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Hot and Cold Cubes (Posted on 2019-04-04) Difficulty: 3 of 5
Suspended in a vacuum you have a red cube at 100 degrees and a blue cube of equal size and shape at 0 degrees.

You want to warm up the blue cube and cool down the red cube. The naive thing to do is touch them together, letting thermal redistribution eventually bring both to 50 degrees.

Lets say that you can slice the cubes up into pieces and touch small pieces together. Is it possible to get the blue cube hotter than 50 degrees? How hot can it get? (In the end you have to put each cube back together and wait for each cube to resolve to its average temperature.)

You may assume that objects touched together will resolve to a temperature that is the weighted average of their individual temperatures. You may also assume that there is no heat lost to the environment.

No Solution Yet Submitted by Brian Smith    
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re: Missing info? Or solution? Example | Comment 2 of 6 |
(In reply to Missing info? Or solution? by Kenny M)

The two cubes are in a vacuum so the only way for heat to transfer is by direct contact.


An example of heat transfer in the problem: 
Cut the blue cube into equal halves, call them B1 and B2.  Touch B1 to the red cube until they equalize - then B1 and Red would each have a temp of 66 2/3 degrees.  
Separate B1 and Red and then touch B2 to Red until they equalize - then B2 and Red would each have a temp of 44 4/9 degrees.
Finally put B1 and B2 back together - then the reassebled blue cube will have a temperature of 55 5/9 degrees.

  Posted by Brian Smith on 2019-04-04 23:35:17
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