Automatic isothermal expansion

I thought of a way to achieve isothermal expansion automatically.

In general, control over the PV-diagram expansion path in a hydrostatic heat engine is maintained by adjusting the height of the surface of the hydrostatic column above the surface of the liquid in the expansion chamber, so that the gas cannot continue to expand until it returns to the isothermal temperature. Part of this happens automatically if the hydrostatic column is a U-tube: the gas expands a little and stops because the pressure increases as the volume increases. Then some liquid must be removed from the column (perhaps by adjusting valves) before any more expansion can occur.

The new idea is a slanted tube with domes at carefully chosen heights. The tube and all domes start full of liquid. The volume of each dome is inversely proportional to the hydrostatic pressure. A load of gas is released into the smallest dome, at the bottom. Heat flows in and it begins to expand. When it expands to full volume, some gas escapes onto a lever arm, which rises and tilts the whole dome releasing all of the gas up to the next dome. The pressure there is slightly less and the volume is more, with the PV product constant, so the gas expands more and cools. It does not expand enough to trip the release. But as it absorbs heat and expands, some gas flows into the lever arm. The dome tilts and essentially all of the gas escapes. A weak spring tips the dome back partly. When more gas bubbles up from below, the dome moves back to the starting position. Work is captured during this process because the expanding gas displaces liquid.

Some work escapes when the gas moves to the next level because liquid moves down from the upper dome into the lower dome. Is it possible to avoid this?

There might be a similar mechanism for isothermal compression.

Originally I was thinking of completely static domes, but having them start full of liquid. Now I think the domes are just a holding area for warming gas. They stay full of gas all the time, avoiding the downward flow of liquid as gas rises. The top dome is refilled with liquid when the gas is released or taken for compression, and liquid is lowered doing work. Then enough gas to fill the top dome is released into the bottom dome. It expands and cools but the gas displaced to the next level is hot gas which has been in the dome for a while. The cold gas continues to expand as it warms, and additional hot gas rises to the next level. Probably the "dome" is really a long coiled pipe so that cold gas entering one end will displace hot gas out the other end. This also provides more heat-transfer surface area. Completely rid of the tilting domes.

Each level has volume inversely proportional to the hydrostatic pressure.  Thus, when a unit volume of gas is released into the bottom level, it displaces a unit of hot gas into the next higher (lower pressure) level.  Initially, that displaces just one unit of hot gas plus the expansion less the temperature decrease.  But as the temperature of the new gas returns to hot, the remainder of the initially present gas is displaced to the next level.  This cascades up to the top level, where a fully expanded unit of gas displaces that much liquid.  Essentially all of the energy absorbed as heat has been converted to work.  (But not in a closed cycle, or course).

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One Response to “Automatic isothermal expansion”

  1. Archimedes Submerged » Blog Archive » Automatic isothermal compression Says:

    […] Archimedes Submerged My water pump is good for things other than pumping water. « Automatic isothermal expansion […]

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