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A Stirling Engine is an engine that runs on a temperature difference. It was invented by an eccentric Scottish clergyman by the name of Robert Stirling around 1816, and believe it or not, the principles behind it were not explained until 1850 by Professor Rankine. It predates the internal combustion engine by a fair margin.
There are two basic types:
This one has a single cylinder filled with gas (usually helium or hydrogen but dry air will do) with two pistons. One end of the cylinder is made hot, the other cold. One piston is a tube (the displacer) and moves the gas from the hot part to the cold part and vice versa; it does not seal. The other piston (the power piston) goes in and out as the gas is alternately heated and cooled. I think the modern version incorporates a wad of mesh heat exchanger material in the cylinder, which increases efficiency by pre-warming the gas as it flows from the cold end to the hot end.
This design simply moves gas between a hot piston and a cold piston, extracting energy as the gas warms up and cools down.
Whichever model you pick, it is very efficient machine, can be made small enough to power a bicycle using sunlight. It has very few wearing parts and works over temperature ranges great and small.
These engines may be run in parallel or radial configurations and -- depending on design -- may be more efficient with linear or rotary generators.
Using a low-boiling-point liquid to transfer the heat is an adaptation once considered for generating power from the temperature difference between the surface and depths of Earth's oceans. While this is not a true Stirling-cycle engine, it may be useful in lunar power storage.
One of the chief difficulties with heat storage is the low thermal conductivity of the moon. This prevents us from driving heat into piles of regolith, and hampers heat withdrawl from them. To be practical, either a solid or liquid heat storage medium is required. Many options exist for the composition of such heat storage media.
Another interesting technique is to use the waste heat generated by the lunar habitats to generate some power in the lunar night. Though this is not a significant source of power, every bit helps.
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