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 7.07080 ohms at the ice point, 34.29338 ohms at the steam point, and 107.05517 ohms at zinc's melting point, find Ro.

Found R0 to be 7.0708 ohms but need help with A and B. Thank you!

Explanation / Answer

variation of resistance with temperature in centigrade is

R = R0*(1 + A*T + B*T^2)

given as R= 7.07080 at T = 0.0

7.07080 =  R0 ...................(1)

R = 34.29338 at T = 100.0

34.29338 = 7.07080*(1 + 100 *A + 10000*B)

34.29338 / 7.07080 = (1 + 100 *A + 10000*B)

4.85000 = 1 + 100 *A + 10000*B

100 *A + 10000*B = 3.85000

A + 100*B = 0.03850 ............................(2)

and R=107.05517 at T = 692.666 K = (692.666 - 273) C = 419.666 C

107.05517 / 7.07080 = 1 + 419.666*A + 176119.55156*B

419.666*A + 176119.55156*B = 14.1406

A + 419.666*B = 0.03369 ...............(3)

eq(3) - eq(2)

319.666*B = -0 .00481

B = -0.00481/319.666 = -0.000015 .........ans

putting the value of B in eq(2)

A - 0.0015 = 0.03850

A = 0.04000 ............ans

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