We Thought Heat Easily Moves From One Place To Another. We Were Wrong

Three objects of same heat capacity with temperature T1=200 KT_1=200~\mbox{K}, T2=400 KT_2=400~\mbox{K} and T3=400 KT_3=400~\mbox{K} exchange heat with each other. They are isolated from the rest of the universe. Find the highest possible temperature one of them can reach in kelvin.

Details and assumptions:

  • You may connect them to a heat engine and/or to a refrigerator
  • The objects do not collide to generate heat energy
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