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Zeroth Law MIT Courseware

  1. Jan 19, 2016 #1
    I was studying zeroth law from MIT Courseware (http://ocw.mit.edu/courses/physics/...-fall-2013/lecture-notes/MIT8_333F13_Lec1.pdf). On page 2, it is mentioned that equation I.4 can be simplified using equation I.5 by cancelling the co-ordinates of C. Could someone guide me justify this fact? I tried working it out by assuming functions and I could construct functions where equation I.4 and equation I.5 are satisfied but it is not possible to cancel C. Am I missing something?
     
  2. jcsd
  3. Jan 20, 2016 #2
    Equation I.4 does not contain C1. Now let' eliminate C2. Differentiate I.4 with respect to A1, then you will get

    F#AC(A1,A2,...,C2,...)=0

    But then you can write this equation as C2=GAC(A1,A2,...,C3,C4,...).

    Similarly, differentiate I.4 with respect to B1. Then you will get
    F#BC(B1,B2,...,C2,....)=0

    But again you can write it as C2=GBC(B1,B2,...,C3,C4,...).

    Since there is equilibrium then,
    GBC(B1,B2,...,C3,C4,...) = GAC(A1,A2,...,C3,C4,...).

    Thus, you eliminated C2. Repeat the procedure unti you eliminate all C's . Then you will end up with
    θA(A1,A2,....)=θB(B1,B2,...).
     
  4. Jan 20, 2016 #3
  5. Feb 12, 2016 #4
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