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1) Did it take energy to compress the gas into the donor tank?
2) Could we get some of that energy back by putting a pneumatic motor/generator in the whip line between the tanks and driving the generator by the pressure differential during the fill?
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Sure
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3) Would the recipient tank and donor tank equalize pressure regardless of whether we put a pneumatic motor/generator in the whip line?
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Depends on details of the generator, but usually yes.
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4) What happens to the energy we could have extracted from the gas with the pneumatic motor/generator if we don't put the pneumatic motor/generator in the whip line?
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A part of it heats the low-pressure tank, another part is lost as friction in the whip line.
The pressure-drop happens in the donor tank only, in the other tank air gets compressed.
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If the two gases were allowed to freely mix or exchange heat energy, the total gas would come to the same original room temperature.
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This could depend on details of the expansion process.