As I'm reading through Chapter 3 of Rocket Propulsion Elements, I found myself getting stuck on the importance of the perfect gas law. Early in the chapter it says, "An ideal rocket propulsion unit is defined as one for which the following assumptions are valid:" and it goes on to list 12 things, and one of those things is:
When I read this I stopped for a moment and thought, "well that doesn't really make any sense." And this lead me down a bit of a rabbit hole with SuperGrok Heavy, and a team of agentic researchers, that finally got me over the hump here."3. The working fluid obeys the perfect gas law"
First, just to make sure we're all on the same page, the perfect gas law, which I remember being taught in school as the ideal gas law, is an equation that describes the relationship between pressure, volume, the amount of a substance (in this case rocket fuel), and temperature.
This comes into play with rockets when doing things like combustion chamber analysis, nozzle expansion and exhaust velocity, thrust and specific impulse, and the list goes on.
The equation itself makes sense to me, and it did when I first learned it. What didn't make sense to me when I was reading this last night, is how can we consider that in a rocket, a wild and crazy, statistically unstable thing, in the real world, would have fluids inside it following the ideal gas law!?!
So I asked SuperGrok Heavy, "don't imperfections in the real world throw everything off?"
And it's response made everything click for me. It said that while yes, real world imperfections do exist, and sure, they matter, they actually rarely throw everything off in rocketry.
Rocket combustion chambers operate at kinda insane temperatures and pressures, 2500 - 3800K (crazy hot) and 20 - 300 bar (crazy pressure) and at these extremes, the mean free path between molecules is large and intermolecular forces are weak compared with the thermal energy. Also, the gas density is low enough that the volume occupied by the molecules themselves is negligible.
So yes, in these conditions, the ideal gas law can predict the chamber pressure, density, and temperature relationships to within ~5% for preliminary design.
Of course, there are still real world effects like I said above. Things like finite molecular volume and attractive forces, variable specific heats and dissociation, and non-isentropic losses in the nozzle are all things to think about. And it turns out rocket engineers do correct for these using things like Thermodynamic tables, Computational Fluid Dynamics, and Real-gas corrections in preliminary sizing.
For something like the SpaceX Raptop or Blue Origin BE-4, it turns out engineers use a compressibility factor Z = PV/nRT of 0.95 - 1.05 so the error is only a few percent, which is within a tolerance where things don't (or at least shouldn't) go horribly wrong.
Here's a great final summary from SuperGrok Heavy, it says it better than I ever could.
