# Have any experiments demonstrated that when a cold plate is brought near an internally heated plate in a vacuum, the hot plate's temperature rises?

Perhaps counter-intuitively, radiative heat transfer equations show that if you have an internally-heated plate with constant energy input (eg electric resistance heating with constant power, or a constant light source) in a vacuum, it will reach a certain equilibrium temperature $$T$$, and if you then bring a cold plate (i.e. one with no heat source) near it but not touching it, the equilibrium temperature of the hot plate will be higher than $$T$$!

Indeed the closer the plates are together, the hotter the hot plate gets, to a point ($$F$$ is the view factor). Finally, when they touch, if conductivity is good they will both equalize to close to the initial equilibrium temperature.

This seems counter-intuitive and that it would violate the second law of thermodynamics. Calculations and models are all well and good, but my question is, have any experiments been done that actually demonstrate this in action?

This paper reproduces the set-up, but they don't show the result of running just the hot plate alone to compare. Plus it isn't in a vacuum so it couldn't fully discount effects of prevention of loss due to convection.

It seems easy enough to try at home in a vacuum chamber but I don't have experience rigging things like this up so it'd be a bit of a learning curve.

• What are the distances involved here? Micrometers? Commented Apr 7, 2023 at 9:43
• @Mauricio: The example at the link is with 1 meter x 1 meter plates with thickness 1 cm. If they are spaced 1 cm apart the view factor is ~0.98 Commented Apr 7, 2023 at 9:47
• Reminder from last time last time we discussed this (link) that if you account for the 300K blackbody walls of your experiment, this is not so counterintuitive. Your "cold body" will need to be hotter than 300K, then it will play the role of insulation. Every experiment involving warm (or cold) samples uses insulation, and many of them model their heat. None of them have found that insulation fundamentally doesn't work. physics.stackexchange.com/questions/756492/… Commented Apr 7, 2023 at 10:08
• Yes the (originally) 300K "cold plate" will be warmed above 300K by the warm body, then it will act as insulation, reducing how much solid angle from the internally heated plate is exposed to 300K radiation. In fact this is always how insulation works - the insulation isn't actively heated, it is first heated by the body it's trying to insulate, then the thing its trying to insulate is seeing higher temperature radiation as it's now looking at something hotter. Indeed, I'm not presently aware of a simple experiment that shows just this effect, which is why I haven't submitted an answer. Commented Apr 7, 2023 at 10:27
• If the hot plate is internally heated, wouldn't it start to get colder as soon as its temperature rises above the temperature of its reservoir? Commented Apr 7, 2023 at 11:43