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Temperature Variance with Resistivity

  1. Mar 25, 2015 #1
    1. The problem statement, all variables and given/known datati
    A resistance thermometer, which measures temperature by measuring the change in resistance of a conductor, is made of platinum and has a resistance of 50.0 Ohms? at 20.0°C. (a) When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 Ohms?. From this information, find the melting point of indium.

    (b) The indium is heated further until it reaches a temperature of 235°C. What is the ratio of the new current in the platinum to the current Imp at the melting point?

    2. Relevant equations

    ## R = R_0 [1+\alpha(T-T_0)] ##
    ##\alpha_{plat} = 3.92 \cdot 10^{-3}##

    3. The attempt at a solution
    For part (a), the answer is 157 degrees Celsius. (Says in the book as well)

    Now, I'm getting 2 different answers for part (b) when using ## T_0 = 20## and ##T_0 = 157##.

    When ##T_0 = 20##, the final resistance is ##50[1+\alpha \cdot 215] = 92.14##

    When ##T_0 = 157##, the final resistance is ##76.8[1+\alpha \cdot 78] = 100.2##

    Why the large discrepancy with calculating the same thing? (The 2nd one is correct, per the book)
     
    Last edited: Mar 25, 2015
  2. jcsd
  3. Mar 25, 2015 #2

    ehild

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    The resistance of the Pt thermometer is almost linear function of the temperature in a wide range.
    You have to keep To= 20 C° and Ro=50 Ω, and calculate the resistance from the formula R(T) = Ro(1+α(T-To)).
     
  4. Mar 25, 2015 #3
    Yes, that is what I did in the first calculation; however, the book performs the second calculation (and obtains diff. answer)
     
  5. Mar 25, 2015 #4

    ehild

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    from where is 185 from?????
     
  6. Mar 25, 2015 #5
    I changed it to 215, which is 235 - 20.
     
  7. Mar 26, 2015 #6
    Anyone can figure out problem?
     
  8. Mar 26, 2015 #7

    ehild

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    Read my post #2. The coefficient α=3.92⋅10−3 °C is valid if To=20 °C, Ro=50Ω. You can not use it for other To-s. The book is wrong.
    Think: If the book was right, changing the temperature by a small amount dT and getting the resistance at T+dT, you would have the equation: R(T+dT)= R(T)(1+αdT).
    If dt is small, R(T+dT) = R(T) +(dR/dT )dT, and the equation is equivalent to the differential equation dR/dT=αR(T), with the solution R(T)= RoeαT, an exponential function instead of a linear one.
     
  9. Mar 26, 2015 #8
    ...are you sure? I'm fairly confident it's a decent book :/
     
  10. Mar 26, 2015 #9

    ehild

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