Tuesday, 24 November 2015

Thermodynamics of the bathtub

We got a cover for the bath tub. It already has a lid, but there's a sizeable air gap between the water and the lid, and the lid is not exactly airtight. As the water is going to be reheated most days, it makes sense to keep it as warm as possible. Putting the lid on makes a big difference, but the heat from the bath is still evaporating away into the air, which is going to be humid and capable of carrying more heat away. They sell bath covers in hardware shops and supermarkets that you can cut to the shape of the bath. They are usually about 4 mm thick plastic foam with one side silvered. I just used a camping mat, essentially the same thing but thicker and presumably better at insulating.

The big question is, of course, do you put the silver side up or down? My initial feeling, probably like yours, is that the silver side should go down, so it is reflecting heat back into the bath. One problem with this, as we experienced in our old house, is that the silver foil can come away from the plastic foam. This was exacerbated when we forgot to take the bath cover off when heating the bath. The bath heater, which was on the outside wall next to the bathroom, sent very hot water back into the bath tub, often bubbling and steaming. The system we now have sends in water at a much more modest temperature.

So here is a plan for finding out, experimentally. After bath time, leave lids and covers in various combinations, for example: lid with no cover; cover, shiny side up with no lid; cover, shiny side down with no lid. Put a thermometer with a data logger into the bath. Repeat a few times to get statistical significance. Observe results and rate of temperature drop, from which we can deduce the heat loss.

For the reliability of the experiment, we need to take a few things into consideration. The volume of water in the bath should be the same, so we may need to add or take out water. The temperature of the bathroom should be the same, so we should be having baths around the same time each day. We should also be measuring the temperature of the bath water in the same place. We have some data loggers attached to thermometers, so it would be easy to put one of these in the bath, but perhaps we need to fix up a rig that can be lowered into the bath when we're not in it. For example a PET bottle with a weight in the bottom, and a thermometer fixed onto its side somewhere.

In the summer we were taking showers rather than running the bath, and also when we did run a bath we wanted to keep the heat in the bath rather than letting it escape into the house, so winter is going too be the best time to carry out this experiment.

We may of course find that any difference is marginal, and that even where there is a difference it is in the steepness of initial temperature drop, and not in the difference of temperatures twenty three hours later when we want to heat up the bath again.

I think we'll find that pointing the shiny side upwards is more effective than pointing it downwards. The shiny side stops radiation, but will have little effect on conduction. Since the bottom of the cover is in contact with the water, heat is mostly going to be conducting, and radiation will make very little difference. At the interface between the top of the cover and the air, there will be less conduction since air can carry something like four thousand times less heat than water. So the radiation is going to make a difference.

The counter-intuitive part is that when it comes to heat, the reflective part is just as good at reflecting heat in as it is as reflecting heat out. Our vision is impairing out judgement.