Recover energy from temperature is possible ?

neufneufneuf

I have another idea if you can help to find the error ?

The goal is to let gas to compress each volume from 0.5 bar to 1 bar without lost energy, after put this volume inside a container where there is 0 bar (or vapor pressure) without energy, after recover energy from depress gas from 1 to 0.5 bar and after pass this volume to the first container without lost energy.

For this, I use gears with teeth like drawing show. Gears don't give a torque or a force, they are only there for assume sealing. So the energy is not recover from gears but from volume when they pass from 1 bar to 0.5 bar: PdV.

For move in a volume inside vacuum container, I place 2 volumes of 1 bar inside a tooth of gear 1 or 2, I can pass without energy, no ?

For move out a volume inside 1 bar container, I place 1 volume of 0.5 bar inside a tooth of gear 3 or 4, I can pass without energy, no ?

Gears 1 and 3 (or 2 /4) are fixed together so they turn at the same rotational speed w. But like radius of gear 3 is 2 times higher of gear 1, when I pass a tooth of gear 1, I pass 2 teeth of gear 3. So the number of volume that move in or move out is the same. I keep always the same number.

Now, gears must assumed sealing (no gas escape), it's possible to imagine gears with very few space between teeth in theory. So I can think the problem come from here.

There are gaskets inside teeth for allow to keep vacuum.

So what's wrong in this case ?









If I lost energy when gear/gear move in : the sum of energy with all gears is 0 in this case (W=win, L=lost):



And if you take the another case, the sum of energy is 0 too.

So where I lost energy?

neufneufneuf

I understood, it's because radius is not the same so torque not too.

But here where I lost energy ?

neufneufneuf

I understood, it's because this works only for one gear not two, so the energy lost is 2PdV.

Now, if I change the gasket and put it here:



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

Gasket is always in the center of blue arrow, look at animation please. Gasket "jump" like in animation (need to remove small area of gas).

I compute torque this will give the same than 2PdV but I found 1/6 + 1 of PdV of it not .

R1 = small radius of gear
R2 = big radius
Pressure = P = 100000 Pa

The function is (1-x)x:



Energy give by 2PdV is 6.3*10^7 and energy need for torque is 4.2*10^7

Plot of he function: