Here is an idea that pretend to be a perpetum mobile. Please find out where is a problem:
- Let say that we have large container of monoatomic ideal gas that is thermally couple with environment
- In the center we have a cylinder that is free to rotate around it’s axis positioned vertically. Let assume that cylinder is perfectly isolated and can spin frictionless w/o disturbing container gas.
- We have also found a way to install directional nozzle that is able to inject gas jet into the cylinder. Nozzle is stationary with the container and injects gas tangentially at the cylinder circumferential wall.
- We start experiment with container in thermal equilibrium with environment and cylinder filled with vacuum spinning very fast.
- The gas is going to enter cylinder through the nozzle. Nozzle is going to convert thermal energy of gas into directional stream of atoms. If we are using supersonic Laval nozzle, I can see web references describing jet stream entering vacuum chamber with 7deg angle deviation and 1% of speed variation in other words: very directional jet.
- Let assume that cylinder is spinning at the velocity that equals that of entering jet speed at the circumference. Basically what observer sitting inside cylinder will see is only residual speed of dispersing gas. And here is a place where a magic happen: from the point of view of container gas leaving through the nozzle caries high entropy and high temperature. From the point of view of the cylinder it receives gas of very low temperature, with low entropy.
- Entering gas is going to be a slowest, coldest point within cylinder confinement. With time gas is going to accumulate and fill container. Assuming that temperature is below evaporation point liquefied gas is going to fill the bottom part of cylinder. The liquid is going to conform to the parabolic shape as per rotational force. Above the liquid gas vapor pressure is going to reach equilibrium with low temperature atoms injected by the nozzle.
- Last, we need only to provide a hole in the center of cylinder that is being open once liquid level is higher then pressure inside container. We keep escaping liquid rate equal to the amount of gas introduced to the cylinder. The conservation of the rotational momentum is going to provide spinning torque, since new material is introduced at the cylinder edge with high angular moment, the escaping liquid has almost none.
- The escaped liquid is going to evaporate inside container and draw the heat from the environment maintaining constant pressure. And the whole process keeps going, going, ….
There are some tricky points here such as lack of friction and perfect insulation. This is just to neglect secondary issues, since I don't want to discuss engineering but physics.
I did some back of the envelope calculations to illustrate a point:
- Gas Xe
- Molecular speed of Xe at 20C(293K) 1atm – 236 m/s in container frame of reference
- Residual speed left after nozzle expension – 28m/s corresponding to 5K in cylinder frame of reference
- Cylinder with radius 3000m and height of 3000m will maintain while spinning at 0.75 rpm speed of 236 m/s at circumference and centrifugal acceleration 1.9G allowing for paraboloidal liquid surface of 2800m in height to fit inside.
-al
- Let say that we have large container of monoatomic ideal gas that is thermally couple with environment
- In the center we have a cylinder that is free to rotate around it’s axis positioned vertically. Let assume that cylinder is perfectly isolated and can spin frictionless w/o disturbing container gas.
- We have also found a way to install directional nozzle that is able to inject gas jet into the cylinder. Nozzle is stationary with the container and injects gas tangentially at the cylinder circumferential wall.
- We start experiment with container in thermal equilibrium with environment and cylinder filled with vacuum spinning very fast.
- The gas is going to enter cylinder through the nozzle. Nozzle is going to convert thermal energy of gas into directional stream of atoms. If we are using supersonic Laval nozzle, I can see web references describing jet stream entering vacuum chamber with 7deg angle deviation and 1% of speed variation in other words: very directional jet.
- Let assume that cylinder is spinning at the velocity that equals that of entering jet speed at the circumference. Basically what observer sitting inside cylinder will see is only residual speed of dispersing gas. And here is a place where a magic happen: from the point of view of container gas leaving through the nozzle caries high entropy and high temperature. From the point of view of the cylinder it receives gas of very low temperature, with low entropy.
- Entering gas is going to be a slowest, coldest point within cylinder confinement. With time gas is going to accumulate and fill container. Assuming that temperature is below evaporation point liquefied gas is going to fill the bottom part of cylinder. The liquid is going to conform to the parabolic shape as per rotational force. Above the liquid gas vapor pressure is going to reach equilibrium with low temperature atoms injected by the nozzle.
- Last, we need only to provide a hole in the center of cylinder that is being open once liquid level is higher then pressure inside container. We keep escaping liquid rate equal to the amount of gas introduced to the cylinder. The conservation of the rotational momentum is going to provide spinning torque, since new material is introduced at the cylinder edge with high angular moment, the escaping liquid has almost none.
- The escaped liquid is going to evaporate inside container and draw the heat from the environment maintaining constant pressure. And the whole process keeps going, going, ….
There are some tricky points here such as lack of friction and perfect insulation. This is just to neglect secondary issues, since I don't want to discuss engineering but physics.
I did some back of the envelope calculations to illustrate a point:
- Gas Xe
- Molecular speed of Xe at 20C(293K) 1atm – 236 m/s in container frame of reference
- Residual speed left after nozzle expension – 28m/s corresponding to 5K in cylinder frame of reference
- Cylinder with radius 3000m and height of 3000m will maintain while spinning at 0.75 rpm speed of 236 m/s at circumference and centrifugal acceleration 1.9G allowing for paraboloidal liquid surface of 2800m in height to fit inside.
-al