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Thermal Equilibrium

  1. Jan 29, 2008 #1


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    1. The problem statement, all variables and given/known data
    Two objects A and B, with an equal number, N, of molecules are brought into thermal contact. The first has entropy [tex] S_A = Nkln(U_A/N)[/tex] and the second has entropy [tex] S_B = 3/2 * Nkln(U_B/N)[/tex]. What is the final temperature?

    2. Relevant equations
    [tex]\frac{1}{T} = \frac{\partial S}{\partial U}[/tex]

    3. The attempt at a solution
    My process would be to take
    [tex]\frac{\partial}{\partial U}Nkln((U_A + \Delta U) / N) = \frac{\partial}{\partial U}3/2 * Nkln((U_b - \Delta U)/N)[/tex]

    And solve for delta U. Is this the best way to approach the problem?
  2. jcsd
  3. Jan 30, 2008 #2


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    I think your way is mostly right. As you said, the criteria at equilibrium is,

    [tex] \left( \frac{\partial S}{\partial U} \right) |_{U_A + \Delta U} = \left( \frac{\partial S}{\partial U} \right) |_{U_A - \Delta U}[/tex]

    Find [itex]\Delta U[/itex], and from that, the final temperature.
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