How to quantify the thermal advantages of a white thermos?

[jon4444]

My understanding is that you could expect a white thermos to hold heat better than a black one as it doesn't lose heat through radiation as much. Is there a way to calculate the difference in heat retention?

 

[Charles Link]

It is the emissivity at the IR (infrared) wavelengths that determines whether the heat is radiated away or not. Having a white color (low absorption=low emissivity) in the visible does not mean that it is low emissivity in the mid-IR (3-6 microns) and slightly longer wavelengths, out to about 20 microns, where most of the thermal radiation will occur at from temperatures around 300-350 Kelvin. (Wien's law and/or the Planck function tells you the wavelengths of interest). For maximum containment of the heat, if the outer surface becomes warm, the outer surface needs to have low emissivity in the infrared, and it will thereby will radiate less. $\\$ For thermos bottle design, it is really more optimal to contain the heat in the interior, by using glass surfaces whose outer coating is metallic. Some metals do have low emissivity throughout the infrared. These surfaces also work for keeping the inside cool in the case of cold beverages, by reflecting away any incident (radiated) thermal energy that comes from the outside. $\\$ Oftentimes, the design in thermos bottles is a vacuum between two glass layers, I believe with metallic coating on the glass surfaces that make up the vacuum cavity. That way, heat conduction is minimized by the vacuum, and radiative transfer is also minimized. $\\$ Meanwhile, even if a thermos bottle uses a high quality solid insulator instead of a vacuum type design, the emissivity of the outer surface is normally of a lower priority for ensuring good containment of the heat.

 

[kuruman]

That way, heat conduction is minimized by the vacuum ...

The vacuum also minimizes convection, don't forget.