Does the width of a vaccum matter (significantly) when used as insulation?
For example,
lets say I have two different thermos bottles. The first has a vaccum space of 1 cm in width in and the second has a vaccum space of 1 inch in width, would one insulate better then the other?
My intuition from experience is that yes, it does, but I can not explain why.
As I understand it any amount of conduction and convection will be stopped cold by any amount of vaccum and I can not think of any reason why width of vaccum would matter to infrared radiation.
The width of the vacuum won’t make a difference to radiation, but we can’t make a perfect vacuum and the width will make a difference to what little convection there is. I doubt that’s significant though. I’m inclined to guess what matters is conduction. Depending on the construction I’d think you could reduce conduction more with more space to work in.
While you can’t make a perfect vacuum, from a heat loss perspective, anything below about 1 milliTorr (1 micron) is essentially perfect. Below this range thermal based gauging fails, and Dewar flasks don’t become measurably better.
At atmospheric pressure, gas flows and convects. At very low pressure this doesn’t happen. Basically, when they are sparse enough, molecules mostly stop interacting with each other. They just bounce around on their own rather than being pushed around by their neighbors like so many Who fans. Warmer molecules just fly faster, they don’t rise. This is known as molecular flow and starts to be noticeable at about 1 Torr, and is totally dominant by the time you get down to ~10 milliTorr.
Once you fully enter the molecular flow pressure range, convection is not a factor. Heat loss will be determined by the remaining pressure and surface area of the isolated body. Each time a molecule bounces off the isolated body it picks up or drops off some heat. How often that happens depends only on the pressure and surface area, not the volume of the evacuated space. Even though you are in almost pure molecular flow, deeper vacuum still insulates better due to fewer collisions, but once you get down to 1 micron or so heat loss is totally dominated by radiation.
Note: I am recalling the pressures where these things happen from memory. These thresholds are not exact, and I am sure that you can find sources that show I am wrong…at these low pressure levels, though, order of magnitude approximations are useful and mostly what people worry about.
I agree that at low enough pressure, radiation dominates and, assuming infinite - flat walls, the distance between the walls does not matter. However, there are better things to put in that space than vacuum. In particular, you want to put many layers of radiation shields, separated by insulators to kill the conductive losses. The standard way to do this is to fill the vacuum space with many layers of “superinsulation” (thin aluminzed mylar), often alternated with a thin insulating material.
Great example! In this image you can see the multiple radiation shields separated by vacuum. The shields are made as reflective as possible. The layer on the sun side will reflect a high percentage of the sun’s radiation, but some will be absorbed, causing it to warm up. It will then emit radiation in proportion to the fourth power of its temperature, this radiation will be intercepted by the second shield and reflected back. The second shield will heat up to a lower temperature than the first. In the picture, you can clearly see five radiation shields protecting the telescope from the sun’s heat.
Another practical consideration is that if your layers are too close together, they might bump together if the container is shaken, jostled, or dented.
Is it safe to assume the following: the second shield is radiating back to the source half the radiation, while the other half is radiating to the third shield. Repeat. In combination with the T^4 law, this allows a geometric drop in temperature as more shields are added.
My WAG. Starting out with a temperature of 373 °C, and five layers of perfect “insulation”, my results for the inner fifth layer is approx. 300 micro Celsius. My assumptions are one dimensional, BTW.
It depends on the relative emissivity of the two sides of the shield. Clearly, you want to make the reflectitivty as close to 100% as possible on the solar side. If the other side of the shield has the same reflectivity, then each side will emit half of the radiation. If the far side is black, 100% of the emission will be from that side.
With high reflectivity on both sides, you need to take into account multiple reflections between layers, but I think this is still the optimum.
If the temperature sink on the side opposite the sun is absolute zero, I think the temperature has to go down geometrically with the number of layers. In reality, you’ll never get into the micro Kelvins, since the temperature of deep space is about 3 K.