Second Law of Thermodynamics, Sadi Carnot and the Steam Engine
by Kent Mayhew (See Dynamical interpretation of Second Law)
The second law of thermodynamics is often used to explain why processes are not reversible or if you prefer possess complete efficiency. Like entropy, the second law has become something for everything. And like entropy, in trying to be something for everything it really has become as meaningless as its counterpart entropy. Certainly each and every process that is not 100% efficient can be explained in numerous other ways than simply pointing a finger at the second law!
Consider friction, which results in heat be radiated. Since the vast majority of man-made devices are not frictionless, then friction is part of any explanation as to why such devices can never be 100% efficient, i.e. friction results in heat production which is dissipated as thermal radiation.
What about heat flow? Again there is no need for the second law or any other entropy based arguments. The net flow of heat is always from hot to cold. That is simple constructive logic! Specifically, heat will tend to flow from high to low concentrations of thermal energy as measured by the parameter temperature! Note it could be a disaster to just say concentrations of thermal energy because condensed-matter tends to absorb and concentrate thermal energy when compared to freespace and even gases.
But there is more to this than just friction in mechanical devices. In my other blog concerning lost work, I discussed that for expanding systems: Lost work occurs during the upwardly displacement of our atmosphere’s mass, when a system expands. This results in a potential energy increase of our atmosphere, a potential energy increase that cannot be harnessed. Hence such work is “lost work”, e.g. work that will never be recovered! Interestingly, this also helps explain why engines like those based upon the Carnot cycle are idealistic rather than realistic.
In analyzing what went wrong one might be inclined to start with entropy (S) as defined in terms of the number of microstates (@) i.e. Boltzmann’s entropy:
And then the second law consideration becomes that the isothermal entropy can never decrease in an isolated system. In other words entropy always increases and arrow of time entropy based arguments became the norm. As mathematically eloquent that such ensemble of particles based argument seems, it is really is meaningless if you realize that no one really knows what entropy really means. See my blog concering Entropy
We can go back further and look at how the second law was conceived. It arguably started with 19th century scientists making the following statements:
1) Clausius: “ It is impossible for heat to be transferred by a cycle from a body to one warmer than itself in the absence of other effects.
2) Thomson (Lord Kelvin): “It is impossible to transform an amount of heat completely into work in a cyclic process in the absence of other effects”
(Reference: “Entropy, Reversibility, Irreversibility And Thermodynamic Cycles” by D.Sands and J. Dunning-Davis)
Obviously expanding systems are ones that most often do work. Or if you prefer mechanical work is generally done onto a system by allowing the expansion of a neigbouring higher pressure system. From a mechanical perspective such systems can be deemed useful systems. Here on Earth useful expanding systems lose work onto the surrounding atmosphere (lost work), thus we now begin to understand Lord Kelvin’s statement in its simplest context i.e. without the need of entropy nor the consideration an ensemble of particles.
Of course the prospect that neither statistical, nor probability, nor any other phase space based arguments are required, may be upsetting to some. Never forget that currently accepted second law is written in terms of the isothermal entropy change of an ensemble of particles within an isolated systems. Hence the second law as written in so many texts does not apply to any useful expanding system here on Earth simply because such systems do work onto their surroundings! Hence are never isolated systems!
One may also ask: If a system witnesses Earth's gravitational force then can it even be considered isolated? Perhaps we need to alter our understanding of isolated systems! Even if we do it does not change our reality, even though it mayb help some sleep at night.
The above was intially discussed in my 2015 paper titled “Second law and lost work” Published in Physics Essays: See my papers. It all bodes the question do isothermal entropy alway increasing arguments even apply? All we can say at this point is that statisical thermodynamics is in dire need of a rethink! Note "isothermal entropy alway increasing in isolated systems" forms the basis of 20th century accepted interpretation of the second law, a concept that not knowing has been likened to not knowing Shakespear, by C.P. Snow.
We can see that both Clausius's and Lord Kelvin's descriptions of the second law are fine, it is what happens afterwords in the late 19th and early 20th centuries is not. Understandably Boltzmann based statistical thermodynamics can be rewitten by the willing but! Also never forget that entropy ensembles are based upon unrealistic elastic collisions, rather than realistic inelastic collisions as described in the new kinetic theory.
However there is more to this. Consider how an engineer contemplates the second law? An engineer might say that: “the second law states that it is not possible to convert all of the heat (or thermal energy) into work in some continuous process.” If you heat a gaseous system, then energy must go into the heating of the gas. As I point out in my 2011 paper (3), kinetic theory tells us that you cannot use all this energy to do work.
In order to understand just think of the kinetic energy (Ek) of a N molecule ideal monatomic gas as given by kinetic theory:
Note: N in eqn 2) is the number of molecules, k is Boltzmann’s constant, T is temperature.
As the gas is heated, its temperature increases (dT) hence its kinetic energy increases, which is defined by:
Although this is all discussed in my book in much more detail, with proper mathematical symbols, the increase in the gas’s ability to do work is based upon the ideal gas law (PV=NkT):
dW(ability) = NkdT 4)
Now 1), 2) and 3) are accepted by traditional thermodynamics wherein 4) is not. Specifically 4) is one of the numerous examples of constructive logic used, which is inherent to this author’s webpages and book.
The point being that obviously all the energy increase of an ideal gas cannot be used to perform work. Seemingly the upper limit is 66%, i.e. NkdT/[(3NkdT)/2]. Certainly this requires more thought on how one argues it but it demonstrates how we should be thinking. To see Rief’s analysis for flux click on box to right. Note for those who do not appreciate this described 66.6% limit, a question really becomes why did thermodynamics allow for 1/6 to be the flux in the traditional analysis when in fact the flux ratio is ¼ (another case to two or more wrongs making a right; yea right).
Certainly the above inability to use all of a gas’ energy to perform work helps add to Lord Kelvin’s insight, again no need for the second law, unless you take Lord Kelvin’s statement as an insight into what is discussed herein, and that the 150 yrs of entropy arguments that followed his statement was simply a delusional understanding of the second law.
Either way Clausius’s consideration is equally troublesome. Certainly there is no need of entropy nor other complex arguments if we simply say that thermal energy flows both ways i.e. from hot to cold, as well as from cold to hot. It is just that the net flow of heat is always from hot to cold: Temperature driven. This removes entropy from any consideration concerning the direction of flow for thermal energy. That in itself should be enough.
We can go back further and consider Sadi Carnot’s intent when in 1824 when he wrote his paper: “Reflections of the Motive Power of Fire and Machines Fitted to Develop that Power”. I really do not know what Carnot was thinking in the early 19th century. Certainly many still considered heat to be a fluid/substance called phlogiston. I expect that Carnot knew of Count Romford’s 1798 consideration that; “heat is merely a form of motion of the particles in a body”. Whatever Carnot’s state of thought was, it is safe to say that neither statistical physics nor kinetic theory was part of it, as they were not even perceived at that time.
Seemingly the original intent of Sadi Carnot’s ideal heat engine/cycle was probably part of an effort to understand why 19th century devices, such as the steam engine, were so inefficient. Again I do not claim to know how Carnot perceived efficiency although his conceptualization was ahead of its time. We now know that steam engines of the 19th century were around 5% efficient and modern ones may, if lucky, attain 12% efficiency.
Okay let us now consider the steam engine: The following is taken from my earlier book (2015 version and is also in my 2018):
Cyclic Inefficiency& Steam
Often an engine functions as a closed system during the power stroke (work producing part of the cycle), and an open system during other parts of the cycle. Consider, the cyclic engine illustrated Fig. 1.8.2, wherein; a high-pressure gas first drives the piston in one direction, and then drives the piston back in the opposite direction. The system of high-pressure gas can be due to: 1) A lower mean molecular volume occupied by the gas molecules, and/or, 2) a higher mean kinetic energy of the gas molecules, than the that associated with the surrounding atmospheric gas. Note: An engine, whose cycle is illustrated in Figures 1.8.2 and 1.8.3, where water is boiled to create the high-pressure gas, is commonly known as a “steam engine”.
Such engines function by starting with valves 1 and 4 being open, causing the high-pressure gas to be on the L.H.S. of the piston thus driving the piston to the right, as shown in Fig. 1.8.2. When, the piston makes it to the end of the cylinder, valves 1 and 4 close, while valves 2 and 3 open. With the high-pressure gas now on the R.H.S. of the piston, the piston is driven back in the other direction, i.e. towards the left.
Now consider that the piston is massless, and frictionless, and that the engine performs no actual mechanical work. In this case, the higher pressure simply pushes the hot gases kinetic energy through the piston onto the surrounding atmosphere, resulting in a continuous upward displacement of the Earth’s atmosphere, i.e. work done onto the atmosphere: . This happens irrelevant of which direction the piston is moving.
In real life, such cyclic engines experience friction whilst running and are constantly displacing the Earth’s atmosphere, hence is constant: . This helps explain why steam engines tend to have such low efficiencies, e.g. steam engines: .
We can now begin to understand why a steam engine are inherently so inefficient. Work is continuously done onto the atmosphere, plus there is the inefficiency of steam and its ability to do work, and plus there are all those frictions within the steam engine itself. And there are obviously numerous other factors that warrant consideration.
Interestingly one can take the above and rather than use it to explain a steam engine’s inefficiency, it can be used to explain why traditional thermodynamics lost sight of remaining a constructive science. And at the heart of the problem lay the poorly conceived, yet universally applied second law of thermodynamics.
Where did the over complication in thermodynamics actually begin. Arguably it was with Boltzmann’s conceptualization of entropy. One could equally argue that Lord Kelvin got it right but for the wrong reasons. Or that Clausius complicated things with the introduction of entropy when all that was need was temperature.
One could also argue the issue is with Gibbs and that dreaded differential shuffle. Perhaps we can argue its Bernoulli and his stance that collisions are elastic, which were unwittingly accepted because we fooled ourselves by blindly using experiments in closed systems.
Perhaps we should blame our arrogance as displayed by Eddington's statement to the right. Or perhaps we all should just accept some humility by acknowledging that we all, may or may not, be "smart for a human". Or if you prefer: To be human is to make mistakes, but in so doing at least it showed that we tried.
Anyway you look it. Currently accepted theory that goes beyond Clauisis's and/or Lord Kelvin's mid 19th century assertions, may form the basis for calling the second law a false postulate.
Other References used:
1) Kent W. Mayhew: “Second Law and Lost work”, Physics Essays Vol 28 152-155 (2015)
2) 1) J. Srinivasan “Sadi Carnot and the Second Law of Thermodynamics” http://www.ias.ac.in/resonance/Volumes/06/11/0042-0048.pdf
3) Kent W. Mayhew: “Improving our Thermodynamic Perspective” Physics Essays Vol 24 Pages 338-344 (2011)