# Apparently easy but super frustrating question about Boyle's Law

## Homework Statement

Okay... everywhere i look, it keeps talking about Boyle's Law applied to THE SAME gas! It's so frustrating and retarded! I get it, p1V1 = p2V2. Yay... I didn't even need to look THAT up!

But my question is, how do you compare 2 different (ideal) gases?? It seems like such an obvious problem to address, but google searching just yields pages and pages of what I said above, rather than addressing this... Grr. Anyway, if I have 2 different containers of gasses, and they're in thermal contact, how do I work with Boyle's Law? (This is for my thermodynamics course.)

My book says that Boyle's Law together with Avagdro's Law implies that p/n is the same for all ideal gases (where n is particle density, N/V). But this is completely NOT obvious to me. How do I prove this? Is it supposed to be intuitive??

Specifically, my example problem asks this... you have nitrogen at 1.26 kg/m^3 at pressure 1 bar and helium at 0.36 kg/m^3 at pressure 2 bar. Molecular weight of nitrogen = 28 and of helium = 4. Are the two gases in thermal equilibrium?

pV = k

## The Attempt at a Solution

Well, the solution is already given in the book (since it's a sample problem), but it doesn't explain why p/n is the same for all gases at same temperature -- it just states it as if it's obvious or something -- and I don't see why that necessarily is obvious, so... how do I prove that it is true? And am I the only one to whom this is not intuitive??

Thanks a lot!

## Answers and Replies

Borek
Mentor
My book says that Boyle's Law together with Avagdro's Law implies that p/n is the same for all ideal gases (where n is particle density, N/V). But this is completely NOT obvious to me. How do I prove this? Is it supposed to be intuitive??

What is characteristic of ideal gas? Or what are assumptions of kinetic theory of gases?