In article , Grant Erwin says...

Why does any expansion of compressed air necessarily do work?

Start with an empty air tank, and hook your compressor up to it.
The compressor runs, and increases the pressure in the tank.
The electrical energy that ran the compressor is now stored,
in a way, inside the now-compressed air in the tank.

So now there is some energy in the tank that one can use for
'doing stuff.'

To use the energy, one must make the compressed gas expand.
You could:

1) hook the tank up to another, empty tank. Now you have a process
(thermodynamic lingo) where some of the gas at one pressure
transfers over to the empty tank, so you now have a larger
volume at a lower pressure. The first tank cools off (if this
is 'adiabatic', or thermally insulated) and the second one heats
up. If you've ever seen a scuba tank filled you will see that
the second tank heats up. This is an outward sign that there
is work going on - work being done to compress the gas in the
second tank.

2) you could hook the tank up to an air piston, and have the
piston move up and lift a weight or do some other mechanical
work, maybe undo a bolt if there is an impact wrench involved.
Like gary says, the total amount of *energy* used in lifting
the weight is the same if it goes up fast, or slow. That is,
if you open the valve to the piston a lot, or a little. Of
course the time rate of energy transformation ("power") is
larger if you whack the valve wide open, rather than crack it
just a bit.

Think of the tank as a storage battery - to get out the
work the compressor did, you need to allow the air to
perform work by expanding. To avoid the (bad) [1] electrical analogy
you should look at the gas law. If you want to add a small
volume of gas to a reservoir at some pressure, you need
to do some work. The process works backwards, you extract
that work out of the system if the same volume of gas
is expanded out.

What if you just take the tank and don't hook it up to
*anything*? That is, simply open the valve and vent it to
the atmosphere? Then you are pretty much at example (1) above,
but the second 'tank' is really, really large. So when the
surrounding environs heat up, the temperature rise is really
tiny - so small you don't notice it.

I hope this provides some insight.

Jim

[1] and do we ever know it's bad.

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