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 Tc2). 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 11.94090 ohms at the ice point, 109.91598 ohms at the steam point, and 375.73766 ohms at zinc's melting point,

find Ro.

What is A?

What is B?

Explanation / Answer

we know that 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 = 11.94090 ohms

now at steam point delta T = 100 ,

   R = R0 (1 + A* delta T)
        A = (R/R0-1)/ delta T
          = ((109.91598/11.94090)-1) / 100
          = 0.082045 /0C

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

   R = R0(1+B delta T)
    

        B = (R/R0-1)/ delta T
          = (375.73766/11.94090 - 1) / 419.516
        B = 0.07262284 /0C

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