Second Law of Thermodynamics, Sadi Carnot and the Steam Engine

The second law of thermodynamics is often used to explain why processes are not 100% efficient. Like entropy, the second law has become something for everything. And like entropy, in trying to be something for everything it really becomes meaningless. Each and every process that is not 100% efficient can be explained in numerous other ways!

Consider friction, which results in heat be radiated. Since the vast majority of man made devices are not 100% efficient, then friction explains why such devices tend to dissipate thermal radiation. What about the dissipated energy? Again there is no need for the second law. The net flow of heat is always from hot to cold. That is constructive logic!

But there is more to this than just friction in mechanical devices. In my other blogs concerning the second law of thermodynamics 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 lost work! Interestingly, this explains why engines like those based upon the Carnot cycle are idealistic rather than realistic.

The above is really based upon the way physicist and chemists like to perceive the science. Herein entropy (S) is defined in terms of the number of microstates (N) i.e.

S=klogN 1)

And then the second law consideration that the isothermal entropy (whatever that really means) can never decrease in an isolated system. As beautiful as that sounds, it is really meaningless to us on Earth. Since the majority of useful systems have expansion (generally isobaric) as one or more of the steps in their cycle, then this involves our atmosphere’s upwardly displacement, which is work done by the system. Since this is doing work onto its surroundings, such useful systems are not isolated and hence the second law does not apply1.

However we are still scratching the surface. How does an engineer contemplate the second law? An engineer might say that (2): “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 gas as given by kinetic theory:

Ek=3NkT/2 2)

Note: N in eqn 2) is the number of molecules, why N in eqn 1 is the number of microstates.

As the gas is heated, its temperature increases (dT) hence its kinetic energy increases, which is defined by:

dEk=3NkdT/2 3)

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) and 2) 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 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 but it demonstrates how we should be thinking.

Well what was 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”

We really do not know. What we do know is that in the early 19th century, many still considered heat to be a fluid/substance called phlogiston. We can 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.

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 we 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 the book:

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: .

The above was an excerpt from my book. 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 probably numerous other factors involved.

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.

1) Kent W. Mayhew: “Second Law and Lost work”, Physics Essays Vol 28 152-155 (2015)

http://physicsessays.org/browse-journal-2/product/1173-24-kent-w-mayhew-second-law-and-lost-work.html

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: “Imporoving our Thermodynamic Perspective” Physics Essays Vol 24 Pages 338-344 (2011)

http://physicsessays.org/browse-journal-2/product/226-4-pdf-kent-w-mayhew-improving-our-thermodynamic-perspective.html