Example

Question:

The resistance of the platinum wire of a platinum resistance thermometer at the ice point is \(5\,\Omega\) and at the steam point is \(5.23\,\Omega\). When the thermometer is inserted in a hot bath, the resistance of the platinum wire is \(5.795\,\Omega\). Calculate the temperature of the bath.

Solution:

Let \(R_0 = 5\,\Omega\), \(R_{100} = 5.23\,\Omega\), and \(R_t = 5.795\,\Omega\).
We use the relation \[ t = \frac{R_t - R_0}{R_{100} - R_0} \times 100 \] Substitute values: \[ t = \frac{5.795-5}{5.23-5} \times 100 = \frac{0.795}{0.23} \times 100 = 345.65^\circ \text{C} \] Therefore, the temperature of the bath is \(345.65^\circ \text{C}\).