A New Thermodynamics


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 returned 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 hence can never be recovered therefore the process is an irreversible one. For this irreversible process:

  Q2=Q1+Qlost         1.7.41

     Of course by definition if Qlost=0, then the process might be considered as being reversible. 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 even if, Qlost=0. Certainly System 2 and System 1 can return to their original states, but only once their radiation of heat dissipates their thermal energy 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. Accordingly, the net flow of any heat is generally an irreversible process unless the temperature difference is infinitesimally small, i.e. net flow of heat approaches zero. Therefore, processes involving the transfer of a significant quantity of heat are generally not reversible.

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.

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 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 andthus  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.

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.


 Reversibility Comentary


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 more often than not, this is an idealistic rather than realistic conceptualization. Consider a mechanical process wherein friction is generated. Since friction creates heats that tends to radiate in all directions. As previously stated the idea of completely controlling and then directing such heat, often nears the impossible.

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


  It does make one ponder what all is reversible beyond frictionless devices and some microscopic processes. One must realize that in traditional thermodynamics reversibility was associated with entropy production. When a science can be simplified by forgoing such entropy based analogies one might be inclined to wonder, what were we thinking.  

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