Measurement of Temperature

To measure temperature scientifically we first need a reliable way to say when two systems are at the SAME temperature, even without touching them together. If two sections of a container are separated by a perfect thermal insulator (an adiabatic wall, through which no heat can pass), each section can independently be brought into thermal equilibrium with a third system C. If the adiabatic wall between the two original sections is then removed and no heat flows between them either, they too must already have been in thermal equilibrium. This is generalised as: if systems A and B are separately in thermal equilibrium with a system C, then A and B are also in mutual thermal equilibrium -- the zeroth law of thermodynamics. It is what makes thermometry possible at all: a thermometer is simply a convenient "system C" that we bring into contact with a body, wait for thermal equilibrium, and then read off a number -- exactly like a doctor waiting for a mercury thermometer to equilibrate with a patient's body before reading it.

To turn this qualitative idea into a numerical scale, we choose two easily reproducible FIXED POINTS -- reference temperatures -- and divide the interval between them into equal degrees, just as the metre is defined via two fixed marks. The two classical fixed points are the ice point (the freezing point of water / melting point of ice) and the steam point (the boiling point of water), both measured at one standard atmospheric pressure.

Two everyday scales built this way are the Celsius scale, where the ice point is 0 and the steam point is 100, with the interval divided into 100 equal parts (each a "degree Celsius", °C) -- originally called the centigrade scale (1750) and later renamed after Anders Celsius -- and the Fahrenheit scale, where the ice point is 32 and the steam point is 212, with the interval divided into 180 equal parts (each a "degree Fahrenheit", °F). Because both scales are linear in the underlying physical property, a straight-line graph of $T_F$ against $T_C$ (Fig. 7.1) gives the conversion relation

More generally, any thermometer works by exploiting some THERMOMETRIC PROPERTY of a THERMOMETRIC SUBSTANCE that varies smoothly and monotonically with temperature -- the length of a liquid column, the electrical resistance of a wire, the pressure of a gas at fixed volume, and so on. If the thermometric property takes values $P_1$ and $P_2$ at the ice point and steam point respectively, and value $P_T$ at the unknown temperature $T$, then

A good thermometer needs sensitivity (a large change in the property for a small temperature change), accuracy, reproducibility, and a quick response (reaching thermal equilibrium with the system fast). …