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How to tell if two system has same temperature?

  1. May 4, 2009 #1


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    Two systems are seperated by a membrane which allow heat and partcle exchange. Both systems have same volume but different (interaction) potential. Do these two systems have same temperature?

    I think they have same temperature because such system could come to equilibrium when time is longer enough, right?

    ps. The whole system is isolated
  2. jcsd
  3. May 4, 2009 #2


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    The standard approach here is to write the internal energy of the systems in differential form (e.g.,

    [tex]dU = T_1\,dS_1 +T_2\,dS_2- p_1\,dV_1 - p_2\,dV_2+ \mu_1\,dN_1+ \mu_2\,dN_2+ E_1\,dq_1+ E_2\,dq_2+\dots[/tex]

    where E is electrical potential and q is charge), solve for dS, and set this to zero to find what would happen at equilibrium.
    Not necessarily; equilibrium doesn't mean that the properties are homogeneous. If energy is coupled to charge (which would be the case for individual particles), then a difference in electrical potential between the two systems could lead to a temperature gradient, as exemplified by the thermoelectric effect.
  4. May 4, 2009 #3


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    I fogot to say, no interaction b/w particles
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