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Why entropy is an extensive quantity ?

  1. Dec 19, 2009 #1
    Why entropy is an extensive quantity ?
  2. jcsd
  3. Dec 19, 2009 #2
    Entropy increase by volume. Gas of 2 m^3 have double entropy than gas of 1 m^3 in the same temperature and pressure.
  4. Dec 20, 2009 #3
    But how do you know that "Entropy increase by volume. "

    Let me restate my question :

    How can ew know that entropy is an extensive quantity by its definition

  5. Dec 20, 2009 #4
    First law of thermodynamics, about the conservation of energy: δQ=dU - dW =dU - pdV
    δQ is extensive because dU and pdV are extenxive. δQ/T and ∫δQ/T are also extensive.
  6. Dec 20, 2009 #5
    But for different systems , their temperature T may not be the same !

    First Law sates that deltaQ=dU+deltaW

    We can only infer that deltaQ is additive !

    Please consider my comment~

  7. Dec 20, 2009 #6

    Thanks for correcting my sign mistake of deltaW.
    You are right. Additive is the essence of extensive quantity. For isolated two different systems
    S1 = ∫dQ1/T1, S2 = ∫dQ2/T2 and the entropy of total system is S = S1 + S2.
  8. Dec 20, 2009 #7
    Ha ha~never mind ~I believe that were just some typos

    But , I cannot understand why entropy is additive ?
  9. Dec 20, 2009 #8
    Definition ∫ δQ/T is already addition of δQ/T , isn't it ?
    Why not additive you think?
  10. Dec 20, 2009 #9
    Using the integral to calculate the (delta)S "OF A SYSTEM" is to calculate the difference of entropy for a particular process , I want to ask why , for different systems , it can also be added ?
  11. Dec 21, 2009 #10
    Hi. How's that?

    1 m^3 of liquid water of the room temperature and in standard pressure has entropy say S.
    Let us remove half of water. Do you agree that the left water has entropy S/2 ?

    We will bring removed water into another isolated room of the same temperature and pressure.
    Do you agree that brought water has entropy S/2?

    Water in the first room and water in the second room are different systems.
    Do you agree that the integrated system of the two has entropy S?

    In room 1 we increase the temperature then the entropy of water becomes S'/2
    Do you agree that the integrated system of the two has entropy S/2 + S'/2 ?
    Change of entropy ∫δQ/T for room 1 system is regarded as change of entropy in the integrated system, isn't it?

    Please show your opinion so that I can surely get the core of your question.
    Last edited: Dec 21, 2009
  12. Dec 21, 2009 #11
    Thank u ~

    I can now fully understand the reason why entropy is additive by ur explaining steps by steps !
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