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The Science of approaching 100% Fuel efficiency
This site explains the science and engineering to build green engines at near 100% fuel efficiency.
(Some topics require non-disclosure agreements, as patents are pending.)
Why?
- Electric Generation from fossil fuel is 35% to 60% efficient
- Automobile engines are 5% to 35% efficient, averaging 10%
What would it mean to me to achieve just 90% fuel efficiency?
- 1/2 (Half) price electricity
- 300 MPG (Miles per gallon) Automobiles
There is a mythology of Thermodynamics, when it comes to heat engines, that energy is inherently lost when converting heat to motion. That heat engines are inherently inefficient. But, the universe only has one rate of exchange for energy. A dollar's worth of energy returns 100 cents worth of energy. 100% every time, every way. This is not a matter of opinion, it is the first law of thermodynamics, the conservation of energy and conservation of momentum.
Thermo-Mythology says something called the Carnot Limit says even an ideal heat engine can achieve only a limited efficiency (under 100%), that no engines are reversible except the Carnot Cycle.
When is this "limit" wrong? Case 1: When the energy powering an engine does not come from the gas (vapor not gasoline) within the engine. Compressed air engines -conventional piston engines powered by compressed air- move cars around Europe at 200 mpg equivalent. Air is compressed to 3000 psi and stored in conventional high pressure air tanks, losing most of the energy to the atmosphere by diffusion, then the stored air used to move pistons. The temperature would drop in both engine and tank, except that the heat energy lost in compression is restored by diffusion as heat from the atmosphere, exactly the amount "lost" in compression acts to make this an isothermal engine. Many devices fall into this category, most of which we are not used to thinking of as heat engines, sails, windmills, wind generators, kites, even helium blimps are all moved by heat from the atmosphere. No measurable temperature drop, yet nevertheless each momentum exchange is exactly equal, exactly 100% energy efficient. Case 2: Two phase engines, most common being steam engines which power our electric grid. In this case, the energy moving the engine is coming from the contained gas (steam), but the energy in steam is not proportional to temperature. The simplest steam engine would just condense back into liquid without a temperature change. Modern steam engines can be built with a boiler pressure of 1500 psi, at a temperature of a bit more than 100 C above what we usually think of as the boiling point. By contrast a 10 to 1 compression car engine with a block temperature of 90 C or about 360 K would have to reach a temperature of 3600 K to achieve 1500 psi, above the melting point of, well, everything. The basis of the so called limit is that energy in a gas is supposed to be proportional to temperature, and with the steam engine where the majority of the energy in the system is heat of vaporization of water, that approximation is beyond wrong, its impossible. Case 3: gas phase engines driven by internal energy: Even for regular gases like air, the energy to raise the temperature 1 degree at room temperature is about 30% less than the energy required at the top end of internal combustion engines. And last, even if the air we breath were an ideal gas, the "limit" ignores the fact that no engine starts at 0 Kelvin, air on earth is around 300 Kelvin in temperate zones. If you start your engine at 300 Kelvin, and raise temperature by X with fuel, and return to 300, you have achieved 100% fuel efficiency, because X was totally converted to work. The "limit" says 100% efficiency occurs when your engine spits out solid blocks of air at Zero Kelvin. Summery, its wrong in every case, but less wrong in gas phase engines.
Whoops, missed a case. If you live on a planet at absolute zero, breathing an ideal gas, then its right.
Sadi Carnot authored the first work on the science of heat engines, which became the foundation of Thermodynamics. Sir William Thompson (Lord Kelvin) co authored the English publication of Carnot's work. The work discusses the Steam Cycle and an air cycle we now call the Carnot Cycle, and importantly explain why BOTH are reversible.
Sadi Carnot did NOT author the "Carnot Limit", the Carnot Ratio, nor the Work/Heat Ratio's. Neither men claimed that the cycles they discussed were in any way superior. On the contrary, Lord Kelvin states the calculations applying to these cycles apply to any conceivable cycle. Neither refer to irreversibility explicitly nor by implication.
Where did the concept of irreversibility come from? Rudolf Julius Emanuel Clausius is credited with the First Law, that energy is permanent, indestructible, uncreatable. Which is exactly backwards (the credit is backwards, the law is spot on, but credit for the law is distributed over physicists the past 150 years.) If you study what it was Clausius was studying, it was the steam cycle and the Carnot (air) cycle. Why was he studying it? Because the steam cycle is not quite as reversible as Carnot and Kelvin believed. If you put steam in a volume, expand it, condensation happens. Recompress it, some condensation remains. Keep cycling it and more and more steam converts to liquid. Clausius produced a formula that claims to calculate whether a process loses energy or not. It has an integral in it, so it must be right. He claims that for a cycle integral of heat (entropy) vs. temperature, that "reversible" processes are always zero, and irreversible processes are less than or equal to zero. Still in Physics books today. About half the physics books have modified his formula to say both types of processes integrate to zero, because we now "know" that no processes lose energy. Problem is, if you plot a steam cycle with his integral, you get a negative number. Plotting a two phase heat pump cycle yields a positive number. Only cycles which are entirely gas phase actually evaluate to zero, because in gas phase processes the energy is a strict mathematical function of temperature, and for the two phase processes the energy in the system cannot be determined by temperature nor can temperature be determined by energy.
Heat engines are introduced in beginning physics as being too complicated so lets pretend they are all driven by ideal gases. And from there ridiculous notions like the above limit were formed, and all hope of understanding steam engines is lost. Particularly embarrassing since steam engines literally began the science of thermodynamics, and today we just give up on teaching how steam engines work. Kind of like an advanced math class starting with "lets pretend all numbers are integers", and concluding dividing 3 by 2 is "proven" as impossible. One bit of myth can be traced thru but not exactly to Carnot. Carnot's (and Kelvin's) book uses a waterfall/water wheel analogy to describe heat engines. One reason is that's the only type of engine that preexisted the steam engine. The other and more pertinent is that for the early 1800's the prevailing theory was heat was an ineffable fluid flowing through all matter. Coupled with the waterfall analogy, Carnot concludes that each heat engine must allow the same amount of heat to flow out that flowed in and work was also done. Otherwise, without letting out the used up heat one would be stuck, as one would be putting a water wheel in a hole. That eventually evolved into the "rule" that all heat engines must produce some heat exhaust, and can never convert all heat to work. A clear counter example is a steam engine, which could in theory allow for expanding steam until it all returns to water. Might need to be as big as Texas, or perhaps as big as the solar system, but clearly and obviously there is a finite point at which all the heat of vaporization energy is removed by doing a finite and equal amount of work. It may be impractical, but clearly not a physical impossibility imposed by the universe. It is possible to build a 2 phase heat engine with 100% fuel heat conversion and no exhausted heat, returning water to its initial liquid state.
Hosted here is a bit of history, a primer to heat engine thermodynamics, and a workable, simple 100% efficient heat engine model. No, real engines will not achieve 100%, but real engines are flying and generating electricity at above 60% efficiency today, while we drive engines with 5% efficiency around town. Our biggest consumer of oil could be 10 times more efficient, just by using the better engines we already have, instead of the wasteful water cooled heat engines we are using.
Comments are welcome. The site is currently being brought up to date with current work.
Authors note: My personal trip down this rabbit hole came from trying to track down what exactly made a reversible engine cycle different from irreversible cycles. Why? Because in evaluating any engine cycle one plots force vs. distance (or pressure vs. volume), takes the definite integral and one has a precise value. The shape of the cycle makes no difference, and if you think you can draw a closed curve clockwise that cannot be drawn counter clockwise, you are smarter than me. The reverse of any closed curve can be implemented by exactly reversing the energy and volume, so there are no cycles possible that cannot be reversed. Volume change alone for steam cycles is insufficient to reverse a condensing curve, because less work is done when compressing a smaller quantity of steam. In the limiting case, one could expand a volume enough to completely condense all the vapor, then compression takes zero work. Reversing a condensing curve requires suplementing the work with heat, not impossible clearly. In 1980 I took a physics class at Rice University where I learned that irreversible processes lost energy and Energy was conserved (1st Law) in the same class, maybe on the same day. Also in that class I was taught heat diffusion was irreversible, and that isothermal compression was reversed when compressed air expanded in pneumatic devices. Probably on different days. But irreversible cycles were blamed in that class on diffusion, ironic since the Carnot cycle depends on diffusion. Was also taught only the Carnot cycle could be reversed to form a heat pump and the Carnot cycle was impossible to build. Putting those together I learned in an air conditioned room that air conditioning was impossible. (I got an A. Not bothered at all by parroting back contradictions.) In researching irreversible engine cycles I studied from various places, such as MIT which states on their online video course that the Carnot Cycle is the only reversible cycle because it is the only one that occurs spontaneously. Pretty sure they don't occur spontaneously at least they are not lying around in nature, and yet also pretty sure everything that happens only happens spontaneously. So if two of the best universities don't agree and also don't have an actual plausible measurable definition of reversibility I trusted math, and math says any curve is reversible. But I also dug further and looked for Carnot's definition only to find he did not author irreversibility, and found Kelvin's actual theorems (now paraphrased exactly backwards and mis-attributed as Carnot theorems in your Physics book. See related chapter.) which says all possible engines produce the same work from the same amount of heat. Kelvin has to be right in a universe in which the 1st Law is right (today's 1st Law, not Clausius's Law of lost energy.). I added this and quite a lot of this page because most Physics people got here and read no further. We are capable of learning completely contradictory things, and the thermodynamics we inherited from 200 years ago is full of them. What follows that I got right is due to dogged perseverance not brilliance and the bits I no doubt got wrong were all on me. Its very clear to me we have made sizable mistakes in mis-teaching heat engine theory, which hopefully this will contribute to improving in some small measure.
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