Question

A platinum resistance thermometer has resistance of 52.5 ohms and 9.75 ohms at 0 degrees celcius and 100 degrees celcius respectively.when the resistance is 8.25 ohms,find the temperature.

Answer 1

Question 30599

The dependence of resistance on temperature is linear. Hence, in general it might be expressed as $R = R_{0}(1 + \alpha t)$ .

Using condition that $R = 52.5\Omega, t = 0C$ obtain $R_0 = 52.5\Omega$

Using the condition that $R = 9.75, t = 100C$ obtain $\alpha = \frac{(9.75 / 52.5) - 1}{100} = -0.081\frac{1}{C}$ .

Hence, for current case, $R = 52.5(1 - 0.0081t)$ .

Plugging $R = 8.25\Omega$ into latter formula and solving for t obtain $t = \frac{(1 - (\frac{8.25}{52.5}))}{0.0081} = 104.06C$ .