Heating object in airless environment

Question

Lets assume I had two containers sitting over a fire or some source of heat. Lets say I also placed two of the same objects with a low melting point in these containers (lets also assume this object isn't water/ice cause I've heard its weird in these environments).Then I remove the air from one of the containers but not the other. Would the object in one container heat up/melt quicker than the other? There is air around both containers if this info is important, just not inside one.

(please forgive me if this is a stupid question I am not a physicist and was just purely curious. I've tried researching this question elsewhere but the answers I keep getting are "there is no heat transfer in a vacuum other than radiation" which I assumed doesn't apply because there is an object in the container for heat to transfer to conductively. If this assumption is wrong then I would love to understand why. Thank you.)

Answer 1

It will depend mostly on the vapor pressure of the sample at the melting point.

A sample with a high vapor pressure will vaporize as the container is evacuated, so the temperature will decrease as heat is spent on the latent heat of vaporization. Or, if its vapor pressure is high when it is melted, but it is solid when we are evacuating the air and is only heated to melting point later, then it will vaporize as quickly as it is melted, greatly slowing the speed at which it increases in temperature until the vapor pressure at the melting point is exceeded by the pressure of vaporized sample in the container.

If you have ever used a "canned air" product you have experienced this effect firsthand. Evacuating the pressurized gas (which is not actually air in this case, despite what the product is called) causes vaporization of the fluid, which dramatically lowers the temperature of the fluid and container.

On the other hand if we have a sample with a very low vapor pressure despite its low melting point, such as mercury, evacuating the air will not cause a significant amount of vaporization, and the samples will melt at about the same rate.

Answer 2

... there is no heat transfer in a vacuum other than radiation ...

This is not really correct. Heat can also transfer by conduction if two surfaces are in contact, even though they are surrounded by vacuum. So the object in the vacuum container will still be heated by conduction from the bottom of the container on which it rests.

Having said that, it will probably heat up less quickly than the object surrounded by air since the object surrounded by air is also heated by convection through the air.

Answer 3

The evacuated container is very similar to a thermos flask (or a cryostat) so the object in there would (under most scenarios) heat up slower and end up melting later.

By removing the air you disabled two mechanisms of heat transfer from the container walls to your object: (1) the convection of air and (2) the conduction through air. The rest remains more or less unchanged, namely you still have: (3) conduction through the support structures that hold your object in place and (4) radiation.

How big effect it would be of course depends on how much heat is/would be transferred by (1) and (2) compared to (3) and (4). If your container and supports for your object are designed well the difference can be huge. If you make the supports from a material with a low heat conductivity and make them long and thin then they will not conduct much heat. Multi-layered walls and or proper surface treatment of the walls will reduce the radiative heat transfer.

Just as an example: if you want to transport liquid helium (very cold and very easy to boil off) you need a Dewar flask - a double wall steel can with vacuum between the walls (there are also many layers of very thin mirror-like plastic sheets - superinsulation - which reduce the radiative heat transfer). If it is well evacuated it will hold the liquid for weeks. If it is not evacuated the liquid will boil off in a matter of seconds.

Now, I wrote: "under most scenarios". There can (always) be counter-scenarios. For example if your can was big, and the object inside was tiny (so it would need only very little heat to warm up or melt) then the heat capacity of the air might come into play - in the evacuated can scenario you only have to heat up the can and the object while if the can is filled with air you have to heat the air too. And if your heat source is not very powerful it might very well happen that the resulting heating rate ends up being slower with the air in the can.

Answer 4

The answer is yes,- there would be heating dynamics difference. For simplicity, let's consider cube-shaped container placed in some weightless environment, say in the Earth orbital station, so that inside object floats exactly in the middle of container without touching it's walls. Also assume that container object has relatively high melting point (metallic-like solid object for example), so that to omit quick effect of vaporization pressure. This container has air inside :

Now, according to Thermal conduction law, because air is not a perfect heat insulator (vacuum is),- it will pass heat to the center object, defined by:

$$ \tag 1 \mathbf {q} =-k\nabla T, $$

where $k$ is air thermal conductivity and $\nabla T$ is temperature gradient between container wall and floating object in the center. Assuming all container walls are heated uniformly, total magnitude of heat flux density from container 6 walls would be :

$$ \tag 2 ||\mathbf q_t|| = -6\times 0.026~Wm^{−1}K^{−1}\times \nabla T.$$

Another container will have vacuum inside, and so it's thermal conductivity $k=0$ and consequently, heat flux density,- $||\mathbf q_t|| = 0$. So object in container with a perfect vacuum inside will heat slower, because the only means of conducting heat to the center object will be radiative ones,- passing electromagnetic radiation from container walls to the center object. While air-based container will additionally have conductive term $\mathbf q_t$ and presumably,- air convection which may speed heating object even faster.