Energy for pressure equalibrium

[Mechanic]

Consider a gas enclosed in a simple piston. Imagine that some type of engine is used to push in the piston until equilibrium is reached – the pressure of the gas exactly countering the pressure/force exerted by the engine. The well known equation “F dot d” describes how work/energy is provided by the engine while the piston is moving the distance d, but how do we describe the energy exerted by the engine to maintain equilibrium? If the engine is turned off the piston will be pushed back out so energy is required to keep the piston from being pushed out. How do we mathematically describe the energy consumption of the engine once equalibrium is reached?

Thanks

 

[russ_watters]

At that point you have a situation where there is no output of work, so your device has 0% efficiency. When you are in a car on a hill, you could use the clutch and engine to hold the car stationary on the hill (expending energy and producing none), or you could just put on your brakes. The device you describe could simply have a brake.

 

[Mechanic]

Russ - I agree, I could "put on the brakes". But that is not my question. My question is "How do I mathematically describe the energy required (consumed by the engine) to maintain equalibrium?"

 

[russ_watters]

You can't. It could literally be anything since the efficiency is zero. Efficiency is always energy out/energy in. so you have 0=0/x. x can be anything, depending on the particulars of the machine.

 

[Mechanic]

Not sure I follow. I'll be able to measure/observe the fuel consumption of the engine so I should be able to mathematically modelthe rate at which that fuel/energy is consumed.

 

[russ_watters]

Not sure I follow. I'll be able to measure/observe the fuel consumption of the engine so I should be able to mathematically modelthe rate at which that fuel/energy is consumed.

You can, of course, measure the input power to the engine, but when you said "mathematically describe", I assumed you meant "calculate". But sure: fuel has a certain energy content, so the flow rate times the energy content is the input energy. My point was that it would be very difficult (near impossible) to predict ahead of time what that energy input (fuel flow rate) is going to be.

 

[QuantumPion]

http://en.wikipedia.org/wiki/Jake_brake

 

[Mechanic]

I would think that with the piston and engine in equalibrium, and the engine consuming fuel/energy, I could somehow calculate the rate of energy consumption based on measured pressure in the piston and dimensions of the piston. Is this braoching the subject of "virtual work"? Maybe that should be another thread. I've never really understood the differences between normal everyday work and virtual work. Virtual work just seems like regular work only on a really small scale?

 

[russ_watters]

I would think that with the piston and engine in equalibrium, and the engine consuming fuel/energy, I could somehow calculate the rate of energy consumption based on measured pressure in the piston and dimensions of the piston.

No, all that gives you is force. Force and energy are not directly related, so having the force tells you nothing about what the energy consumption might be.

Is this braoching the subject of "virtual work"?

No. It's a real work of 0 (output).

Maybe that should be another thread. I've never really understood the differences between normal everyday work and virtual work. Virtual work just seems like regular work only on a really small scale?

No, it doesn't have anything to do with scale. Virtual work is just a mathematical tool. What you are looking for is the real work required to generate a force and like I said, there is no relation to be drawn between force and work like that.

Perhaps if I knew what your goal was here, I could better help you: are you trying to design/analyze a real device of some sort? What is it's purpose?

 

[russ_watters]

http://en.wikipedia.org/wiki/Jake_brake

A Jake Brake is turning the crankshaft and slows the truck via compression of the air in the cylinders. It isn't a static situation like the one being described by the OP.