Concerning thermodynamics, in 1894 Planck wrote (28): ”it is completely unfounded, simply to assume that changes in nature always proceed in the direction of greater lesser to greater probability”.

 

  Clifford Trudesdell stated (29): ”I hesitate to use the term first law and second law, because there are almost as many first laws as there are thermodynamicists, and I have been told by these people for so many years that I disobey their laws that now I prefer to exult in my criminal status and non condemning names to the concrete mathematical axioms I wish to use in my outlaw studies of heat and temperature. The term entropy seems superfluous, also, since it suggests nothing to ordinary persons and only intense headaches to those who have studied thermodynamics but have not given in and joined the professionals.” Let us reconsider the various thermodynamic laws and entropy.

Zeroth Law of Thermodynamics

   The Zeroth law of thermodynamics is based upon “thermal equilibrium”, i.e. the equality of temperature: “If two systems are in thermal equilibrium with a third system, they must be in thermal equilibrium with each other7pg 282: The true purpose of the Zeroth law of thermodynamics is that it allows us to use a thermometer to measure temperature and then compare that measurement to other systems. 

First Law of Thermodynamics

    The traditional statement  “An equilibrium macrostate of a system can be characterized by a quantity E (called its internal energy), which has the property that for an isolated system: E=constant. If the system is allowed to interact and thus go from one macrostate to another, the resulting change in E can be written in the form:

 

                                                            (Delta)E=W + (Delta)Q                                                                                     1.16.1 

                      

 where W is the macroscopic work done on the system as a result of changes of the external parameters of the system. The quantity (Delta Q) is called the heat absorbed by the system”(7pg282):

 

   In terms of our new perspective the writing of eqn 1.16.1, may need reconsideration. E.g. in our new perspective, the concept of work (W) has been altered in Section 1.6. Ditto for our understanding of internal energy. And the notion that work can only use 2/3 of a gas’s kinetic energy change may alter its application.

 

   The true purpose of the first law of thermodynamics is to affirm that energy is conserved! To this end, we remain in total agreement with traditional thermodynamics. It should be noted that depending upon the writer and the application, you might see the first law of thermodynamics written in different formats, which is fine. Rather then get hung up with all the parameters, as is traditionally done, the first law should simply read: The energy change within a system must equal the total influx of energy into a system minus the efflux of energy from that system. Which is to say that energy can be converted from one form to another but it cannot be created, or destroyed.

 

Second Law of Thermodynamics & Entropy

 

   Consider the following traditional statements (7pg 283):“An equilibrium macrostate of a system can be characterized by a quantity S (called entropy), which has the following properties:

 

• In any infinitesimal quasi-static process in which a system absorbs heat, its entropy changes by an amount:      dS=dQ/T    1.16.2

  Where T is a parameter characteristic of the macrostate of the system and is called its absolute temperature

 

• In any process in which a thermally isolated system changes from one macrostate to another, its entropy tends to increase, e.g.                                                                            (Delta)S (greater than or equal to) 0                                   1.16.3

 

   Throughout this text, we realized that a system’s volume increases, often requires the displacement its surroundings. And if its surrounding has mass that is displaced against a gravitational field, then this requires work e.g. Earth’s atmosphere wherein this work often becomes “lost work”, i.e. explaining Maxwell’s demon, and dethroning the second law.

 

   Eqn 1.16.2, being the differential equivalent to the Clausius equation (eqn 1.2.1), is applicable to any process where there is an isothermal transfer of heat (Q). As such, both traditional thermodynamics and our new perspective accept the usefulness of entropy as a mathematical tool that may be applicable to empirical research. However, any agreement stops there. Specifically, traditional thermodynamics wrongly embraces entropy as a tool for enlightening the previously unexplainable!

 

   One of the better explanations for the second law of thermodynamics was found on the internet, written by Matt McIrvin30: “A physical system will, if isolated (that is, if energy cannot get in or out), tend toward the available macroscopic state in which the number of possible microscopic states is largest.”

 

   In other words, an isolated system will tend towards an equilibrium macrostate, which is as random as possible. Therefore, its total entropy becomes as large as possible, meaning that the number of microstates is the largest possible. From a statistical/quantum understanding, such a realization is vital, however this does not necessitate that entropy is reason, rather than a result!! Being a result, entropy would still be:

     

                                                                        S=klogN                                                       1.16.4

where N is number of microstates, k is Boltzmann’s constant

If two systems are put into thermal contact then, the number of microstates is still obtained by multiplying the number of microstates of each system, i.e.:

                                                Nf=(N1)(N2)                                                                              1.16.5

 

 And the new final total entropy () still remains as large as possible, that being:

                                         

                                                Sf=k(logN1+logN2)                                                                    1.16.6

 

   Throughout this text, we have treated both entropy and the second law in a circumlocutory manner. Do we still need the second law to explain why heat engines lose energy? No, our new understanding of ”lost work” explained it in undeniably simple terms. As for mechanical devices: Friction creates heat, resulting in energy loss i.e. dissipated energy. Neither entropy, nor the second law, is required to realize that such heat radiated into the atmosphere is not recoverable. It also becomes inherently obvious that the perpetual motion is not possible? Again there is no need for entropy, or it accomplice i.e. the second law.

 

   When contemplating latent heat, we realized that the latent heat of vaporization should be greater than that of condensation by the amount of work lost during vaporization. The point was: It takes work to upwardly displace the weight of our atmosphere, but the converse does not hold. Specifically when the atmosphere is displaced downwards, the only net effect is a transformation of potential energy into kinetic energy by any downwardly displaced atmospheric gas molecules. Obviously, the energy that was lost in vaporization cannot be magically found in condensation.

In terms of randomness, the act of increasing volume is the act of increasing the mathematical result of the number of possible states that molecules can access. And the work required for the volume increase, is generally unrecoverable. Hence such processes are generally irreversible. Interestingly, as a system’s volume increases then molecular dispersion will cause the molecules to become evenly distributed, which is the maximum state of molecular randomness. Is entropy still needed? The answer is an emphatic NO!

 

   Given a sufficient amount of time then dispersion will cause maximum randomness, allowing us to say that in terms of molecular volume (v):

• With a given set of constraints, any molecule with a given energy, will attempt to attain a maximum mean molecular volume (v).

• As we add energy to certain systems (especially gas’s), the molecules within that system, often will attain a higher mean molecular volume (v).

• In any expanding system, the mean molecular volume (v) will continuously increase.

 

 

   Nothing is extraordinary about the above three common sense statements. Yet similar statements concerning entropy are traditionally deemed profound! Yes entropy can remain that wondrous mathematical tool allowing statistical thermodynamics to function. But at the end of the day one cannot forget most useful expanding systems displace the Earth’s atmosphere against gravity. Moreover, we comprehend why the second law of thermodynamics was ever even envisioned, and for the first time, we attain clarity concerning entropy’s validity, and its limitations.

 

   Since work often involves the displacement of Earth’s atmosphere’s weight, then such displacements maybe partially responsible for the blundering eqn 1.16.3. Furthermore, if it wasn’t for gravity then the natural state would be disorder but again eqn 1.16.3 is not required. Interestingly, we now realize that Boltzmann’s constant (k) correlates to Earth’s gravity through the enthalpy equation. Perhaps from this point on science will accept that Boltzmann’s constant has a gravitational correlation, as well as a thermal one.

 

   The accepted innovator for the Second Law of Thermodynamics conceptualization was Lord William Thompson Kelvin (1824-1907). Namely, as eqn 1.16.3 states, if its entropy always increased, then the universe would eventually reach a state of uniform temperature and maximum entropy from, which it would be impossible to extract any work. Lord Kelvin named this point of finality the “Heat Death of the Universe”. Ultimately: If our universe as a whole is expanding then it must be cooling down. However this may have little to do with entropy and everything to do with the dispersal of matter and energy.

 

   Certainly, one may envision our universe as obtaining some uniform cold temperature but if one does, then he/she has seemingly forgotten about gravity. Specifically, gravity tends to pull matter together creating hot spots throughout our universe. And so long as matter is gathered into clumps by gravity, then both the pressures and the temperatures associated with those clumps will be elevated. 

 

   Is the universe’s entropy really increasing? That depends up entropy’s definition. An expanding universe implies a volume, hence randomness increasing. So the answer is seemingly: Yes! But what about all those clumps of matter that gravity assembles? Perhaps not! And then, the other cosmology extreme: black holes, wherein the second law paradox exists. Sure one can circumnavigate the second law with a complicated path of logic. Is it necessary?  

 

    Numerous challenges to the second law are well documented31. Interestingly, D. Sheehan32 states: “The second law of thermodynamics is an empirical law. It has no fully satisfactory theoretical proof. This being the case, its absolute validity depends upon its continued experimental verification in all thermodynamic regimes.” Realizing that the second law and entropy were in part construed, formulated & equated to “lost work” renders the fact that they are empirically validated somewhat superficial. Empathy can be given to scientists focusing upon a heat engine, and thinking solely in terms of internal molecular motion and probabilities. Of course the man on the moon simplifies our perspective by witnessing the atmosphere’s volume increase.

 

   Furthermore Ben-Naim in his book33 discusses that when applied to thermodynamics, that the term entropy could be replaced by the term information. Interestingly, Ben-Naim demonstrates something this author has been saying for years. That entropy is a mathematical contrivance30pg7. How important of one remains in the eye of the beholder.

 

   An isothermal volume increase cannot happen without the addition of thermal energy. For an expanding system: Sometimes this added thermal energy is freely given, e.g. absorbed from the surroundings. Other times it is driven into the system, e.g. heating resulting in isothermal isobaric expansion. Sure, when compared to the other energies, a system’s thermal radiation tends to be negligibly small, exception blast furnace. Even so, thermal radiation’s omission has enabled misunderstandings to prosper, i.e. isothermal entropy increases by quasi-static expansion of a system, and/or the traditional belief that a vacuum has no temperature. 

Finally, there are those who believe that the second law prevents net thermal energy from being transferred from a cold system to a hotter system. In terms of our new perspective, logic simply dictates that although heat flows both ways the net flow is always from hot to cold.

 

The Third Law of Thermodynamics

 

  The traditional statement: The entropy of a system has the limiting property that as:

 

   T approaches zero then  S appraoches S0

 

   where is a constant independent of the structure of the system 7pg284:

 

   The reason that the third law exists is due to eqn 1.16.2, and the implication of absolute zero. More precisely as, what happens to dS? Without the third law, then in traditional thermodynamics entropy change as defined by eqn 1.16.2, would approach infinity as.

With the realization that entropy, no longer holds the theoretical reigns of thermodynamics! Then in terms of our new perspective: As temperature approaches zero, then the thermal energy approaches zero. Certainly, near absolute zero, thermal energy would no longer be linearly proportional to temperature, as was discussed in Section 1.10.   And that is that!

 

Traditional Teaching

 

   Entropy based thermodynamics is enshrined early in most scientist’s psyche. We are taught probability functions, and about the number of possible energy states within a system. Certainly learning about entropy, probabilities and their results, has provided remarkable insights in thermodynamics. Einstein realized that the entropy of radiation has the same form as that of a gas34pg509.  It sounds grand, but it is really just a mathematical consequence of eqn 1.4.28:, and the fact that it all correlates to the thermal radiation density from our Sun.

 

   Remember that statistical analysis is merely an eloquent mathematical language. Be humble because too often, learning heartens our benevolence! And it can encourage faulty logic to dominant our thought processes, especially when it enshrined in circular logic? For any given problem there is often more than one solution, each based upon a chosen perspective. This author’s distain arises when one claims that there exists only one language to explain things, and then arrogantly states that it has to be. Only when something can be explained several different ways, in more than one language, in its simplistic context can we take such a stance.

 

   Our confidence in our ability to communicate separates mankind from the rest. If we want language to distinguish mankind, whether it is mere words, or complex mathematics, we must be able to visualize that of which we speak. Without visualization, language is worthless. Perhaps, it is due to a lack of insight but this author remains unconvinced, that all, which is traditionally professed could be visualized.

Entropy: It is One, or the Other

 

  Reconsider Section 1.10, wherein we discussed that entropy is either:

• Something that when multiplied by temperature change gives changes to a system’s ability to perform work in which case: Eqn 1.1.1: is valid

OR

• Something that when multiplied by temperature change gives changes to a system’s energy in which case: Eqn 1.16.2: is valid. I.e. entropy becomes the specific heat for inhomogeneous systems.                                                                                                              

 

   As a mathematical contrivance entropy must be defined in terms of either 1) or 2). It cannot remain both as is traditionally perceived. Perhaps we should leave Eqn 1.16.2 as valid, in which case entropy becomes a mathematical contrivance signifying the specific heat for non-homogeneous systems. In which case a new term should be used for the mathematical contrivance in Eqn:1.1.1. Perhaps call it kentropy (Sk).

Mother of all Heat Baths

 

   So how did we get into our mess? It is really a matter of where we reside, e.g. on isothermal, isobaric mother Earth. But there is more. As previously discussed: Our Sun’s radiation of thermal energy density can be approximated by the Rayleigh-Jeans; Eqn 1.4.27:.

Interestingly, the microcanonical ensemble functions best for systems in thermal contact with heat baths otherwise it becomes an approximation. In other words statistical thermodynamics is based upon idealized heat bath systems, while the mother of all heat baths, e.g. our Earth’s atmosphere & oceans & the Earth’s exterior, have their thermal energy density approximated by the above linear function of temperature. We now understand how and why traditional thermodynamics became so logically derailed.

 

Closing Remarks

 

   This author likes to think that this text would have been endorsed by the likes of Mayer and Planck. To those whom have traditional thermodynamics engrained into your souls. I am not sorry but: Not realizing that volume increases signify work done in displacing our atmosphere was missing the obvious.

 

   A sad reality concerning our new perspective remains: As happened with phlogiston, it may take a few generations (if at all) before mankind accepts that thermodynamics is what it is. Whether or not, this actually turns out to be the case is purely up to you the reader. If you still insist beholding traditional entropy based thermodynamics, so be it. But please arrive at one conclusive all encompassing interpretation/definition of entropy so that simple folk like me can actually argue against its virtues.

 

   The ultimate question that you, the reader, should ask is: Which approach is simpler? We are back to Occam’s razor! If you answer the new perspective presented herein, then you will eventually realize that our new perspective also provide answers, where none existed before. This is especially true in systems wherein both the volume and pressure change, i.e. subjects like nucleation and cosmology.