# Derivation for ideal gas law in 2d

So it's easy to find the derivation of the ideal gas laws in 3d, however when considering a 2d system, I was wondering if these equations would still apply?

Or would, for example, pressure be $$p =\frac{NmV^2}{2A}$$? And what would the derivation of this be?

• does this help? en.wikipedia.org/wiki/Ideal_gas_law#Other_dimensions
– peep
Commented Nov 24, 2022 at 12:33
• I’m quite sure I disagree with the assessment that it is “quite easy” in 3D. If you do a proper kinetic molecular analysis it is pretty hard. Commented Oct 26, 2023 at 1:13

The same thought process as in that of the derivation for the 3D case can be used. However, you should note that in 2D there is no such thing as volume. You should use instead area, whenever the corresponding physical quantity in 3D space is volume. In the same way, area in 3D is substituted by length in 2D. For example, say I have a 2D container, so basically in a rectangle. The equation of state becomes $$pA=nRT$$. You can see here that the pressure doesn't have the same unit as in 3D space but you shouldn't worry about that. It becomes Newton/meter, and that's dimensionally correct in this 2D world.