Question

7 A platinum resistance thermometer has resistance of 52.5 ohms and 9.75 ohms at 0 degrees Celsius and 100 degrees Celsius
respectively. When the resistance is 8.25 ohms, find the temperatur

Answer 1

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

Solution

As is well known, resistance is growing when the temperature is growing.

So, we have from condition of the problem, that platinum resistance thermometer has resistance of $R_{1} = 52.5$ ohms at $t_{1} = 100$ degrees Celsius and $R_{0} = 9.75$ ohms at $t_{0} = 0$ degrees Celsius.

If the resistance depends on temperature due to linear law $R = R_{0} + at \Rightarrow$,

$$\begin{array}{l} R_{0} = 9.75 \text{Ohms} \\ a = \frac{R_{1} - R_{0}}{t_{1} - t_{0}} = \frac{52.5 \text{Ohms} - 9.75 \text{Ohms}}{100 \text{deg}} = 0.4275 \frac{\text{Ohms}}{\text{deg}} \end{array}$$

From whence we have that the temperature for the resistance $R_{2} = 8.25$ ohms is

$$t_{2} = t_{0} + \frac{R_{2} - R_{0}}{a} = 0 - \frac{1.5 \text{Ohms}}{0.4275 \frac{\text{Ohms}}{\text{deg}}} \approx -3.51 \text{deg}$$

Answer

$$t_{2} \approx -3.51 \text{deg}$$