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[Phys-L] Re: The power of compressed air



On Monday, Jul 25, 2005, at 11:45 America/New_York, Bob Sciamanda wrote:

Ludwik,
I cannot completely follow just what you or Brian are doing, but here
is my
shot. The question as you stated it is:
| "How much energy would be stored, approximately, in a
| perfectly rigid bottle (say V=4 liters)
| by changing the air pressure from 1 to 10 atmospheres?

I infer that the temperature remains constant and that the higher
pressure
is achieved by varying the value of n (by pumping more moles into the 4
liter rigid container). I also use monatomic ideal gas behavior as an
initial approximation:

E = (3/2)nRT = (3/2)PV

E2 - E1 = (3/2)V(P2-P1) = 1.5*4*9 =54 liter atmospheres = 5472 Joules

If you use a diatomic model you would replace the above leading factor
(3/2)
with:
a) (5/2) to include only the two rotational modes, or
b) (7/2) to include both the rotational and vibrational modes.

a) gives E2-E1 = gives 9119 Joules,
b) gives E2-E1 = 12767Joules.

1) Which of these two answers would be closer to what can be measured?

2) One of your answers is nearly identical with mine; the difference is
probably caused by rounding, and by the assumed molecular weight of air
(I think I used 29 and ignored fractions. I also assumed that T=300 K
and not 293 K).

3) Brian used the so-called "Fermi method." In that context his answer
is about right because the goal is to get a very crude estimate (often
only the order of magnitude). In any other context the sum under p(V),
from 4 to 40 liters, is not expected to be identical to the sum under
the V(p), from 1 to 10 atmospheres.

Ludwik Kowalski
Let the perfect not be the enemy of the good.
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