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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.