The concept of temperature is one which we readilly accept because, of all the thermal properties, is is perhaps the most apparent to our senses. Moreover, it would appear at casual glance that is is one of the most readily measurable quantities. The precise definition of an adequate thermodynamic scale of temperature, however, represents one of the most elusive concepts in the history of thermodynamics. It was Lord Kelvin who realized that it was necessary to introduce another concept - that of entropy - in order to make it possible to find a precise
It would seem logical at first glance that a thermometer constructed
with a liquid in a glass tube could adequately define a scale of
temperature by merely designating two reproducible calibration
points (such as the melting point of ice and the boiling point of
pure water) as 0 and 100 
.
By marking such points on the tube and subdividing the interval
into 100 equal parts, a temperature scale is defined.
Now suppose that a second thermometer is constructed with a
different
liquid, and a scale established on this thermometer in the
same way. If these thermometers are intercompared at some
point between 0 and 100 in a common bath then the
reading on one will not agree with the reading on the other
no matter how precise the construction of the tubes and subdivision
may be. The difference is due to the different thermal
characteristics of the two fluids.
In essence, the problem of thermometry is that of finding a temperature scale which is not dependent upon the particular thermal properties of any one fluid. The early attempts at solving this problem led to the important experiments of Boyle and others in search of the ``perfect gas.'' The empirical findings in regard to the thermal behavior of real gases led to some important deductions by Carnot and culminated in the eventual enunciation by Kelvin of an important hypothesis regarding temperature and entropy which represents the foundation of modern thermodynamcis.
The experiments concerning the thermal behavior of fluids may be
divided essentially into two parts: (1) the establishment
for a particular fluid of the relation between p and
for an isothermal process, and (2) the
establishment of the relation between p and for an
adiabatic process (dQ = 0). It is apparent that even
without a numerical measure of temperature, that any one of
the ``thermometers'' described above can be used to indicate
a constant temperature, thus making it possible to determine
through experiments a set of isothermal curves on a
diagram for any fluid.
The early findings disclosed a disparity in the forms of the
isotherms and adiabatic curves on the plane
for gases. The importance of the discovery that each fluid is
characterized by two reproducible families of curves
on the diagram, rather than one, is that it requires
the introduction of the concept of entropy. First, it should be
noted that if the isotherms are closely related to a unique
thermal quantity - the temperature - then it should be expected
that the adiabatic curves (at least for a reversible process) are
indicative of another unique thermal quantity - the entropy.
The reversible adiabatic curves are then each characterized
by a particular value of entropy. These isentropic curves on
the diagram to not uniquely define the entropy nor
do the isothermal curves define the temperature. To make the
definition unique an additional relation between temperature and
entropy is required.
Kelvin postulated that entropy, like specific volume, is an extensive property of the fluid and that for a reversible isothermal process the change of entropy is directly proportional to the amount of heat added to the fluid at any stage during the process. Moreover, he proposed that the absolute thermodynamic temperature, like pressure, is an intensive property and that it represents the proportionality factor in the above relation. By extending this same idea to any reversible process, we have in essence Kelvin's hypothesis, i.e.
for a reversible process in a finite volume of fluid, where H is the total entropy of the volume and T is the absolute thermodynamic temperature, or simply Kelvin temperature. The zero of the latter is some 273.16 below the ice point in terms of centigrade units.
It should be emphasized that the mercury-in-glass scale of
temperature is not simply a linear transformation of the
Kelvin temperature. Assuming that the mercury-in-glass
scale is established by dividing the interval between the
ice point and the boiling point into 100 equal intervals in
a precise manner, then 50 on this scale will correspond to
about 323.04 Kelvin or 323.13 Kelvin depending on whether
Jena 16III or Jen 59III glass is used in the construction
of the thermometer. Thus, the thermal properties of the
glass as well as of the mercury enter into the distortion
of the mercury-in-glass scale of temperature. It is noted
that the amount of distortion for Jena 16III is
at the nominal temperature of
centigrade. It is apparent then that
if the mercury-in-glass temperature is to yield the correct
thermodynamic temperature (except for an added constant of
it must be constructed with slightly
nonuniform subdivisions with the mark being
not at the half way position between the ice point and the
boiling point.