Question

The resistance of a platinum resistance thermometer is 10 ohms at 0oC and 10.4 ohms at 1000C. What is the temperature when the resistance of the platinum is 10.30 ohms?

Answer 1

The equation for the resistance of a platinum resistance is linear:

$$R(T) = kT + b$$

where $T$ is the temperature and $k, b$ are coefficients. According to the provided data:

$$R(0) = k\cdot 0 + b = 10\Omega \Rightarrow b = 10\Omega$$

and:

$$R(1000\degree C) = k\cdot 1000\degree C + 10\Omega = 10.4\Omega \Rightarrow k = 0.4\cdot 10^{-3}\Omega/\degree C$$

Thus, when the resistance is 0.30 ohms, the temperature will be:

$$R(T) = 0.4\cdot 10^{-3}\cdot T + 10\Omega = 10.3\Omega \\ T = 750 \degree C$$

Answer. T = 750 C.