# Greatest volumetric heat capacity at very low temperatures

There is a theoretical device that I want to keep at a temperature of 3 K using a liquid helium coolant loop, and a block of material as heat sink, initially at 0.1 K. The main limitation is the volume of the heat sink material. Cost, practicality or pressure are secondary here.

To absorb as much heat as possible while keeping it at 3 K, for a given volume, what is the best material?

Helium seems a good first choice: its heat of fusion can be used (boiling point below 1 K). However, its density and specific heat capacity are both low, which seems to go against it. I could not find much data on specific heat capacity of other materials at those temperatures, so is there something denser with a high enough heat capacity for compensate the lack of phase change?

Space astronomy platforms seem to use liquid helium to cool sensors down to about 4 K (its boiling point), but this may have to do with engineering considerations (using a boiling liquid instead of a solid block), and those are out of scope here.

As a side-note, the device can use a low-performance mode where it is cooled down as much as possible, but can still be useful at up to a few dozen K. How would such material fare then? Are there significantly better materials for that second case? I would suspect liquid hydrogen (for its boiling point at 15 K), but again, its low density seems to go against it.

This question is asking about volumetric heat capacity at more human temperatures, where water seems to be one of the best, if not the best choice. But heat capacities significantly change at super-cryogenic temperatures, so water is not necessarily a good choice.

This other question (disclaimer: I asked that one) is about specific heat capacity for the best mass, where hydrogen seems to be the best one over a wide range of temperatures. But hydrogen specific heat is significantly lower at low temperatures, and its low density goes against volumetric specific heat.

As noted above, this would be applicable to theoretical space telescopes. But if you are curious, the device I had in mind is a hydrogen stealth steamer. Leaving aside whether the scheme would work, the main limitation to heat sink autonomy in the inner Solar system is volume: more volume means more exposition to sunlight.

Hydrogen seems like the obvious first choice. As noted above, this would be for a "good enough" low-performance mode at 15 K. To extend the optimal 3 K mode, again, the best choice would be helium, which also makes for a good propellant.

However, ignoring delta-v considerations means ignoring mass and propellant performance, leaving only volume. A denser heat sink material could then increase the performances for a stationary device.

• Is the heat sink sinking to your coolant loop? If so, I don't understand why you care about the heat capacity of the heat sink material at all. Any heat in should just be pushed over to the coolant loop. Dec 5, 2018 at 0:01
• @BowlOfRed The heat is going from the device to the coolant loop, and from the coolant loop to the heat sink. The device is kept at 3 K, while the heat sink starts at less than 1 K. You're right, I should edit to make that more obvious.
– Eth
Dec 5, 2018 at 10:14

Without a phase change, I can't believe you'll find anything better than ice from a total heat perspective. But ice is fairly insulating and as a solid can't convect, so may make a poor heatsink.

Helium does have a particularly low enthalpy of vaporization. And after it boils, you don't have enough left to worry about, so let's just see the heat for 1 cc of liquid helium.

$$Q = \Delta H_{vap} \rho V = 21kJ/kg \times 0.125g/cm^3 \times 1cm^3 = 2.6J$$

I would normally suggest water(ice), but as pointed out to me, the heat capacity falls to nearly zero as it approaches 0K. (There is a discontinuity as it crosses the Ih/XI boundary, but the capacity still approaches zero)

Given that, I would probably suggest (dense) metals. But finding accurate heat capacities near 0K will be a challenge.

• Insulation is an engineering problem, but let's assume it is solvable here. Is ice (ice XI?) still that good at near-absolute zero temperatures? According to the formula given at en.wikipedia.org/wiki/Ice it actually drops below zero at 0 K - so the formula doesn't work at those temperatures, but it seems ice is not that good at those temperatures...
– Eth
Dec 5, 2018 at 19:00
• Also, is it realistic to have frozen helium so we can also use heat of fusion?
– Eth
Dec 5, 2018 at 19:01
• You're correct. I've used a generic figure for ice (probably @0C) which is horribly wrong for this usage. Dec 5, 2018 at 20:01
• Frozen helium does not appear to be especially useful. It actually has a negative enthalpy of fusion. Dec 5, 2018 at 20:12