In the interval between the freezing point (ice point) of water and 700.0deg-C,

Question

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 12.88350 ohms at the ice point, 88.31639 ohms at the steam point, and 304.28989 ohms at zinc's melting point, find Ro. What is A? What is B?

Explanation / Answer

the resistance of the substance changes with temperature
as follows

   R = R0 (1 + alpha * delta T)

R0 is resistance at 0 0C and R is resistance at temperature difference delta T

according to given data at ice point delta T is zero so

   R = R0(1+0) ==> R at ice point is R0 = 12.88350 ohms

now at steam point delta T = 100 ,

   R = R0 (1 + A* delta T)

        A = (R/R0-1)/ delta T
          = ((88.31639/12.88350)-1) / 100
          = 0.05855 /0C

at meltingpoint of zinc 692.666k = 419.516 0c
delt T = 419.516

   R = R0(1+B delta T^2)
  

        B = (R/R0-1)/ delta T^2
           = (304.28989/12.88350 - 1) / 419.516^2
        B = 0.0001285192 /0C

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