I wasn't the first one who ever figured this out. That's why there have been so many inventors making incredible claims, ever since the dawn of the industrial age. It's obvious to an intuitive inventor but to a paper pusher like me who believes what he is told, I'd always assumed that a compressor puts its own work into an air tank and that's where the energy of compressed air comes from. The truth has been so effectively wiped out of textbooks for so long now, that even very intelligent and well-trained engineers have never heard it. It's one of those things that, if not explicitly stated, no one is going to notice.
Q: Where does the usable energy in compressed air come from?
A: Compressed air energy is solar energy. It comes from the sun or any other source of atmospheric heat.
The implication of this statement, which you will find paraphrased in many of the textbooks quoted below, is that the source of compressed air's ability to do work is the heat it got from the sun. Here is what the textbooks said back when textbooks had something to say, so you can judge for yourself.
The U.S. Patent Office gives patents to designers of self-fueling air engines all the time. The patent office will not grant patents for perpetual motion machines that have no energy source, and although neither the patent office nor the patentees are forthcoming with the energy source that make these machines patentable, when you see how many of these patents exist, you have to know that something is up. Here's the documentation proving the Solar-Pneumatic Connection.
In compressing the gas ...All of this work (assuming a frictionless piston and no loss of heat) is converted into heat in the compressed gas. Thereby the temperature of the gas is increased. When the gas is permitted to expand, it does work .... Its heat content and temperature are thereby decreased accordingly.
Practical Heat, Terrell Croft, New York: McGraw-Hill, 1923, p. 189.
Phenomena of Compression. Thermodynamics is the science of the relation between heat and energy. It is based on two fundamental laws, only the first of which has a bearing on the discussion of compressed air.
The First Law of Thermodynamics states that where heat is converted into mechanical energy, or mechanical energy is converted into heat, the quantity of heat is exactly equivalent to the amount of mechanical energy.
This law demands that when work is done upon a volume of air in compressing it from a lower to a higher pressure, a quantity of heat must be developed exactly equivalent to the energy expended in compression.
In other words, when a volume of air is compressed to a higher pressure, all the work done upon that air volume is converted into heat; and that heat acts to increase the temperature of the air volume, whether the process of compression be slow or fast.
Compressed Air, Lucius Wightman, Chicago: American Technical Society, 1914, p. 6.
Availability. By the First Law of Thermodynamics and the principle of the Conservation of Energy, a complete accounting can be made of all relevant forms of energy entering, leaving, or contained in the compressed air....
However, the First Law, being simply an energy balance, provides little insight into the nature of the energy. For example, it takes no account of the capacity of energy to do useful work or of the inevitable dissipation, or degradation, of energy that accompanies all real processes. For this the Second Law of Thermodynamics is required.
The Second Law has an undeservedly poor reputation, mainly because of its apparent abstractions and its seeming irrelevance to practical problem solving. By combining the concepts of the First and Second Laws in a practical manner, energy may be classed as "available", "unavailable" or "degraded". Basic to this classification is the concept that the purpose of energy is to do useful work. Energy that is capable of doing work is "available," that which cannot be employed for work is "unavailable" and the available energy that is eroded by friction or other dissipative processes is "degraded."
The work potential of compressed air is related to its initial and final states. For example, an air receiver charged to a high pressure clearly can provide more work if the air is expanded in a tool and exhausted to atmosphere than if it were exhausted at a higher pressure. It is equally clear that the work potential will be reduced if there is a pressure drop in the piping between the receiver and the tool.
Moreover, there is no doubt that the work potential will be wasted entirely if the air is allowed to expand directly to atmosphere.
The availability of compressed air One of the sometimes puzzling aspects of compressed air, which is not explained by the First Law, is that in most cases the compressed air arriving at the tool contains no more energy than the atmospheric air.... for an isothermal (constant temperature) process the energy possessed by the air is unchanged .... The heat equivalent of the input work is removed by cooling. It might appear therefore that compressed air has been obtained with no net expenditure of energy and that the eventual work is "free." This is manifestly incorrect, but it is a fact that in compressed air installations heat is removed from the air by cylinder jacket or internal cooling and by intercoolers, aftercoolers and by heat transfers from surfaces. The result is that shortly after compression storage and treatment, the compressed air has the same temperature as at the inlet to the compressor.
The South African Mechanical Engineer, vol. 35, August 1985, "A different view of compressed air," Dick Shone.
Case of Isothermal Compression. It will be shown presently that the most economical compressor mechanically would be one in which heat is abstracted during compression, so that the compression is isothermal. In that case the effective work is...exactly equal to the absolute work of compression ...But the heat abstracted during compression is equal to the same quantity. Hence the curious result is arrived at that in the most economical compression, the effective work of compression is entirely abstracted as heat and wasted. All the compression does is to put the air in a condition to do work in a motor at the expense of its intrinsic energy. In that way there is obtained an amount of work nearly equal to the work done in compression. But the work in the motor is not strictly the restoration of the energy expended in the compressor, but energy borrowed from the air....
On the Development and Transmission of Power from Central Stations, William Cawthorne Unwin, London: Longmans, Green. 1894.
Important Fundamentals. We know that work is a force overcoming resistance and is measured in foot-pounds. Energy, which exists in a number of forms, is the capacity to do work and can also be measured in foot-pounds. Heat, measured in BTU, is one form of energy. Power is the rate of doing work, the unit being the horsepower, or 33,000 ft-lb per min. Temperature is an indication of the direction in which heat will flow if it has the opportunity to do so. The internal energy of air depends on its temperature.
Work done in compressing air increases the air's internal energy and raises its temperature. As the compressor cylinder and piping are heat conductors, the whole of this heat soon dissipates to surrounding bodies and the air's internal energy gradually returns to its original value as the temperature falls to initial value.
Although 1 lb of air at 1,000 psi and atmospheric temperature has no more internal energy than 1 lb at atmospheric pressure and temperature, still the energy contained in the air under pressure is available for use because this air can expand, suffer a loss of pressure and temperature, and give up a portion of its internal energy. The greater the fall of pressure during expansion, the greater the fall in temperature and the greater the amount of internal energy available for use. The energy used in compressing air is not actually stored up in the air unless the heat of compression is retained. A portable compressor without cooling facilities furnishing air for immediate use approaches this condition. This internal energy depends on the temperature alone, and the energy that may be available for use depends on the fall of pressure and drop in temperature permissible.
Air Compressors, Eugene W. F. Feller, New York: McGraw-Hill, 1944, p. 400-401.
It should be noted that the heat of compression, as already explained, represents work done upon the air for which there is usually no equivalent obtained, since the heat is all lost by radiation, before the air is used.
Audel's Handy Book of Practical Electricity, Frank D. Graham, New York: Audel, 1942, p. 5607.
It is interesting to note that, from the viewpoint of the conservation of energy, isothermal operation is not as advantageous as adiabatic. The object of using the air expansively is to utilize some of the internal energy of the working substance which enters the engine. If the expansion is isothermal no work can be done at the expense of such energy; on the contrary, heat equivalent in quantity to the work done during the expansion period must be supplied from an external source. With an adiabatic expansion, however, all of the work done during such an expansion will be at the expense of the internal energy of the gas.
The apparent discrepancy between these two cases is due to the fact that during the isothermal expansion it is assumed that the required amount of heat is supplied from the atmosphere, and that it costs nothing, and may, therefore, be freely used without decreasing the commercial efficiency of the process.
Heat-Power Engineering, William N. Barnard, Frank O. Ellenwood, Clarence F. Hirshfeld, 3rd ed., New York: Wiley, 1926, p148.
There is nothing abnormal to an efficiency greater than 1, when reheating is used; this will occur (regardless of pipe and other friction) whenever the temperature of reheating is higher than the temperature of compression.
Modern Machinery, January 1899, "The Two-Pipe System of Air Compression", A. E. Chodzko, p. 11.
In isothermal compression there is no gain of internal energy, or in pressure energy, since the temperature remains constant...therefore by the Conservation Law, the entire work of compression is discharged to the cooling water.
On these considerations it would appear useless to compress a gas; actually, however, the increased pressure of the gas enables it to expand to a lower pressure...
The Theory and Practice of Heat Engines, Digby Alfred Wrangham, The Cambridge University Press, p. 88.
Effect Of Loss Of Heat, Generated During Compression, On The Ultimate Useful Energy Residing In A Given Quantity Of Compressed Air
By an accepted law of thermodynamics, work and heat are mutually convertible at the ratio of about 778 ft.-lb. of work for every B.T.U.
In Article 41a it was stated that the work expended in compressing air is all converted into heat. According to the law quoted, we should expect the compressed, and therefore heated, air to be capable of performing useful work, equal to the amount expended in compressing it. Neglecting friction in the air engine, this would actually be the case, if the compressed air could be used immediately after compression and before it has lost any of its heat.
If, on the other hand, the compressed air be allowed to cool down to the temperature which it possessed before compression, as happens in all compressed air installations, it would seem logical, by applying the same law quoted above, to reason as follows:
Since the work of compression is all converted into heat, the ability for doing useful work must have disappeared after all this heat has been abstracted.
In the following articles it will be shown:
a. That the work of compression is all converted into heat.
b. That, after all the heat of compression has been abstracted, there still remains in the compressed air a certain amount of energy for doing useful work.
c. That this is due to the energy residing in the air before compression.
Compressed Air , Theodore Simons, 2nd ed., New York: McGraw-Hill, 1921, p. 113-123.