Kerem

Practical corollary for anyone dealing with cylinders: this is why some gas cylinders have a liquid level and others do not.

Propane and carbon dioxide are stored as liquids under modest pressure, so the cylinder's weight tells you how full it is and the pressure barely changes until it is nearly empty. Nitrogen, oxygen and hydrogen are stored as compressed gas, so the pressure gauge tracks the contents directly and there is no liquid in there at all.

Same steel bottle, two completely different relationships between gauge and remaining contents, and the critical temperature is the whole reason.

The comparison to physics is a bit unfair to chemistry, and it is worth saying why.

Physics predicts a trajectory beautifully for the cases where it can. Ask it to predict the weather in two weeks, or exactly where a specific leaf will land, and it gives you the same kind of answer chemistry gives: general behaviour, statistical confidence, sensitivity to conditions you cannot measure precisely enough.

Chemistry's problems are almost all of the second type. Every reaction is a many-body problem with sensitive dependence on conditions. The subject is not less rigorous — it is working in a regime where the rigorous answer is a distribution rather than a point.

"Cumulated double bonds have to be linear" is the specific fact I was missing, and it makes the whole thing obvious in hindsight.

It also explains why the kit felt fine — those joints flex far more than real bonding does, which is exactly what makes them usable and exactly what makes them misleading here.

A number that makes it tangible: R is about 8.3 joules per mole per kelvin.

So warming a mole of gas by one degree costs you a few joules of the energy that shows up as translational motion. A mole of air is roughly the amount in a two-litre bottle at ordinary conditions. Warm that by a degree and the energy involved is comparable to lifting a small apple a metre.

Having one concrete anchor like that stops the constant feeling like an abstraction. It is a small number because a degree is a small change and a molecule is a small thing.

For a temperature reference specifically, I would push you towards the purpose-made products rather than hunting for a material.

Welders and heat treaters use temperature-indicating sticks — they look like a crayon, you mark the workpiece, and the mark liquefies within a few degrees of a stated temperature. They are made in closely spaced increments right through your range and they are cheap.

There are also indicating lacquers and self-adhesive labels that change colour irreversibly at a rated temperature, which are better if you need a record afterwards rather than a real-time signal.

All of these are formulated mixtures chosen for a precise melting point, which is exactly the thing that is hard to find among ordinary single substances. Somebody already solved the problem you are solving.

From the practical end, this behaviour is used deliberately and you can see it in any foundry.

Molten metal is covered with a salt flux precisely because the two do not mix. The salt layer floats, keeps air off the metal, and collects oxides and rubbish out of the melt, and then you skim it off as a separate solid layer.

That process would not work at all if salts were freely soluble in liquid metals. The whole technique depends on the answer to your question being "barely".