I want to understand a set of issues related to how much energy you can
store in compressed air.
Given a fixed volume tank of one cubic meter:
- Is normal atmospheric pressure called 1 bar?
- How much does the air inside it weigh at normal atmospheric pressure?
- If you add an equal amount of air [weight wise] to the container,
  the air in the container will now weight twice as much.
  Will it be at pressure 2 bars?
- How much energy will it take to do this?
- Given that we now have our cubic meter tank at 2 bars,
  to raise it to 3 bars, do we simply introduce the same weight of air
  into the tank?
- Does going from 1 bar to 2 bars take the same amount of energy as going from
  2 bars to 3 bars? IN other words:
  Does the amount of energy per bar change as we get to higher compression?
- What is the limit? Ie can I go to 1000 bars given a strong enough tank? 
  

Caveots: Here's what I hate about traditional Science formulas:
- They use a single letter to indicate a variable, ie P to mean Pressure.
  Please use longer descriptive terms in presenting equasions.
- Give units ie PV=TX doesn't help me figure out anything.
   I want to know pressure in bars, energy in watt_hours,
   weight in kilograms, etc. 
   An example of actual numbers and units of an equasion that holds true
   is more valuable than 10 pages of abstract physics.
- I'm interested in both "ideal" energy storge and extraction from such a tank
  and in practical efficienies that have or can be achieved.
  Ie given close to the best available system, 
   IF you expend X kwh of electricity to pump up a tank,
   then turn around and run a compressor that drives a generator to produce
   electricity, how much do you get back?
   I'm not so conserned with exact numbers. Are we taking 80%? 50% 30%?
-I understand that temperature has a big effect here and most equasions include a T
  term. I don't really care much about temperature other than the inefficiences
  that not managing it effectively can lead to. For example, if it helps 
  efficiencies to have the tank heavily insulated, that's ok by me.

Most of your questions will be answered indirectly in a course called
pnumatics. I never studied the subject, but I will make educated
guesses on your questions. Generally you are thinking correctly. 
Normal sealevel pressure is correctly called one bar. The air in a
cubic meter weighs about 1/10 kilogram. Adding an equal weight will
double the pressure to two bars. Air pumps and air driven motors are
about 50% efficient, so you will recover 1/4 of the energy you used to
compressed the air. I'll guess it takes 1000 watt hour (10 cents) to
compress a cubic meter from 1 bar to 2 bar. Energy required may
increase as the square of the pressure. To get to 1000 bar we would
typically pump to ten bar, then 100 bar, then to 1000 bar, either with
three separate pumps or a device called a three stage pump. Typical
efficiency may be as low as 10%. The other 90% is heat. Air gets hot
when we compress it. It needs to be cooled, and dehumidified/dried
between each of the three stages. It may be practical to do something
useful with this heat.
 A missle I worked on 55 years ago used nitrogen (much like air, but
less corrosive) at 408 bars stored in one cm tubing as an energy
source for some auxillary purposes. At several thousand bars, strength
of materials becomes the major engineering concern. Small diameter
tubing is the most practical way to store very high pressure air or
other gas. A sphere with an inside volume of one cubic meter, may need
one meter wall thickness to be reasonably safe at 1000 atmospheres =
1000 bars. If it bursts, the schrapnel is deadly. Thermal insulation
for the tank, etc is not generally useful.  Neil

Some corrections to neilzero's comment:

One atmosphere is equal to 1.01325 bars, so a bar is approximately the
same as "normal atmospheric pressure" but not exactly.  At atmospheric
pressure, the air in a cubic meter weighs about 1 kg (depends on
pressure).  Doubling the weight of air in a tank will only double the
pressure if you keep the temperature the same.  When you compress air,
it gets warmer, so if you pump in the air reasonably quickly, or if
your tank is insulated, doubling the weight of air will more than
double the pressure.  If no heat is transferred out of the tank, and
you're using air (nitrogen and oxygen) then the pressure would
increase by a factor of 2.64.  The amount of energy it takes to
increase the pressure in a 1 m^3 tank by 1 bar is 100,000 Joules,
which is less than 30 watt-hours.  If it's true that the pump is about
50% efficient, then you will have to supply 60 watt-hours.

If you plan to store energy in the tank for a short time only, then
insulation will help a lot.  As you pump in air, it will get hot, and
if you can keep it from losing that heat, you can theortically get all
the energy back.  On the other hand, if you plan to store the energy
for a long time and use it very slowly, it is better to have a tank
that conducts heat very well.  You pump the air in slowly enough so
that heat can flow out of the air, and the temperature stays nearly
constant.  Then when you slowly use up the air in the tank, heat flows
into the tank from the surroundings, (expanding air cools), and again
you can theoretically get all the energy back (assuming ambient
temperature is constant).  If, however, you allow the tank to come to
thermal equilibrium with its surroundings and then quickly use up the
air, all the energy that escaped as heat is lost and not recovered.

Just a very short recomendation re:

 " Give units ie PV=TX doesn't help me figure out anything.
   I want to know pressure in bars, energy in watt_hours,
   weight in kilograms .."

It would REALLY become much more simple if you would use SI units
http://www.science.uwaterloo.ca/~cchieh/cact/c120/idealgas.html

for example:
Weight is a force, and is measured in Newtons, not kg
Energy is measured in J (watseconds  .. not kWh ..)
pressure should be measured in Pascals, not Bars
 (atmospheric p is about 100 kPa

..
http://www.shodor.org/UNChem/advanced/gas/

You do not HAVE too - but fact is,
 it is much  easier to understand
and compute things that way

http://www.physchem.co.za/Kinetic/Gas Laws.htm#Properties

I know it is hard to change -- it reminds me what happened in Europe:
 
 In Florence they once prohibited to use 'new-fangled' arabic numbers
 as they were 'too complicated' for accounting purposes. 

 May be Homeland Security now will prohibit SI units as having clear connection
to al-gebra and originating in France !! ?? :-)

Quote:
 Perhaps the strongest evidence of the numerals? use is official
attempts to block them:  a 1299 ordinance of the Florentine bankers?
guild prohibited members from recording accounts in ?what is known as
the style or script of the abacus? and required them to ?write openly
and at length, using letters? ? the fact that the ordinance had to be
repeated three more times meant that by 1299, bankers in Florence had
found it faster and more convenient to use the Hindu-Arabic numerals
rather than write ?at length? in the old script.
 http://www.stevesachs.com/papers/paper_90a.html

As a rule of thumb, it takes about 1 HP to create 4.5 cfm (cubic feet
per minute) of air at 100 psi.  Compressors are the most inefficient
convertors of energy, which can be seen in the large BTUs (heat) that
is wasted out the top of the compressors during the compression
process.  (You can recover the BTUs by using it to heat your
surroundings in the winter)  Most standard compressors only go to 200
psi.(14 bar)  You can go to higher psi, but it will cost you.