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Thermodyamics, two balls with same temperature, different elevation

  1. Mar 17, 2007 #1
    1. The problem statement, all variables and given/known data
    Two identical balls, A and B, of uniform composition and initially
    at the same temperature, each absorb exactly the same
    amount of heat. A is hanging down from the ceiling while
    B rests on the horizontal floor in the same room. Assuming
    no subsequent heat loss by the balls, which of the following
    statements is correct about their final temperatures, TA and
    TB, once the balls have reached their final dimension?

    (a) TA < TB; (b) TA > TB;
    (c) TA= TB; (d) TA <= TB.


    2. Relevant equations
    no idea


    3. The attempt at a solution

    no idea
     
  2. jcsd
  3. Mar 17, 2007 #2
    Think about all the forms of energy (potential, kinetic, heat, etc.) that the balls have, and how they change when the balls are heated.
     
  4. Mar 17, 2007 #3
    i'm very bad at thermodynamics and i need a few sol'ns before i get this topic. So if you can give me the solution, that would be great. I'm not doing this for hw or anything, just preparing for a contest
     
  5. Mar 17, 2007 #4
    Okay, I'll tell you how to do it since this is a qualitative problem.

    Both spheres expand when heated.

    This is the key point: The center of mass of the ball on the floor rises, while the center of mass of the ball on the thread falls. Therefore, the potential energy of the floor ball increases, and the potential energy of the string ball decreases.

    Now, the first law of thermodynamics says that the heat added goes towards work and internal energy. Both spheres have to do the same amount of work to expand against the air, so that's not the key. The important thing is that one sphere has to do work to expand against gravity, while the other just lets gravity do the work.

    The heat given to the ball on the floor will go into doing work against gravity, therefore less of the heat will go towards internal energy.

    The heat given to the ball on the string will go into internal energy, and gravity also contributes positive work. Because the ball on the string has a higher change in internal energy, the ball on the string has a higher temperature.

    (PS: Out of curiosity, what contest are you preparing for?)
     
  6. Mar 17, 2007 #5
    So temperature increase is related to the internal energy increase right? Ok, i understand most of your sol'n, very clear thanks a lot. I'm preparing for the CAP exam which is a Canadian physics contest. I might need your help further down the road. Thanks
     
  7. Mar 17, 2007 #6
    Yes, temperature is related to internal energy.

    Internal energy
    is often written in terms of heat capacity and temperature changes, if that rings any bells.
     
  8. Mar 17, 2007 #7
    oh duh :bugeye: i really suck at thermodynamics
     
  9. Mar 17, 2007 #8
    Everyone is bad at a subject before they learn it, so don't worry about not knowing much! :cool:

    I advise, however, that you work on more quantitative problems because this one only involved a bit of physical insight. And, as reassurance, this is one of the most difficult problems in elementary thermodynamics, in my opinion.
     
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