EDIT: the question has been solved. The confusion below arises from the fact that it's not actually a 97 cf tank, it's a 550 cubic inch tank (that could hold up to 97 cubic feet of uncompressed air)
Suppose I have a 97 cf tank at 4500 psi, and a 13 ci tank at 3000 psi. Every time the little tank gets down to 2000 psi, I refill it from the big tank. How many times can I refill it to 3000 psi?
My attempted solution:
For the small tank, 13 ci * (1 cf/1728 ci) = 0.00752315 cf
On the small tank, using the ideal gas law, I first compute the volume of air if reduced to 2000 psi:
V3 = 3000/2000*13 = 19.5
This means that if I run it down to 2000 psi, then I have 13/19.5 or 66% air left...which means I used 33% of the original air. Therefore, each time I refill, I am adding back 0.33*0.00752315 cf = 0.0024826395 cf at 3000 psi
For the big tank, using the ideal gas law, I compute the equivalent storage capacity at 3000 psi.
V2 = 97*4500/3000 = 145.5 cf at 3000 psi
However, I wan't to ignore the air once it gets down to 3000 psi, so I have to calculate the volume of air left at 3000 psi:
97/145.5 = 66%
So, my "real" volume of air (before getting down to 3000 psi) is actually 0.33*145.5 = 48
So, I can do 48 / 0.0024826395 = 19,334 refills.
This seems insanely high, so I'm assuming I made a math or logic error...can anyone sanity check me here?
Suppose I have a 97 cf tank at 4500 psi, and a 13 ci tank at 3000 psi. Every time the little tank gets down to 2000 psi, I refill it from the big tank. How many times can I refill it to 3000 psi?
My attempted solution:
For the small tank, 13 ci * (1 cf/1728 ci) = 0.00752315 cf
On the small tank, using the ideal gas law, I first compute the volume of air if reduced to 2000 psi:
V3 = 3000/2000*13 = 19.5
This means that if I run it down to 2000 psi, then I have 13/19.5 or 66% air left...which means I used 33% of the original air. Therefore, each time I refill, I am adding back 0.33*0.00752315 cf = 0.0024826395 cf at 3000 psi
For the big tank, using the ideal gas law, I compute the equivalent storage capacity at 3000 psi.
V2 = 97*4500/3000 = 145.5 cf at 3000 psi
However, I wan't to ignore the air once it gets down to 3000 psi, so I have to calculate the volume of air left at 3000 psi:
97/145.5 = 66%
So, my "real" volume of air (before getting down to 3000 psi) is actually 0.33*145.5 = 48
So, I can do 48 / 0.0024826395 = 19,334 refills.
This seems insanely high, so I'm assuming I made a math or logic error...can anyone sanity check me here?