The first published graph dealing with the quantum theory of the solid state: Einstein's
expression for the specific heat of solids [given in Eq. 20.4] plotted versus hv/kT. The
little circles are Weber's experimental data for diamond. Einstein's best fit to Weber's
measurements corresponds to hv/k = 1300K.
The story begins in 1819, when two young Frenchmen, Pierre Louis Dulong
and Alexis Therese Petit, made an unexpected discovery during the researches in
thermometry on which they had been jointly engaged for a number of years. For
a dozen metals and for sulfur (all at room temperature), they found that c, the
specific heat per gram-atom* (referred to as the specific heat hereafter), had prac-
tically the same value, approximately 6 cal/mole-deg [PI]. They did, of course,
not regard this as a mere coincidence: 'One is allowed to infer [from these data]
the following law: the atoms of all simple bodies [elements] have exactly the same
heat capacity.' They did not restrict this statement to elements in solid form, but
initially believed that improved experiments might show their law to hold for gases
also. By 1830 it was clear, however, that the rule could at best apply only to solids.
Much remained to be learned about atomic weights in those early days of mod-
ern chemistry. In fact, in several instances Dulong and Petit correctly halved val-
ues of atomic weights obtained earlier by other means in order to bring their data
into line with their law [Fl]. For many years, their rule continued to be an
important tool for atomic weight determinations.
*To be precise, these and other measurements on solids to be mentioned hereafter refer to cp at
atmospheric pressure. Later on, a comparison will be made with theoretical values for c,. This
requires a tiny correction to go from cp to cv. This correction will be ignored [LI].
390 THE QUANTUM THEORY