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Extensive quantity

  1. Feb 4, 2008 #1
    [SOLVED] extensive quantity

    1. The problem statement, all variables and given/known data
    My teacher said that E=E(S,V,N) implies that c E = E(cS,cV,cN) where c is some constant. The justification was that E is an extensive parameter. I know what an extensive parameter is (proportional to N), but I do not see how that relation follows.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 5, 2008 #2

    Mapes

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    1. E, S, V, and N are extensive quantities.
    2. You have a system with a certain S, V, and N, and you calculate the energy E.
    3. I replace the system with one twice as big.
    4. You can either double S, V, and N and recalculate or just double E, right? This statement is identical to your equation.
     
  4. Dec 22, 2011 #3
    Re: [SOLVED] extensive quantity

    the proper definition of an extensive quantity is: if there is a system with extensive quanty X' and another system with X" then the two systems together has property X, with X=X'+X". (the property is additive). This is independent of the existence of a function X(a,b,c) where a b and c are also extensive quantities. For example take the internal energy of systems consisting of mono-atomic ideal gases with for helium U'=n'(3/2)RT' and for neon U"=n"(3/2)RT". (Hence U=U(n,T)). Now if we take the systems together U=U'+U" and n=n'+n", independent of the actual values of T'and T". (and we do not need the constant c)
    U (=E) is and extensive quantity independent from the suggested function, that is actually non-existent for most systems.
     
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