Can you help us analyze some of the thermodynamic and mechanical properties of a hypothetical compressor-and-tank system? Diagram and explanation provided.
My coworkers and I have been puzzling over a thought experiment involving the compressor and tank system in the following diagram:
Note: Valves I1, I2, O1, and O2 are check valves
; they only permit fluid to flow in the direction shown by their arrow. In this diagram, that direction is always toward the right.
At t=0, the system is completely filled with a gas and the valve at the top is open so that all parts of the system are at equal pressure.
To begin, the operator starts operating the compressor by pushing and pulling on the compressor handle, which is attached to a piston-like device inside the compressor. The operator does this at a steady pace and establishes a (relatively - except for when he reverses directions) consistent flow of gas through the system, where the pressure difference between gas cylinder 1 and gas cylinder 2 remains small.
Then, an assistant closes the valve at the top of the system. Our question is what happens to the amount of work needed to move the compressor handle? Does it get easier to move, more difficult to move, or is there no change in difficulty? Further, if there is a change in difficulty, does the change continue in the same direction as the compressor continues to operate, or might the difficulty decrease at first and later increase (or vice-versa)?
We all agree that the difficulty of ejecting gas through the compressor's outputs would seem to increase as the pressure on the output side increases, and that the difficulty of drawing gas in through the compressor's inputs would seem to increase as the suction on the input side increases. However, it also seems to us that as the pressure on the input side decreases, fewer molecules of gas would be drawn into the compressor on each stroke and hence less work would be required to exhaust those molecules, even against a higher pressure on the output side.
We are all computer science / I.T. guys, not mechanical or chemical engineers, so none of us know how to correctly analyze the situation.
Use the following assumptions:
-the gas is an ideal gas
-no part of the system leaks
-there is no friction between any moving parts
-there is no backward flow through any check valves
-everything that is supposed to be sealed is perfectly sealed