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 11.15540 ohms at the ice point, 31.62556 ohmsat the steam point, and -2.40255 ohms at zinc's melting point, find Ro.

What is A?

What is B?

Explanation / Answer

Resistance, R = Ro*(1 + A*Tc + B*Tc^2)
(i)
At the ice point, temperature Tc = 0 and R = 11.15540 ohm
R= Ro*(1 + A*Tc + B*Tc^2) = Ro*(1+A*0+B*0^2) = 11.1554
Ro = 11.1554 ohm

(ii)
At the steam point, temperature Tc = 100 and R = 31.62556 ohm
R = Ro*(1 + A*Tc + B*Tc^2) = 11.1554*(1+A*100+B*100^2) = 31.62556
1+A*100+B*10000= 31.62556/11.1554 = 2.835
A*100+B*10000= 1.835
A = 1.835/100 - B*100 = 0.01835 - B*100 --------------------Equation(1)

At the melting point of zinc, temperature Tc = 692.666 and R = -2.40255 ohm
R= Ro*(1 + A*Tc + B*Tc^2) = 11.1554*(1+A*692.666+B*692.666^2) = -2.40255
1+A*692.666+B*692.666^2 = -2.40255/11.1554 = -0.2154
A*692.666+B*479786.2 = -1.2154

Substitute A = 0.01835 - B*100 from Equation(1)
( 0.01835 - B*100)*692.666+B*479786.2 = -1.2154
12.71 + B*410519.6 = -1.2154
B*410519.6 = -1.2154 - 12.71 = -13.9254
B = -3.392E-5
A = 0.01835 - B*100 = 0.01835 - (-3.392E-5)*100 = 0.021742

R = 11.1554*(1 + 0.021742*Tc -3.392E-5*Tc^2)

Tc = 100 and R = 31.62556 ohm
R = 11.1554*(1 + 0.021742*Tc -3.392E-5*Tc^2) = 11.1554*(1 + 0.021742*100- 3.392E-5*100^2)
= 11.1554*(1 + 2.1742 - 0.3392) = 31.62

At the melting point of zinc, temperature Tc = 692.666
R= 11.1554*(1 + 0.021742*Tc -3.392E-5*Tc^2) = 11.1554*(1 + 0.021742*692.666 - 3.392E-5*692.666 ^2)
= 11.1554*(1 + 15.06 - 16.274) = -2.4 ohm

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