jim rozen writes:

To reiterate what has been said a dozen times befo

Any energy not used remains in the reservoir, behind
the restriction.

Let me show the absurdity of this, one more time.

Say we operate a compressed air system at some specific requirement of a
given mass flow and pressure (forget the "cfm" canard for now and just
specify it mass flow). The mass flow of air is the same everywhere in
the output circuit, starting with what leaves the compressor/reservoir,
which then goes into the regulator, and then out of the regulator. The
pressure drops across the regulator, the volume of a unit of gas mass
expands, but the mass flow is still the same everywhere. This is just
conservation of mass, aka Kirchoff's law.

You say the reservoir can be kept at an excess pressure, then regulated
down, and the energy output from the reservoir is the same in either
case, the difference "not used remains in the reservoir".

But the *mass flow* at the reservoir is *equal* in either case, while
the reservoir output pressure is different. Thus the energy flow out of
the reservoir is higher with the regulator, and lower without. The
difference is being wasted by the regulator. This difference does not
"stay in the reservoir", it has gone into the output.

You don't even need to know any equations for how energy relates to mass
and pressure, just that energy in compressed air is an increasing
function of both mass and pressure. This should all be clear enough with
simple mechanical intuition. No need for quantitative thermodynamic
analysis.