Boiling Water question, lid on or off?

What Cheesesteak said. The amount of heat entering the water, and thus the temperature rise, depends among other things on the difference in temperature bwteen the flame and the water. The flame temperature is probably 1100-1200 F and the water temperature can’t be over 212 F at 1 atmosphere. Ergo the difference between flame and water temperatures is relatively constant in the beginning of the heating and so there is a relatively constant temperature rise.

Suppose the flame is at 1200 F, if the water is at 72 F the temperature rise is proportional to 1128 F. When the water rises to 100 F the rise is proportional to 1100 or 97.5% of the initial rise. In other words the rise only departs from a straight line rise by 2.5%. Your temperature cirve does bend down ever so slightly which is what is expected in the first part of an exponential curve.

I understand that. I just thought, for some reason, that the closer water gets to its boiling point, the more energy is required to push it over the edge, so to speak. I was expecting a graph like this.

I must be confusing some half-remembered high school physics ideas.

Well, yes, to push the water from liquid to gas, there is the heat of evaporation you must add. I think that the fact that your graph is nearly linear is not bad. If you really have the stove crankin’, then the heat flux into the pot will be relatively constant. Your curves are pretty linear most of the way, but start to curve around 200 F. I would imagine that one main reason that the backpacker’s curves are, well, more curved, would have to do with the heat being lost out of their (I’m assuming) smaller test pots. Goes back to the smaller pot having more surface area : mass to have a higher heat flux out (per unit mass).
I actually do have one possible piece of (hopefully) insight to give you on why the results are not that different. If you look at, instead of the temperatures, the difference between two adjacent temperatures, you will see some pretty good fluctuations. Without knowing more about your kitchen, I would question just how steady of a heat flow does your stove create. It is possible that there is enough fluctuations that (in this run) the differences are being masked. I would bet that, if you choose to run your test again, you may find that the differences between the finishing times are greater.

Pulykamell’s numbers show first one pot pulling ahead, then the other.

On a stove, the heat source is at the bottom, and upcurrents would bring the hottest water up toward the top as the water heats. You’d expect the upcurrents to flow chaotically. That might explain the reading variations at the point where the thermometer was measuring.

Even after steam bubbles began to form at the bottom, the whole contents wouldn’t be uniformly just at the boiling point.

Maybe giving the pot a good stir just before each measurement might give more consistent results.

From above it would appear the consensus is that most of the heat loss is though evaporation/vapourisation, so glass or metal would not make a difference to the heat loss through generaly steamy goings on.
Some energy would be lost through radiation - a nice shiny lid would be best at cutting that sort of nonsense out
Some energy would be lost through conduction of heat form the vapour through the lid to the kitchen. I’d say glass lid would be the best choice here.

Which one is less - no idea I’d hazard a geuss at more heat loss through conduction.

That said - assuming you have a tight fitting lid which wont wobble when boiling and you don’t have a whistle type attachment to tell you when it is boiling, I’d say the one with the glass lid will boil faster as you won’t have to keep taking the lid off to check how the water is comming along.
Blondchap

Obviously, an experiment is needed, since these things often don’t follow our expectations.

However, I’d expect the metal lid to work best. The glass will be partially transparent to infrared, so extra heat would be lost that would be reflected back on the water by a metal lid.

This radiation loss would be a minor component of the inefficiency of lidless boiling as well, greatly overshadowed by the convection loss.