Gary Coffman writes:

Not for adiabatic conditions, which is what practical compressed air
systems most resemble:

p1 * v1^(5/3) = p2 * v2^(5/3)

not:

p1 * v1 = p2 * v2.

Irrelevant. PV=nRT. With RT relatively constant,
PV=kn, or P=kn/V, and ignoring k, P is proportional
to n/V just as I said.

Repeat, "adiabatic", quite relevant. T is not constant.