In the previous article “A Joke by a Great Scientist or Reality?”, we touched upon the seemingly utopian idea of creating cars that use the operating principle described in that article - Maxwell’s demon.

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Let’s make it clear from the very beginning that this has nothing to do with water and the car will use as fuel… warm air from the atmosphere. How do you like it? But is this idea that utopian?

Let us try and look into the hypothetical future.

Since we know that the air surrounding us contains a considerable amount of energy, it is quite realistic to imagine a car working literally on air. To all appearances, it will have a large air inlet to suck in warm air, and its exhaust will be… air cooled to, let’s say, minus 30 degrees, which will immediately mix with the ambient warm air and will be ready again for the operation of the car moving behind.

 Curiously, these cars will automatically keep a distance between themselves because it is impossible to move in “the exhaust” of the car moving in front and they will have to wait till the “fuel mixture” becomes ready for the following car.

It is true, though, that the cars will move smoothly only in warm latitudes and in summer. As for cold latitudes, cars emitting an exhaust with a temperature of minus 70 to 80 degrees will have to be manufactured. However, roads would then have to be isolated from pedestrians. But can we not put up with this for the sake of clean air?

Under no circumstances should such a car have the usual type of engine - a heat engine. Otherwise, Carnot’s formula will devour all the energy extracted from the air and will leave nothing for Maxwell’s demon.

Is this utopia?

 Let us consider everything in detail.

To start with, let us calculate how much energy is contained in the air surrounding us and see whether it will be sufficient to move a car if it is extracted from the air.

Calculation: (the calculation is approximate, only an estimate, and does not take into consideration some details such as the change in the air’s thermal capacity when the temperature changes)

 The air’s thermal capacity C = 1 kJ/kg*K

Density of the air p = 1.28 kg/m³

 Let us take the temperature of the ambient air as equal to 20 degrees Celsius.

Cooling 1 m³ of air by 50 degrees releases energy

E = V * p * C * T (1)

E = 1(m³) * 1.28 (kg/m³) * 1 (kJ/kg* K) * 50 (K) = 64 kJ (2)

 The weight of an object multiplied by its thermal capacity and multiplied by the difference between its initial and final temperature.

A car needs 250 kJ of energy (10 grams of petrol) to move 100 m at a velocity of 60 km/h (the petrol’s calorific value = 46 MJ/kg, the efficiency of the car’s internal combustion engine is 40 to 60 %).

A car with an air inlet that has an area of 0.5 m² will pass 50m³ of air through while moving this distance. By cooling all this air by 50 degrees, it is possible to release

E = 50 (m³) * 1.28 (kg/m3) * 1 (kJ/kg * K) * 50 (K) = 3,200 kJ (3)

 As we already know, Maxwell’s demon also needs energy to work, and therefore some of this energy will have to be given to him. Some of the energy will be lost, but 3,200 – 250 = 2,950 kJ (92 %) is a huge reserve. Because there’s a huge reserve, the area of the air inlet and the exhaust temperature can be varied.

Let us say that with an air inlet with an area of 0.3 m² (which is roughly equal to the area of the ordinary car’s radiator) and an exhaust temperature of minus 10 degrees, we will have the following amount of energy

E = 30 (m³) * 1.28 (kg/m3) * 1 (kJ/kg * K) * 30 (K) = 1,160 kJ (4)

 As you can see, the reserve of energy is still quite high.

The calculation shows, then, that if we manage to extract energy from the air, it will be quite enough to move a car.

 And now to the main component of the hypothetical car – its energy device, the engine.

What kind of device should it be, to be able to take away energy from a cold body and give it to a hot one, thus violating the fundamental law of the universe – the Second Law of Thermodynamics? Does such a device exist? Yes, as it turns out! It was invented almost 80 years ago. It is the vortecal generator or Ranque’s vortex tube. It was patented by French engineer Georges Ranque in 1933. Everyone apart from the very disinterested should know by now that the device does work and even generates more energy than it consumes.

It’s true, though, that so far they have managed to generate from such devices only thermal energy, which exceeds the expended energy by a factor of 1.5 to 2.

 Does this mean that it violates the law of conservation of energy? For its output-input ratio calculated with the usual formula (generated energy divided by expended energy) exceeds 100 %. The output-input ratio of such machines is now cautiously called “efficiency” (even though this parameter is not the output-input ratio, in fact) to avoid coming into conflict with the fundamental laws of physics.

However, this does not change the meaning. They generate more energy than they consume, and what’s more they separate the flow of gas or liquid (the working medium (agent) for these machines) into two flows: hot and cold. It’s noteworthy that that the cold flow is colder than the initial (incoming) flow of the working agent, and the hot flow is hotter, which is, as the theory goes, what is to be supposed to be done by the oft-debated Maxwell’s demon that we have mentioned already.

Performing calculations for the machines is no trivial task, and no-one has done them with precision as yet, which is evidently the stumbling block for introducing them universally.

 In this case, by the way, another interesting aspect and a reason for such insignificant use of Ranque Tube should be considered. It should be noted that this device is mostly used only as refrigerator (thermal pump). However, the majority of the users of these units have acknowledged that these machines’ efficiency is extremely low and that is why they are not often used.

Nevertheless, let us consider this aspect more attentively.

Unlike heaters, in other words, the units transforming any type of energy – electrical, chemical or kinetic, into internal energy (that is, into heat), those devices that are used to cool anything lower than the temperature of environment are heat pumps (refrigerators).

In this case, they should not be mistaken for coolers in which objects are cooled down to the environment’s temperature only by transferring heat without using external energy. These include radiators of all types, heat exchangers, cooling ponds and water cooling towers at heat power stations and so on. The only energy that is used in this case is the energy that a ventilator or a pump uses to force the circulation of cooling agent (air, water, machine oil and etc). However, the temperature in any part of this cooler in no case drops lower than the environment’s temperature (according to the second law of thermodynamics).

 In heat pumps, heat is a mandatory “co-product”, which is simply thrown out as wastes into the environment. However, we keep forgetting that this heat is energy, and by throwing it out we only decrease the unit’s efficiency (this energy is represented in the dominator of the performance index formula).

But it is indeed the main principle of refrigerating devices’ work – unless we throw out “extra” heat, we will not get the cold that we need. This energy is in no way utilized yet because, in most of the cases, it is of low-grade energy against the environment and extremely inefficient, and it is often just useless to try to utilize it with available means.

At the same time, the following fact is interesting – the more we want to cool an object, the more heat we will have to throw out, thus decreasing the device’s efficiency – this is obvious, isn’t it? In addition, if the hot air flow “thrown out” by Ranque Tube, which is used as a refrigerator, has significant pressure and speed, then it also decreases the efficiency of this kind of refrigerator.

By the way, one may think whether the term “efficiency” can be applied (in a sense to which we got used to) to heat pumps at all. The thing is the product we get from heat pumps is cold. In other words, it is the negative energy against the environment. At the same time, the efficiency, which is calculated with the standard scheme (the derived energy divided by the consumed energy), takes on negative value. In the same way, by the way, the efficiency of a heat pump, which is used as heat source, proves to be absurd. It usually becomes more than 100 %!… It depends on the type of a heat pump is being used, be it Ranque Tube, heaters using Peltier effect or any other devices.

(V.M. Brodyanksiy “Exergic analysis. Energy: the problem of quality” “Íàóêà è Æèçíü” [Science and Life] 3, 1982) (http://www.erg.glb.net/exergy.doc)

 Should one be surprised that the efficiency of this kind of refrigerator will decrease as we cool the object more and not use in any way the energy that is thrown out in the form of heat. Further, a method of using this energy to increase the efficiency of a device will be offered.

 However, let’s get back to the principle of Ranque Tube.

There are many theories for these machines, explaining the reason why one flow cools down and the other heats up. One theory says that the flow heats up because of friction with the walls of the device, but that does not explain the cooling process.

Another theory explains this as an adiabatic expansion of one part of the gas and contraction of the other part, but this does not explain the appearance of additional energy.

 Some theories for liquids (for water in particular) explain this as the emergence of cavitation, others as resonance, and still others as interaction between free molecules of hydrogen and oxygen that are present in water, or, on the contrary, as bond disruption. There are even theories explaining this as extraction of energy from a “physical vacuum” that emerges while the device is working.

These effects may take place to a varying degree in Ranque’s tube even though they often come into conflict with one another.

 We’d like to offer our own theory, which we think does not conflict with any of the theories described above, and which explains this effect from a single standpoint for both liquids and gases.

To do this, we will need some additional data.

The velocity of molecules of the air at 0 degrees Celsius is equal to 400 m/s. However, this is the root-mean-square velocity.

There are fast and slow molecules in any gas (in the air, in particular). Their distribution by velocity is determined by a graph – Maxwell’s distribution graph (Fig. 1). It was precisely this distribution that Maxwell used as the basis to voice his supposition about the possibility of sorting molecules using the hypothetical “demon”.

Fig. 1. Maxwell’s distribution by molecular speed

(on the X-axis – the absolute velocity of molecules, on the Y-axis – their relative quantity in a volume of gas)

Let us imagine for a minute that we have the “demon”. Let us see what he can accomplish by sorting molecules of air by velocity.

Logic suggests that we can extract the maximum amount of energy by dividing a volume of air into two parts strictly down the peak in Maxwell’s graph. The graph shows that the volume of hot air will be somewhat greater than that of cold air. It should also be noted that with such a division neither the temperature of the hot flow nor that of the cold one will have their maximum values.

 To increase the temperature of the discharged hot flow, we will need to shift the dividing point (“the working point”) to the right. The shift will increase the hot flow’s temperature whereas its volume will decrease because the percentage of high-velocity molecules in it will increase but their absolute quantity will decrease. As for the discharged cold flow, its volume will increase and its temperature will also rise.

 It is difficult to say what maximum temperature the discharged air flow could reach in this way. Judging by the graph, it is unlimited. But in practice, there must be a limit. All the more so as the quantity of discharged hot air will keep decreasing and it will be increasingly difficult to measure its temperature without the measurements themselves causing errors in the flow. For example, how can we possibly measure the “temperature” of the fastest molecule that we can find in the surrounding air?

 If we need to lower the temperature of the discharged cold air, the “working point” will have to be moved to the left. The temperature of the discharged cold flow will thus tend towards absolute zero (-273 Celsius), while its volume will simultaneously decrease to almost zero too.

 But let us return to the process of extracting the maximum energy from the air (this is what we need). The root-mean-square velocity of the molecules that have entered the hot flow will be approximately 700-800 m/s, which approximately corresponds to 500-600 degrees Celsius. In the cold flow, the speed will be approximately 200 m/s, that is a temperature of minus 100 degrees.

(These values are approximate, they may be corrected in further drafts of the article.)

 Let us now consider possible processes taking place in Ranque’s tube. Let us not go into details about its design. All the more so as there are a large number of them. Let us consider it schematically, in longitudinal and cross-section.

Fig 2. Ranque’s vortex tube (scheme)

(The dotted line shows the provisional border between the tangential and axial flows; the arrows show the movement of air flows.)

An energy carrier (air hereinafter) is injected into the tube under high pressure. It will spiral along the tube’s wall, turning into the tangential flow. Thanks to the tube’s design, the axial flow appears in the tube’s centre. It moves in the direction opposite to the tangential flow.

 The ratio of the volumes of the two flows is usually 1:4, 1:2 and 2:3, depending on the initial pressure of the compressed air, its temperature and the device’s design. That is to say, there is usually more hot air than cold air. Therefore, “the working point” for sorting molecules is somewhere to the left of the middle of the graph.

 What happens in the gas flows? The velocity of the flows’ motion adds to the velocity of the Brownian motion. However because on average the fast moving molecules travel greater distances than the slow-moving molecules do, the probability of them being caught in the tangential flow is higher than for slow molecules.

An example of this could be a conventional still molecule located in the centre of the axial flow. Its velocity will be set by the speed of the flow itself. The molecule, as well as other molecules that do not wind up in the tangential flow while the axial flow moves to the exit from the device, will be discharged within the axial flow and will determine its temperature.

Let us move on. A fast molecule, once it has been caught in the tangential flow, is now even less likely to return to the axial flow because in addition to Brownian motion, it is now impacted also by the centrifugal forces that seek to move it away from the centre and thus prevent it from returning to the axial flow.

Therefore, fast molecules will accumulate in the tangential flow while slower molecules will stay in the axial flow. Due to this, the average velocity of the molecules in the tangential flow will be higher than that of the incoming air and, therefore its temperature will be higher while the opposite will be true for the axial flow.

 However, the linear velocity of molecules cannot be used in the calculations for such devices. It is necessary to use for these purposes the speed of diffusion, which is considerably less than the average velocity of the molecules. But this does not impact the principle of sorting molecules by velocity. And the high-velocity molecules are still more likely to get into the tangential flow than low-velocity molecules are.

Well then? We have learned how to extract energy from the air. But our energy device seems to lack something… This is what it lacks. The device consumes external energy – compressed air. But because more energy is produced at the exit, why not return part of the energy to the entry point, thus ensuring feedback between the flows of the energy carrier?

How? Simply by returning part or all of the hot flow back into the compressor (Fig. 3). This will increase the pressure and temperature of the incoming compressed air and, therefore, will increase the tangential speed and the molecule-sorting effect.

Fig. 3

It should be remembered that besides the compressor must receive air from the atmosphere because that is where we remove the energy from. In addition, no losses of heat (energy) should occur in the compressor, i.e. the air compression should be adiabatic. Due to this, the air may heat up to significant values (500-1,000 degrees Celsius). But the temperature of the fuel mixture in the cylinders of the ordinary car engine is also about 800 degrees Celsius.

How to take away the excess energy to move the car? By using the difference between the temperatures of the hot and cold flows to work a thermal machine? Under no circumstances! Otherwise Carnot’s formula will “eat up” all the energy that was extracted with such great difficulty.

One possible way of removing energy is to install a turbine somewhere on the periphery of the tangential flow. It will simultaneously feed both the car engine and the compressor. With efficient feedback, the speed of the tangential flow will be sufficiently high to cover all of the machine’s energy expenditure. After being processed in the turbine, the tangential flow should have a lower speed, low pressure and lowered temperature.

And now look here …

Fig. 4

Here it is – Maxwell’s demon in the purest form, as created by the nature itself!

Let us look at the tornado. The quantity of energy in the planet’s noosphere is always practically constant. However, clusters of energy (whirlwinds, tornadoes, typhoons) appear in it all the time. A tornado “pumps out” energy from the surrounding air, which has greater entropy than the tornado itself, and decreases the entropy inside itself! Who can argue with this?

It remains a mystery how under such circumstances one could possibly conclude that entropy always grows. But this is the Second Law of Thermodynamics – the Emperor of all of the laws of physics, which has set the direction of developing energy engineering on the planet for almost a century and a half!

Because the authority of the scientists who formulated this law is extremely great, thus far no-one has had the courage to say: “ But the Emperor has no clothes on! ”.

 The similarity between the tornado and Ranque’s tube is almost complete. The middle of the tornado, its “eye”, cools down considerably with a considerable drop of pressure inside it. There appears an ascending flow, which is directed upwards from the earth’s surface. The tornado receives additional energy from the near-surface air sucked in at its base.

And how do you like this one? Is this just coincidence, isn’t it ?

Fig. 5

Spiral, whirlwind, cyclone, a tornado – SPINNING – this is the very essence of the indefinite existence of the Universe!

Spinning can start from anything whatsoever, from the spinning of the Earth on its axis, its spinning around the Sun, the Sun’s spinning around the centre of the Galaxy, etc.

This effect of energy redistribution manifests itself at any speed of spirally-twisted matter. It increases to a greater degree when the speed increases. After one vortex breaks up, another one appears, which again redistributes all the energy, and so on ad infinitum.

In the next article we will reveal how the “demon” turns into an “angel”.

Translated and edited by

Bibliography:

1. V. Brodyanskiy “Exergetic analysis. Energy: the Problem of Quality”, Nauka I Zhizn, No 3, 1982
2. N. Gulia “In Search of an Energy Capsule”, a web publication
3. E. Oparin “Physical Foundations of Fuelless Power-Engineering. The Limitation of the Principle of Entropy Increase”, Moscow, URSS, 2004
4. L. Landau, A. Kitaygorodskiy “Physics for Everyone”, Nauka, 1974.
5. B.M. Yavorskiy, A. A. Detlaf, “Reference Book on Physics”. Publisher: Nauka. The main editorial office on physics and mathematics literature, Moscow, 1979.

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