Q.In a random temperature scale X, water boils at 200 °X and freezes at 20 °X. Find the boiling point of a liquid in this scale if it boils at 62 ºC.

Thermometry -- the science of measuring temperature -- rests on the zeroth law of thermodynamics: if two systems are each separately in thermal equilibrium with a third system, they are also in thermal equilibrium with each other. This justifies using a single instrument, a thermometer, as that "third system," brought briefly into contact with a body until equilibrium is reached and then read off. A temperature scale is built by choosing two easily reproducible fixed points -- classically the ice point (melting point of ice) and the steam point (boiling point of water), both at one standard atmosphere -- assigning them reference numbers, and dividing the interval between into equal degrees; the Celsius scale (0 to 100) and Fahrenheit scale (32 to 212) are the two everyday examples, related by $(T_F-32)/180 = T_C/100$. More generally, any thermometer exploits some thermometric property (length of a liquid column, electrical resistance …