Boyle's Law question

[rx7diver]

To go from P1V1 = P2V2 to P1/V2 = P2/V1 using middle school algebra, simply:
1. Start with P1V1 = P2V2.
2. Then divide both sides of the equation by V2. (V2 is not zero, of course.) This yields P1V1/V2 = P2.
3. Then divide both sides of this equation by V1. (V1 is not zero, of course.) This yields P1/V2 = P2/V1. Done.

So, the two equations P1V1 = P2V2 and P1/V2 = P2/V1 are equivalent. Use whichever equivalent equation is more convenient at the given moment. (Your choice.)


It's impossible to get from P1V1 = P2V2 to P1/V1 = P2/V2 (except in special, trivial cases). So, P1/V1 = P2/V2 can NOT be an alternate expression of Boyle's Law!

EDIT: The equation P1/V1 = P2/V2 *is* useful, though, in non-Boyle's Law situations. For example, if you want to know how much free gas an Al 80 contains when its SPG reads 500 psig, you can solve the equation
(3000 psig) / (77.4 cu ft) = (500 psig) / V2 for V2. In this case, V2 = 12.9 cu ft.

Safe Diving,

rx7diver

 

[oszillodrom]

I actually think it's admirable and essential on a certain level to master the complex physics associated with using gas under pressure. My comment was meant only as a touch of levity. After all, this was in the 'Basic Scuba Discussions' forum, and forum appropriateness is an issue to which my attention has occasionally been called.

Yes, no harm meant. I didn't mean to direct my anger at you, I was just a bit annnoyed in general, because quite often theoretical discussion and thought experiments get turned down with the argument that you don't actually NEED that knowledge for diving.

 

[dumpsterDiver]

WOW.. what I think people are not understanding is that the P1V1 = p2v2 pertains to one chunk of gas. As described this is a simplification of the idea gas law where the explicit assumption has been made that the temperature and n (quantity of molecules, i,e, :chunk") is FIXED.

It is used to describe the relationship between the pressure and volume of a fixed amount of gas.

 

[BradMM]

Wow, four pages of comments! Didn't know I was going to stir up such a hot topic!

 

[rx7diver]

Wow, four pages of comments! Didn't know I was going to stir up such a hot topic!

BradMM,

Yes, but did you learn anything? (The four pages would be such a waste if you didn't.) I did.

Safe Diving,

rx7diver

 

[The Chairman]

WOW.. what I think people are not understanding is that the P1V1 = p2v2 pertains to one chunk of gas.

Actually, Boyle's law is a simple inverse relationship: as the pressure increases the volume of gas decreases. It's a small part of the ideal gas law which can be used to quantify a change in the mass of the gas.

​

 

[dumpsterDiver]

Actually, Boyle's law is a simple inverse relationship: as the pressure increases the volume of gas decreases. It's a small part of the ideal gas law which can be used to quantify a change in the mass of the gas.

​

Sorry, no cigar... Not sure how else to splain it. Even the shape of the graph is wrong in the graphic?

 

[oszillodrom]

No, the shape is right. If pV = const., then V = const. / p and the graph has the shape of y = 1/x.

See: plot 1/x - Wolfram|Alpha

I like the diagram too, very intuitive.

 

[The Chairman]

It's perfect for Boyle's Law. Bolye's law is clearly NOT used where mass changes. It's all about pressure versus volume where mass and temperature remain a constant. Could the line have been completely straight or at least straighter? Sure. We tend to ignore that at 3,000 psi gas is less than "ideal".

But trying to use Boyle's Law where the volume remains constant is just silly. It's like using a hammer on a screw: it's not the right tool for the job. If you don't understand that graphic, then you don't understand Boyle's Law. As Elena pointed out, the real take away from an understanding of Boyle's Law is how we teach it: Breathe Or Your Lungs Explode Stupid! If you want to figure out what's in the tank, you'll have to use Avogodro's or the Ideal Gas Law in order in order to fully understand how much air is in your tank. Check out Wikipedia if you're still lost: Gas laws - Wikipedia, the free encyclopedia

 

[oszillodrom]

Actually, the shape of the graph is right, even though my first feeling was that it should be straight too. See my post before.