To retain heat in the water, heat from the water has to be given up into the surrounding material, and/or the material has to be insulated to not radiate the heat into the room.

Cast iron is the worst material for transferring all the heat out of the water and into the room. While it has a high thermal mass to retain a good deal of the heat, it is also highly conductive. It readily transfers heat, just like a cast iron radiator. You have to continually add more hot water as the hest is transferred from the water into the room, through the iron.

Acrylic is the best at slow heat transfer, as it is not nearly as conductive as iron or steel. Resin is just a fancy name for acrylic with additives, so they can charge you triple.

And, typically, an acrylic tub is not solid, but hollow. That means it has an air gap like a thermopane window, which helps slow down heat loss. Agree that cast iron is the worst.

Interesting--we're actually switching to cast iron because we've found it so much better in real-life use at retaining heat! Much better than the acrylic and enameled steel tubs we have for comparison, but maybe some of that varies by brand if the material composition or insulation is different. (Only have experience with Kohler cast iron tubs, but that is also what we're getting since it's a known quantity.) No idea what brand the acrylic tubs we've used are, since they've been in hotels. Will look next time to see--maybe that affects it, but they get cold so much faster than the cast iron tub we use regularly. (Both are better than the enameled steel tub we currently have in our own home, though.)

I've been out of college for, well, a few years, but I'm brushing off my thermodynamics hat for this research

For a metal, cast iron has a relatively poor thermal conductivity. That's part of why it's such a good cooking material - it holds the heat you apply. That said, compared to acrylic, it has a significantly higher thermal conductivity.

Also, cooking and bathing are different, of course. When cooking, you have the skillet over a heat source. With a bathtub, you add the hot water, and then the heat begins to transfer through the tub and into the room. A cast iron tub has a high thermal mass vs acrylic, so it can hold a lot of heat. I found this website, where they actually did measure it (yay, quantitative data!) and found the cast iron bath water cooled faster than this company's "coreacryl" which is a bit more than just plain acrylic:

https://www.bathsofdistinction.com/coreacryl-vs-cast-iron-bathtubs-s/82.htm

@artemis78 - with your cast iron tub, do you fill it with really hot water? I'm thinking that if one runs the hot water say at 120F, that would give enough extra heat to get the tub up to temperature, while the water cools to a more comfortable bath temp of say 100-105F. I noticed that link above doesn't show continuous temperature drop. My guess is the cast iron starts to stabilize a bit once the tub temperature and water temperature get more into equilibrium.

Cast iron pulls heat initially but than holds the left over heat longer than acrylic or resin. The best material would be soapstone but that is very pricy.

@stm25rs good question--I'd never thought about that! I do usually draw baths by turning the water on as hot as it will go and then turning it down near the end to get it to the target temperature. At least for the houses with the enameled steel and cast iron tubs (mine and parents'/in-laws') I know the water heaters are all set around 120F. No idea what they're set to in the places where I've tried acrylic tubs. I just know that functionally, the two cast iron tubs easily get to an hour at a comfortable temperature, and the acrylic and steel tubs need to be topped off before then. (All three seem okay for baths under half an hour, though, so if that's the most you'd ever need, it probably doesn't much matter.)

Trust me on the thermodynamics: if you fill a cast iron tub and an acrylic tub with the same volume of water at the same initial temperature, the cast iron tub will suck out more heat from the water and radiate it away than the acrylic, and lower the overall water temperature faster. However, the cast iron may give the illusion of being warmer because your body is in direct contact with something that has higher thermal mass than acrylic so your senses tell you it's warmer. It's like if someone dropped a button and a penny in your hand and both were at the same high temperature: the penny would feel a lot hotter than the button because of the much greater amount of energy contained in the metal.

I guess in the context of a bath, I care more about which feels warmer than which may actually be warmer--my goal is just to avoid needing to add additional hot water midway through. :) Cast iron has been a good solution for that, whatever the reason.

artemis-

Well, I should explain that your butt and back may feel a little warmer, but the overall temperature of the water will be a little lower in the cast iron tub because the tub will transfer heat out of the water faster and radiate it to the room faster. In the long run, it may not be a big enough difference to worry about. I just have a problem with people claiming cast iron performs better at retaining heat when thermodynamics tell us just the opposite.