For a car modification project, it would be nice to have a function to express the pressure in a volume, as a function of the size of this volume, the amount of air moved by a compressor per unit of time, and the time for how long this compressor has been spinning (assume constant speed). To simplify I will assume that no gas can escape the compressed volume at any given time. Not that I think this will actually be that useful, I'm just curious how you would express this as something that can at least roughly approximate it. Is it possible to derive something useful from the ideal gas equation? The gas that is being pressurized is air at sea level, taken directly from the atmosphere. The reason this is interesting at all is that it is claimed sometimes that reducing this volume will lower the so-called "turbo lag" in a turbocharged engine. E.g. on Wikipedia we have: It makes intuitive sense that "lower overall pipe and intercooler length (size)" is simply the size of the volume defined by the combined set of pipes plus the intercooler itself that the compressor (turbo) needs to pressurize. If this volume is larger, it should take more time for the same compressor at the same speed to pressurize it. I'd like to know what this relationship looks like just for fun, and maybe I will learn something. Is it oversimplification to assume that no air escapes? At least some amount of air will escape into the engine itself. Is it an oversimplification to assume that the compressor will spin at a constant speed? If the volume is larger, I assume it is easier for the compressor to spin up initially.