The shouting in your post is indicated by the capitalized "NOT"'s which I tried to point out by duplicating at the end of my own post. Maybe you are not aware that capitalization = shouting. If you are not, I apologize for taking offense. The formula's I gave are not only for gas, they are also for liquids as a high enough T turns them into gas. "Liquid" and "gas" only refer to the state something is in at atmospheric pressure and a specific temp and can be manipulated by those two same variables. Brake fluid is no majic liquid. It behaves the same way. Higher temps will drive some of into a gas state, regardless of the amount of air. Air in the system would actually give the volume of fluid somewhere to go as air will compress and then you would be even less likely to see a change at the master cylinder. Same reason brakes don't work when they have a lot of air in them - it compresses and no work is done. At any rate, at a high enough temp (a badly dragging brake can create temps in the neighborhood of 300 C) the brake fluid itself becomes a gas (reaches it's boiling point). DOT ratings on brake fluid have a lot to do with boiling points as a result. I have seen a dragging brake blow the cap of off a master cylinder. My objection was (is) based on my interpretation of your yelling as condescension and that with regards to my word choice, splitting hairs. Here's an analogy to explain what I mean: Someone asks about why to leave a nail's width gap between boards on an outside deck. I answer because wood expands and contracts with change in temperature. You then counter with an emphatic answer stating that for all practical puposes, wood does NOT expand, but that the air trapped inside and between the individual fibers and cells may, but that is safe to say the wood, per se, expanding is not the reason. See, in reality, for all 'practical' purposes, wood and liquids do expand. It is only 'technically' that they do not.
1982 Mercedes-Benz 300CD
1982 Mercedes-Benz 240D - stick