# Half of a Hot Plate

You walk into physics class with your friends, and your teacher is already there. She's left what looks like a large, thick, plate out by an old-fashioned coal heater (for some reason, your school has one of those), and she's currently extinguishing it.

Once you've sat down, she turns around and asks the class, "Now, why might the side of this plate farther away from the heater be hotter than the side closer?"

The students already there (and you too) think and think and can't come up with a correct answer. What is the reason?

## 3 Answers

This story is told here:

where the stated answer is that

the teacher turned the plate around before the students came into the class.

• Darn. I tried googling for it, but couldn't remember the exactly where I heard of it - thanks for that. – logitropicity Jul 14 '16 at 22:53
• (I'm not sure why the three downvotes on the question, btw.) – Gareth McCaughan Jul 15 '16 at 9:33
• @GarethMcCaughan possibly because he didn't give credit where it was due? – dcfyj Jul 15 '16 at 12:04
• Yeah, that's possible. (I was going to remark that there are any number of other derivative puzzles here without attribution, but actually I think they tend to get downvoted too.) – Gareth McCaughan Jul 15 '16 at 12:33
• Well, I suppose that's fair - but it's a little bit hard to cite when you can't find the source. – logitropicity Jul 15 '16 at 18:45

Of course there are a number of alternative equally possible answers (well perhaps not exactly equally possible):

Likely scenarios

Teacher heated the far side (before arrival of students) with a blow-torch, soldering-iron, heat-gun or whatever. Then the outside could be above local ambient temperature and be warmer than be inside.

Teacher cooled the near side with ice, cold-spray, rapidly evaporable liquid or whatever. Then the inside could be below ambient and hence colder than the outside.

The plate is coated with a thin coating with highly variable thermal conductivity (or the plate itself has highly variable thermal conductivity) - with conductivity varying from high (outside section) to low (inside section). Then the inside could be warmer (or equi-temperature) relative to outside, but would be perceived as colder by touch.

Inside could be cooled by a draft of cold air, or (more likely) outside is heated by warm air current rising from the lower section of the stove that bypasses the inside section.

The large 10 kA AC cable that runs through the wall of the class-room is inductively heating the outer part of the electrically conductive plate.

Less likely scenarios

Plate is manufactured from plutonium alloy with higher plutonium concentration at the outside.

There is a powerful microwave or infrared beam aimed at the outside, (or for that matter a beam of neutrons, alpha particles, etc doing a similar job).

The students have been hypnotized, or the teacher has manipulated their expectations to the extent that they all 'perceive' or believe the outside to be warmer. Or similarly they live in a totalitarian state and know to keep their mouths shut if reality appears to conflict with state-provided dogma.

Unlikely scenarios (but not literally impossible)

Using Boltzmann's model of statistical entropy, the plate could spontaneously heat on the far side.

It is a miracle...or magic

I'm sure there are more scenarios that could easily be imagined for each of the above categories.

Serious answer

The answer is

I don't know

Since

The students already there (and you too) think and think and can't come up with a correct answer

Then obviously

I can't know what the actual reason is