The question was: "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?
= = = = = = = = = = = = = = = = = = = = = =
Brian posted this estimate:
1 pascal is one joule per cubic meter
1 atmos = 101300 N/m^2 = 0.1013 MPa
9 extra atmos = 9 X 101300 N/m^2 = 0.9117 MPa
Volume in question = 4 l = 4E-3 m^3
Energy stored is dP.V = 911700 . 4E-3 joules
= 3647 joules.
If it is released in 1 ms then the rate is
3.64 MW
Notice that this energy estimate is based on V.dP not P.dV
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
On Sunday, Jul 24, 2005 Ludwik Kowalski wrote:
In other words, following the suggestion made by John Berrer, to solve
the problem one could perform an equivalent transformation. Start with
the amount of ideal gas needed to create the pressure of 10 atmospheres
in 4 liters. Allow that gas to be initially at p=1 atm (in 40 liters)
and compress it to V=4 liters. The integral p(V)*dV terms should be an
acceptable answer. Yes, I know that air is only approximately ideal.
I am going to outline my calculation because the final answer, 9190 J,
differs from that posted by Brian. One of us must have made an error
somewhere. Where is it?
a) How much air is there in 40 liters (0.04 m^3) of air at room
temperature (~300 K) when p=1 atmosphere (~10^5 Pa)? The ideal gas
equation p*V=n*R*T leads to n=1.60 moles (46.5 grams).
b) Assuming T remains constant one has p(V)=3991 / V
c) Integrating this from 0.04 to 0.004 m^3 (from 40 liters to 4 liters)
I find that the work done (its potential energy) is equal to
3991*ln(10) or 9190 J. That is much larger than 3647 J reported by
Brian (see above). Note that the potential energy of an 1 kg object
increases by 9190 J when it is elevated to 938 meters; that is more
that 1/2 mile.
Ludwik Kowalski
Let the perfect not be the enemy of the good.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu https://www.physics.buffalo.edu/mailman/listinfo/phys-l