- #1
JohnnyGui
- 796
- 51
I probably haven’t thought this through. A sideview of a closed container filled with air consisting of two vertical cylinders (with radius ##r_1## and ##r_2##) are connected by two horizontal tubes. The container is separated by a small and a large lid (red) that are circular and can move up and down freely. Furthermore, the small lid is connected to a handle that sticks out of the container to move it up and down. There is a pressure equilibrium; ##P_1 = P_2##
Pushing the handle down with a force ##F_1## makes the small lid move down by a distance of ##d_1##. The work done on the small lid would be ##E_1 = F_1 \cdot d_1##.
This would make the pressure ##P_2## increase and the large lid would undergo a force ##F_2## which makes it move upwards by a certain distance ##d_2##. According to the conservation of energy ##F_1 \cdot d_1 = F_2 \cdot d_2##.
Here’s the thing however. When pushing the small lid down, a vacuum arises in the upper container half which would counter the force ##F_1## and make the moved distance ##d_1## smaller than expected. At the same time, that same arised vacuum would support the force ##F_2## and thus make the moved distance ##d_2## of the large lid larger than expected. The work done on the smaller lid would therefore seem smaller than the work done on the large lid. Wouldn’t this vacuum thus break the conservation of energy ##F_1 \cdot d_1 = F_2 \cdot d_2##?