Q.How is a thermometer calibrated?

[!TLDR] Two fixed points (ice point, steam point) are assigned reference numbers, and the interval between them is divided into equal degrees. [!ANSWER] Calibration uses the ice point and steam point as fixed reference temperatures, divided into a fixed number of equal degrees.

Calibrating a thermometer (§7.3) means giving numerical meaning to the readings of its thermometric property. Two easily reproducible fixed points are chosen -- conventionally the ICE POINT (melting point of pure ice at one standard atmosphere) and the STEAM POINT (boiling point of pure water at one standard atmosphere). Each fixed point is assigned a reference number (0 and 100 on the Celsius scale; 32 and 212 on the Fahrenheit scale), and the interval between them is divided into a fixed number of equal parts, each called one degree of that scale (100 for Celsius, 180 for Fahrenheit). Any other temperature is then found from where the chosen thermometric property (length of mercury column, resistance, etc.) falls between its value at the ice point and its value at the steam point, using the general formula $T = \frac{P_T-P_1}{P_2-P_1}\times100$ (Eq. 7.2). Modern calibration instead anchors the scale to a SINGLE fixed point, the triple point of water (273.16 K exactly), for greater precision (§7.4.1). [!ANSWER] Calibration uses the ice point and steam point as fixed reference temperatures, divided into a fixed number of equal degrees.

Describe the two-fixed-point calibration procedure and the general thermometric-property formula (Eq. 7.2).

Forgetting that the choice of fixed points and the number of divisions between them is a human CONVENTION, not a law of physics -- different scales (Celsius vs Fahrenheit) are equally valid, just numbered differently.