Fluids,Molecules and Paradoxes of Infinity

Several paradoxes of infinity have recently featured in this journal involving gases distributed in a denumerable infinite series of compartments. I shall demonstrate in this paper that:

a) None of these new paradoxes applies where the gases comply with both Boyle’s law and Avogadro’s law. As several of these new paradoxes expressly require compliance with Boyle’s law, it is unclear, in principle, as to whether there is a plausible model of gas that is able to uphold them all.

b) Notwithstanding a), any of the above paradoxes (and their variations) can be reinstated by acknowledging (contrary to what is widely assumed in the literature) that there are two distinct, non-equivalent concepts of ideal gas. Indeed, the various infinity puzzles actually enable a distinction to be made between the two concepts (which is a particularly elegant way of doing so).