Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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


    which can be integrated to give your original expression.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?