Recover energy from temperature

[rc4]

Yes, I understood the torque is not the same, one part act on small radius for one gear and one part act on big radius for another gear.

But here, in the image, if I cancel pressure when the tooth is inside pressure = 0, all the time gas act for 4 surfaces so no torque, and for cancel pressure of this small volume of gas I lost less energy no ? Could you explain please ?

[MarkE]

Yes, I understood the torque is not the same, one part act on small radius for one gear and one part act on big radius for another gear.

But here, in the image, if I cancel pressure when the tooth is inside pressure = 0, all the time gas act for 4 surfaces so no torque, and for cancel pressure of this small volume of gas I lost less energy no ? Could you explain please ?

Your illustration shows operation of a gear pump.  If the lower gear rotates CCW gas is being pumped to the lower left.  If the lower gear rotates CW, gas is being pumped towards the upper right.

[rc4]

No, it's not a pump, look at images, where tooth are one inside other, I don't pump gas, I use gears like gasket. Each tooth has a valve, this valve recover PdV for each step. The only place I can loose energy is at the middle, but if the volume between teeth (at the middle) is near 0 (image big radius for gears), I don't lost PdV.

[rc4]

I understood, it's because gaskets are usefull for one gear, this not works for second. So I lost that I won :  2 PdV

Now if I put the gasket in the center of blue arrow:

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

I compute torque, it must be the same energy than 2 PdV.

R1 = small radius of gear
R2 = big radius of gear
P = 100 000 Pa


I found the result in the second image, so 1/6 of PdV, where is the error please ?

[rc4]

Another idea:

Take a screw (worm drive) with N starts (increase lead). The thread is used for move out vacuum objects and recover energy from temperature. The torque I need to give of the screw is T/N with N the number of starts and T the torque I need with one start. In one turn I can move out the same volume of vacuum object than with one start (The slope change when N increase) but here the torque is lower and divided by N. I drawn an image with 3 starts for example. Imagine walls of threads like very (very) thin for put N very high.

The part of thread inside vacuum: add wall for full the thread to obtain a cylinder (a perfect cylinder). Like the screw turn, all object with vacuum in it move up. I need to give a torque for turn the screw, but I recover N times I need to give.

Second image: multiple starts, but imagine thin of thread very thin (where the is solid on the thread)

Third image: I need to give a torque of the slope of one start only, but the lead so the volume of vacuum move out is multiplied by 2. The energy needed fot the torque is C*Θ, Θ = 2pi for one turn. C is the torque for one slope, but the lead is multiplied by 2 so the volume of vacuum object is pi(R2²-R1²)*lead.