Merko, could you expand on how that turbine works a bit better?
Here's why. You don't seem to by analyzing the exhaust. If you are exhausting into the room where you are gathering the molecules from, it should be getting hit very strongly with millions of molecules. Now, when a single atom strikes the turbine from the other side, it's not going to be able to do anything.
If when you inserted this device into the room it had a hard vacuum in it, then you have a tiny temperature differential (lots of molecules moving energetically in the room, none, or very few moving inside your device). Your device may work for a few nanoseconds until you reach temperature equillibrium with the outside, but after that, the door will recieve more pressure from the inside (all those molecules plus the spring force) than the outside, and remain forever shut. The forces on the turbine will be in equillibrium, and it will not turn. But even here, won't all the work end up being done on the spring, where you will lose all the energy to heat losses?
On the other hand, if you are exhausting into vacuum, which you seem to be assuming, then you have introduced a temperature differential. You will get energy, but in exactly the same way you get energy from a water dam or a windmill.
I think the problem here is analyzing the system in isolation. You have to sum the energy over the entire system. The other side of the exhaust is part of the system.
ETA: the question about losing the heat to the spring is probably the most telling one. Why not just simplify this device to the front part - a door with a narrow opening, and replace the spring with an energy gathering device. No box, no turbine. Stick that in a room, and you'll see immediately that it won't work. The door will be hit equally from both sides. The enclosed box and turbine obsfucates this point, because we all forgot to analyze the forces on the turbine. Show me how a molecule has the ability to move all the way from the door, through the turbine, and out back into the room, despite losing energy to the door, spring, walls, and turbine.