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High-pressure compressed air is a very paradoxical substance. It is often imagined as a reservoir of potential energy. Actually, absolutely all (excluding effects of non-ideal behavior) of the energy added to air by the compression process is rejected as heat if the temperature of the air is held constant. When the air is permitted to expand, it cools and produces much less work than was used to compress it. However, if the temperature of the air is held constant while the air expands, the heat energy which was rejected during compression is re-absorbed and used to produce the same amount of work as went into the compression.

That applies if the two temperatures are equal. If the expansion temperature is higher, the heat added to raise the gas temperature is stored in the gas as kinetic energy. When the gas is then allowed to expand while being held at the higher temperature, the gas will do more work than was done in compressing it. The gas (together with the apparatus containing it) obtained the additional energy required to do this work by gathering heat from the surroundings, and concentrating it into force applied in a single direction.

This is a more precise statement of the next paragraph: entropy increases on expansion into a vacuum. The energy content is the same. Continuing to expand further with no input of heat (adiabatic process), the gas can do the same amount of work regardless of the starting pressure if the ending temperature is the same.

Another paradoxical fact about compressed gas is that if it is allowed to expand into a vacuum, there is no change in the energy content. The available pressure is less, but the distance over which the pressure can act is correspondingly greater. This is exactly like the lever principle. Allowing gas to expand without doing work is just like moving the fulcrum of the lever to reduce the mechanical advantage. The force applied to the object at the other end of the lever is less, but the object is moved a greater distance.

Using compressed air to convert fuel to work without paying the entropy tax Edit

To convert all of the chemical energy would apparently require expansion into an infinitely large vacuum, so this article needs to be rechecked.

High pressure compressed air can be used together with biomass to extract an otherwise impossible fraction of the chemical energy in the biomass. This happens because the engine in which the biomass is burned is not required to return the compressed air to its initial state. Therefore, essentially all of the energy in the biomass can be converted to work as the compressed air expands. The required thermodynamic payback occurs elsewhere, at the hydrostatic Stirling cycle air compressor site, where the replacement air is compressed to high pressure using additional energy from a hot heat source and dumping very large amounts of energy into the cold heat sink.

Some of the high-pressure compressed air is diverted from the machine into storage tanks. Some uses of this air can be viewed as a continuation of the thermodynamic cycle, in which the expansion step is carried out for example in an automobile. If fuel is used to heat this compressed air before it is allowed to expand and escape at atmospheric pressure, then the thermodynamic constraints apply to the open cycle taken as a whole. In theory, all of the chemical energy of the fuel can be converted to useful work by an engine which uses both fuel and compressed air, because the energy entering the thermodynamic cycle includes both the heat absorbed by the stationary machine as it raises water, as well as the heat produced by burning fuel. Since the stationary machine delivers essentially all of the heat energy it absorbs from its heat source while raising water to its heat sink while lowering water and compressing air, it has already "paid" the thermodynamic toll which normally limits the efficiency of fuel-burning engines to much lower values.

The actual amount of energy extracted is simply the area under the PV curve of the part of the cycle included in the mobile engine. Now it seems reasonable to subtract the work which could have been obtained from the compressed air without heating it. That depends on the outside temperature. In extreme cold, it really pays to heat up the air. But then more fuel would be required to reach a given temperature.

Steam turbine vs. isothermal expansion of high pressure compressed gas Edit

The idea is to run a turbine and electric generator using high temperature high pressure compressed gas. The turbine would operate at constant temperature, running the gas across a set of blades as it expands and cools, then passing it through the heat source to reheat it before returning it to the turbine for the next pass.

Is the above better than isentropic expansion ususally used with turbines? It does seem to have a large area on PV chart. It is if the heat that is added to maintain the constant temperature is "free" ie extracted from the warmer environment as opposed to being supplied by the burning of fuel. If the expansion process occurs at a higher temperature than the environment (as in a steam turbine) the highest efficiency possible occurs only with isentropic expansion.Gruntguru 09:05, 8 March 2008 (UTC)

When the gas has expanded to atmospheric pressure, run it through a CCHEX to heat up input cold compressed gas. This would appear to consume all of the input heat, converting it to electricity except for non-thermodynamic inefficiency. Since the gas ends near the same temperature as it started due to the CCHEX, there isn't any extra heat left to do anything else with. The thermodynamic inefficiency applies to the process of compressing the gas.

Compress cold air using a hydrostatic compressor, running off gravitational potential of a liquid and dumping heat of compression into cold heat sink. But this requires operating an expansion driven pump using high temperature high pressure compressed gas to raise the liquid, which can't be water due to the temperature. It can't be a low melting metal either because of the cold temperature. It would probably have to be mercury, which is toxic and requires a closed cycle for the gas. The hot gas cannot be released but must be cooled very cold to condense the mercury vapor. This would involve a CCHEX large enough to hold the low pressure gas.

Can this extract more work than a steam turbine? It might. It might be operating against a lower temperature cold sink. The compressor may be more efficient, having no solid moving parts.

Why do steam turbines need to actually cool the output? So that heat is rejected from the cycle at the lowest possible temperature.Gruntguru 09:05, 8 March 2008 (UTC) Is it because they need a closed cycle of steam because the steam has to be very pure? So they have to actually condense it to water, which requires cool input air. They prefer to use evaporative cooling: water on the heat exchanger evaporates and carries heat away. Again, evaporative cooling is preferred to reduce the temperature of the cold sink to the lowest possible temperature. (wet bulb temp is lower than dry bulb) In dry climates where water is expensive, forced air is needed (and thermodynamic efficiency is reduced because wet bulb temp will be substantially lower in a dry climate (low humidity))Gruntguru 09:05, 8 March 2008 (UTC).

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