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KELVIN scale-Can't make sense of the last step of this solution

  1. Oct 24, 2008 #1
    [​IMG]

    I do not understand how they went from [itex]\ln T_c-\lnT_H=\theta_c-\theta_H[/itex]
    to
    [itex]\theta=\ln T+C[/itex]

    Why did the subscripts drop out? What just happened?
     
  2. jcsd
  3. Oct 25, 2008 #2
    exp means e^thethac if that is thetha

    so you get e^(thethac-thethah) is Tc/Th.

    If you ln both sides, you'll get ln(Tc/Th) = lnTc-lnTh and on the other side lne^(thethac-thethah) = (thethac-thethah)lne. lne is one.

    Thus

    lnTc-lnTh = thethac-thethah
     
  4. Oct 25, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    "C" and "H" just represent different measurements of the temperature. Since you take TH to be a fixed temperature, that just leaves one temperature- you don't need the "C" to distinguish it form "H".
     
  5. Oct 26, 2008 #4
    I am sorry Halls, I don't quite follow. What do you mean I take TH to be fixed?
     
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