Gallium Bed energy creation in a bedroom that’s 16 C.

Question

If two people both 1.5 m tall and similar shape slept under a blanket both without a temperature (37 degrees C) for 8 hours. Would any energy transfer from the bed as, Phase change of the gallium from solid to liquid? The bedroom is a cool 17 degrees Celsius and the bed is 2 m x 2 m.

Answer 1

Short answer: no. With the room at 17 degrees C (your title says 16 C - it does not change anything below), essentially none of the sleepers heat shows up as gallium melting. The obstacle is not how much energy two people can supply in 8 hours. It is that the gallium surface never gets anywhere near its melting point.

The gallium numbers you need:

melting point       29.76 degrees C
heat of fusion      5.59 kJ/mol = 80.2 J/g
specific heat, s    0.372 J/g per degree C
density, solid      5.91 g/cm3
conductivity        about 40 W/m per degree C

1) The contact temperature is the whole problem.

When skin meets a big slab, the interface does not settle at the average of the two temperatures. It is weighted by thermal effusivity, e = sqrt(k x rho x c):

skin and tissue   k 0.37,  rho 1050, c 3500  gives e about 1170
solid gallium     k 40.6,  rho 5910, c 372   gives e about 9450

T_contact = (T_skin x e_skin + T_gallium x e_gallium) / (e_skin + e_gallium)

Skin under a blanket runs about 33 degrees C, and the bed is at 17, so T_contact is about 18.8 degrees C. Use full core temperature, 37 degrees C, and it only moves to about 19.2. Gallium beats skin on effusivity by a factor of roughly 8, so the metal wins and pins the interface within about two degrees of the room.

Run the equation backwards and ask what skin temperature would drag the interface up to 29.76 degrees C. The answer is about 133 degrees C. That is the clearest way to see this is not a close call.

2) The energy budget agrees, from a completely different direction.

A sleeping adult puts out roughly 70 W. Under a blanket only about 20 to 25 percent of that goes downward into the bed; the rest leaves through the blanket and through breathing. Two people for 8 hours:

40 W x 28800 s = about 1.2 MJ

But before a single gram melts, the gallium has to be walked from 17 up to 29.76 degrees C. Take a 2 m x 2 m slab only 1 cm thick, which is already 236 kg:

236000 g x 0.372 J/g per degree C x 12.76 degrees C = 1.12 MJ

So the entire nights heat input is spent just closing the 12.76 degree gap on a thin slab, and that is with the bed perfectly insulated from everything else. It is not. A 4 m2 surface sitting even 3 degrees above a 17 degree room sheds about 8 W/m2 per degree x 4 m2 x 3 degrees = 96 W, more than twice what the sleepers deliver. The bed never climbs. It settles a hair above room temperature and stays there.

3) What their heat actually does

It becomes sensible heat, and then it leaves for the room. Notice how cheap that sensible term is next to the latent one: warming gallium through the full 12.76 degrees costs 4.7 J/g, while melting it costs 80.2 J/g, a factor of 17. That asymmetry is exactly why gallium is attractive as a phase change material, and exactly why it does nothing for you here. The latent reservoir is enormous, but it sits behind a temperature threshold you never cross.

If the gallium were already sitting at 29.76 degrees C, that same 1.2 MJ would melt about 15 kg. Spread under the roughly 0.7 m2 two reclining adults actually touch, that is a melt layer about 3.6 mm deep. Even at a generous upper bound, all 140 W of both peoples metabolic output driven straight downward for 8 hours, 4.0 MJ, you melt about 50 kg and the layer is about 1.2 cm. Conduction would smear both figures wider and shallower.

bed starts at 17.0 C   no melting at all, interface stalls near 19 C
bed starts at 29.8 C   about 15 kg melted, roughly 3.6 mm under the contact patch

4) The design lesson, which is the useful part

A gallium bed only functions as a phase change device if the gallium is already held at its melting point, and its purpose would be cooling rather than heating. Melting absorbs 80.2 J/g while holding a fixed 29.76 degrees C, and that happens to be a pleasant temperature to be pressed against. Start the night 13 degrees below the melting point and the same slab is just a large, very conductive cold sink. It would feel like lying on a metal plate, because it is one.

Two practical footnotes. Gallium expands when it freezes, 5.91 solid against 6.095 g/cm3 liquid, the same way water does, so a sealed bed has to leave room for that. And gallium wets and embrittles aluminum, so whatever holds it cannot be aluminum.