A New Thermodynamics


By Kent W. Mayhew

Reversibility by Kent W. Mayhew

A reversible process can equally proceed forwards, or backwards. Another way of viewing this: Reversibility is an idealistic concept for a system’s state, wherein it can be changed, and then readily return to its original state. Conversely, an irreversible process is a process that cannot be readily returned to its original state without an input of resources, such as energy.

Consider the systems shown in Fig 1.7.14. 

Heat (thermal energy) warms System 2 (Q2), which in turn increases the energy within System 1 (Q1). However in this case, heat (Qlost) is dissipated through the walls of System 2 and is lost into our surrounding atmosphere (heat sink) hence can never be recovered therefore the process is an irreversible one. For this irreversible process:

 Q2=Q1+Qlost          (1)

     Of course by definition if Qlost=0, then the process might be considered as being reversible i.e. Qlost is considered as being infintesimal. Remember that the net flow of heat is always from hot to cold therefore the best one could reasonably expect is that both systems reach thermal equilibrium, when the external heat that is warming System 2 is then turned off i.e.Q2=0. The reality is that such supplied heat can never be fully returned hence such heating processes could never be fully reversed unless Qlost=0. Certainly System 2 and System 1 can return to their original states, but only once the heat is dissipated down to the point that all system’s temperature equates to that of the surroundings. In which case all of the thermal energy that was originally supplied is now lost for good, i.e. Q1=Qlost.

Furthermore, the net flow of heat is always from hot to cold. This has to do with temperature and NOT entropy! Accordingly, the net flow of any heat is generally an irreversible process unless the temperature difference is infinitesimally small, i.e. the net flow of heat approaches zero. Therefore, processes involving the transfer of a significant quantity of heat are generally not reversible. see Law of Work vs Energy  and Illusional Reversibility (in Boiling).

Similarly, no real mechanical process can be reversible! Specifically, the motions for all man-made devices involve friction resulting in more dissipated heat, i.e. heat radiates into the surroundings. Okay, systems can be insulated from their surroundings but the gathering and then trying to directionally control the flow of frictional heat with 100% efficiency is an idealistic, rather than realistic concept.

Another major reason as to why many useful processes are irreversible being: The displacement of our atmosphere by expanding systems requires work, which generally cannot be recovered. Specifically, isobaric processes wherein an expanding system displaces our atmosphere cannot be reversible, because energy/work is lost into our atmosphere, i.e. lost work. Realizing that most useful processes require system expansion then the concept of lost work is unavoidable. Note: “Useful processes/systems” are those that can move man and/or machine.  To better understand expanding systems see expanding piston-cylinder. And Illusional Reversibility (in Boiling).

If you think about it the above considered lost work can never be returned simply because in order for the atmosphere be able to do work onto a system then the atmosphere must be at a higher pressure than that system. And in order for that system to be at a lower pressure, then something was done to that system in order for its temperature to be lower. And that something required energy. Just reconsider the lowering of a system's  pressure by expanding a hermetically sealed syringe. The syringe's expansion required energy and that was negative work onto the contents of the system contained within expanded syringe. 

The above is no different than in order for the atmosphere to transfer thermal energy into a system then the atmosphere must be at a higher temperature than that system. Again if the system is at a lower temperature than the surrounding atmosphere, then something was done to that system in order for its temperature to be lower. And that something required energy.

There are numerous other reasons that result in a given process being irreversible such as: Electrical resistance, shock waves in fluids (considered as part of viscous dissipation), inelastic deformation, magnetic hysteresis, mixing of substances, osmosis, flow of a viscous fluid along a solid surface, internal damping, viscous disspation (all forms includes drag) and mixing of similar substances at different temperature (perhaps considered as part of spontaneous heat transfer).

However things are not all that discernable. Reconsider the compression/expansion of a hermetically sealed piston-cylinder apparatus, as was discussed previously in the blog on negative work. See Negative work

  Omitting friction, is such work is reversible? When the hermetically sealed apparatus is expanded and thus  then the force is removed, the atmosphere’s weight drives the piston inwardly until both the apparatus, and surrounding atmosphere, have returned to their original states. From the view of the piston-cylinder apparatus, the answer is yes, the process reversed. Also, the same amount of work can be extracted from the system’s contraction, as was used for its expansion. In many ways its no different than lifting a rock, having that rock gain potential energy and then harnessing that potential energy gain by tying a rope to the rock and letting the rock fall. see Reversible Work.

Perhaps a better realization is to say that an external force caused the expansion, hence the apparatus can be considered as an isolated system. That being a system whose total energy remains constant throughout the process, i.e. no change to its ability to do work. We are assuming that heat can freely enter the cylinder-piston apparatus during its expansion in order for its contents to remain isothermal. Note: This freely given heat only constitutes the additional blackbody radiation required to fill the volume, which would generally be small when compared to the energy associated with any gas molecules, and thus may generally be deemed as immeasurable.   

Yet another way to view this is to say that during expansion negative work was done onto the volume occupied by the piston-cylinder apparatus, but not its contents. The concept of negative work will be dealt with when we deal with cavitations in the next book: Part 2 of this series.See Book

 The answer may be trickier when the particulars are considered. What about the kinetic energy increase to those gaseous molecules that plummet towards the Earth once the expansion force was removed? Does this mean that there is a correlation between pressure and a system’s natural temperature, during expansion? Perhaps!

Consider the piston is pushed into a cylinder, increasing the pressure within. When the force is removed, then the piston will return to its original position. What is omitted from this: As the piston is forced into the cylinder, the atmosphere’s gases that plummet towards Earth experience a change of potential into kinetic energy i.e. result is atmospheric heat. Remove the compressing force: As piston-cylinder expands, it cools because it is doing work onto the atmosphere. This cooling must equate to the atmosphere heat gained during compression, e.g. over time this heat will flow back into the piston-cylinder, reversing the process.  See expansion  and/or  see Compression


 Reversibility Commentary


So far we have considered that a process is reversible if no energy is lost, i.e. lost work = 0 and there is no friction. There is another aspect that should be discussed. Reversible processes must also have equal abilities for energy to naturally flow either forward or reverse, in a process. Such equality may be better suited to microscopic processes than macroscopic ones

Interestingly, a process that involved lost energy could conceivably be reversible if the lost energy could be controlled and redirected back into the process itself.  Again, this is more of an idealistic rather than realistic conceptualization. Consider any mechanical process wherein friction is generated is not reversible. Specifically friction creates heats that tends to radiate hence disperse in all directions (radially). As previously stated the idea of completely controlling and then directing such heat, often nears the impossible.

It is hard to envision any work that is reversible. Even if you lift a rock it is not fully reversible as you personally can never recover the energy that you exerted. A pendulum may be closer to reversible because the pendulum's motion is the continuous exchange of potential and kinetic energy. But the pendulum experiences friction at its pivot point as well as with the surrounding atmosphere as it moves i.e. drag AKA viscous dissipation, hence your grandfather clock requires a windable spring in order for it to keep time. Even  Newton's cradle experiences drag as its balls oscillate through the atmosphere. Moreover, both the pendulum and Newton's cradle require your hand to provide the intial lift, an activity that can never be reversed, as was the case for the rock.  For more see my blog on Perpetual Motion.

Similarly when work is lost into the surrounding atmosphere by any useful expanding system, then the likelihood of the atmosphere being able to return that lost work back into that system is zero. In thermodynamic terms lost work as defined by PdV is irreversible work!

And if you require an input of energy to manipulate any lost energy, then the energy of manipulation must be deemed energy that is lost in the process, hence the process cannot be reversible.


Reversibility of Infinitesimal


 Often you will read how such and such a process is reversible when infintesimal change is considered. This is a dangerous mathematical result, that is weak logically. Infinitesinal change when applied to work or energy change really mean that the change is so small that it is often fundamentally meaningless. For example consider that System A does infintesimal change to system B, this is reversible but really it says that the change is so small that it is not measureable, in other words the work done approximates zero. 


 Okay when applied to heat sinks or heat baths infinitesinmal change can equally apply in principle because the change in terms of the heat sink/bath is immeasureable although the change is real in terms of the system in thermal contact with the heat sink/bath. Again if such a change occurrs a massive number (near infinite?) number of times then even in terms of the heatsink/bath that change becomes measureable. I.e.Reversibility more closely approaches reality as infinitesimal change approaches zero.


Sad Commentary


   It does make one ponder what all is reversible beyond frictionless devices and some microscopic processes that do not alter the dynamics of the surrounding atmosphere. Interestingly processes at the quantum level are often reversible, and this has more to do with the fact that such processes do not alter the dynamics of their surroundings i.e. atmosphere! This makes sense without the illogical use of either entropy or the second law.


Reconsider that in traditional thermodynamics reversibility was associated with entropy production i.e. there are those who claimed that irreversible can only be understood by excessively complex mathematical theory. Perhaps people who make such claims may now have to face that wailing wall of human indignity I am sorry but I used to believe such claims and all I can now say is: "What were we thinking?


  For more on lost work and irreversible processes see blog Isobaric vs isometric heating

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