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2 Identical Objects in Thermal Contact

  1. Oct 30, 2008 #1
    If 2 identical objects with initial temperatures X and Y are placed together in thermal contact, then the final temperature is T= (X + Y)/2, X and Y actually being equal and excluding any heatloss to surroundings.

    I understand this intuitively, but is there a precise mathematical proof? It's perhaps really simple, but the situation seems so straightforward to me I can't even think of a proof.
     
  2. jcsd
  3. Oct 30, 2008 #2

    Mapes

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    The proof is based on law of conservation of energy (the energy lost by object X must be gained by object Y) and a way of writing energy in differential form, [itex]dE=C_V dT[/itex], where E is energy, CV is heat capacity, and T is temperature.

    Putting these together, we have

    [tex]dE_X=C_{V,X}dT_X=-C_{V,Y}dT_Y=-dE_Y[/itex]

    which can be integrated to give your original expression.
     
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