Could this device theoretically continue in motion forever? If not, why not? (click below for images):
- The device is less dense than air, so it rises. The propeller spins slightly (maybe) charging the device battery.
- After rising some distance X, the device compressor turns on to deflate the device.
- The device becomes more dense than air and falls quickly spinning the propeller, charging the battery.
- After falling X, the compressor releases and the device becomes less dense than air, going back to step 1.
The logic here is that there must be some distance X that the device can rise than will generate more energy than what is needed by the compressor.
Here is the underlying math to help:
$$PE = mgh$$
- $m$ = mass of the device
- $g$ = coefficient of gravity
- $h$ = height device has traveled up
- $PE$ = potential energy of the device as it travels up
$$CW = nRT(\ln(V_b) - \ln(V_a))$$
- $n$ = number of moles of gas in balloon of device
- $R$ = ideal gas constant
- $T$ = temperature of the gas
- $V_b$ = volume of the balloon after compression
- $V_a$ = volume of the balloon before compression
- $CW$ = work to compress the balloon
As $h$ increases $PE$ increases but $CW$ stays the same resulting in energy gain of the system.