Recover energy from temperature

[MarkE]

rc4 this looks like a gear pump.  Are you thinking that somehow this pump will run itself to increase the pressure difference?  The external forces will operate so as to attempt to equalize the pressures.

[rc4]

Look at images please, it's not a gear pump, gear don't press gas. I use gears only for prevent the gas at 1 bar to move inside vacuum. Gas press volume, and I recover energy inside vacuum recipient. If you see a torque somewhere I will be ok, but here I don't find a torque, so where is lost energy ? The only energy I can see it's lost is the small space between teeth when gears are in action. It can be very low:

http://commons.wikimedia.org/wiki/File:Involute_wheel.gif

You can imagine big radius for wheel, like that the volume lost for each volume is very low. There are gaskets inside teeth of gears.

g5 image: W = win energy, L = lost energy. If I consider gear/gear move in => lost energy, the sum is 0 and is I consider gear/gear move out => lost energy, the sum is 0 too. Look at direction of gears.

[MarkE]

Look at images please, it's not a gear pump, gear don't press gas. I use gears only for prevent the gas at 1 bar to move inside vacuum. Gas press volume, and I recover energy inside vacuum recipient. If you see a torque somewhere I will be ok, but here I don't find a torque, so where is lost energy ? The only energy I can see it's lost is the small space between teeth when gears are in action. It can be very low:

http://commons.wikimedia.org/wiki/File:Involute_wheel.gif

You can imagine big radius for wheel, like that the volume lost for each volume is very low. There are gaskets inside teeth of gears.

g5 image: W = win energy, L = lost energy. If I consider gear/gear move in => lost energy, the sum is 0 and is I consider gear/gear move out => lost energy, the sum is 0 too. Look at direction of gears.

If your mating gear tooth faces  are not gas tight then it just leaks.  If they are gas tight then it is an air pump.  In either case as air pressure changes there will be loss to heating / cooling.  This machine like the last one is subject to the Second Law of Thermodynamics like all others.

[rc4]

There is no gas inside between tooth, it's not an air pump. But, if energy is not lost here, where is it ? I can pass volume with 1 bar (look at 4 images please) inside vacuum container without need energy and I can pass volume of 0.5 bar inside container of 1 bar without energy. Could you help me to find the error ?

[MarkE]

rc4 if the gears rotate then volume between any pair of teeth on one gear and the meshing tooth of the other gear varies as the two gears rotate relative to one another.