In the early days of thermometry (and still in laboratory practice today), temperatures
were related to the length of a column of liquid, and the difference in lengths
shown when the thermometer was first in contact with melting ice and then with boiling
water was divided into 100 steps called ‘degrees’, the lower point being labelled 0.
This procedure led to the Celsius scale of temperature. In this text, temperatures on
the Celsius scale are denoted θ (theta) and expressed in degrees Celsius (°C). However,
because different liquids expand to different extents, and do not always expand
uniformly over a given range, thermometers constructed from different materials
showed different numerical values of the temperature between their fixed points. The
pressure of a gas, however, can be used to construct a perfect-gas temperature scale
that is independent of the identity of the gas. The perfect-gas scale turns out to be
identical to the thermodynamic temperature scale to be introduced in Section 3.2d,
so we shall use the latter term from now on to avoid a proliferation of names. On the
thermodynamic temperature scale, temperatures are denoted T and are normally
reported in kelvins (K; not °K). Thermodynamic and Celsius temperatures are related
by the exact expression