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Platinium Resistance Thermometer

  1. Dec 4, 2015 #1
    1. The problem statement, all variables and given/known data
    In the interval between the freezing point (ice point) of water and 700.0deg-C, a platinum resistance thermometer is to be used for interpolating temperatures from 0 °C to the melting point of zinc, 692.666 K. The temperature, in Celcius or Centigrade, is given by a formula for the variation of the resistance of the thermometer with temperature: R = R,o(1 + A Tc + B Tc^2). Ro, A, and B are constants determined by measurements at the ice point, the steam point, and the melting point of zinc. If R equals 7.85630 ohms at the ice point, 65.56082 ohms at the steam point, and 233.60848 ohms at zinc's melting point, find Ro.



    2. Relevant equations


    3. The attempt at a solution
    (0, 7.85630) (100, 65.56080) (692.666-273.15, 233.608)
    These are three ordered pairs of data for the equation
    I found Ro by just plugging in 0 and finding that Ro is 7.85630
    I then plugged in the other ordered pairs and used algebra to eliminate A
    65.56082=7.8563+7.8563(100A)+7.8563(10000B)
    57.7045=785.63(A+10B)
    .07345=A+10B (used for elimination)

    233.608=7.8563+7.8563(419.514A)+7.8563(175992B)
    225.7417=3295.83(A+419.514B)
    .0685= A +419.514B (used for elimination)

    after subtracting the two equations to find B and cancel A I find that B= -1.209x10^(-5)
    then plugging back into one of the shorter equations above find A to be .0736, but both of these are supposedly wrong...
     
  2. jcsd
  3. Dec 5, 2015 #2

    epenguin

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    Homework Helper
    Gold Member

    Approach appears valid.

    There is no 'supposedly' about it - you obtained your constants from the experimental points. When you feed these constants and the temperatures back into the equation they must give you back your original experimental points. Anything else must be due to an algebraic or arithmetic mistake.
    That is the test, not anything anyone says.

    I get constants not wildly different from yours so I think this is basically OK.
    They give a visible but not great departure from linearity over the relevant range.

    More to add on the science of this if the OP comes back.
     
    Last edited: Dec 6, 2015
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