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

Question

n 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 8.95600 ohms at the ice point, 18.94194 ohms at the steam point, and 4.63165 ohms at zinc's melting point,

find Ro.

What is A?

What is B?

Explanation / Answer

We have 3 equations corresponding to the 3 scenarios

R = R,o(1 + A Tc + B Tc2), we need to set all three up and solve them for unknowns

8.956    =R,o(1 + A 273 + B (273)^2) ----- for ice

18.94194 =R,o(1 + A 373 + B (373)^2) ----- for steam

4.63165 =R,o(1 + A 692.666 + B (692.666)^2) ----- for melting point of zinc

Solve these 3 equations for 3 unknowns

R0 = -53.3 ohms

A = 0.3224 K-1

B= -0.000344 K-2

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