The Specific Heat of Solids and Lattice Vibrations

Abstract

According to the first law of thermodynamics, the amount of heat dQ added to a system must be equal to the increase in energy dE of the system plus the amount of work done by the system. In case the work done by the system is of a mechanical nature only, one may thus write

$$$$

(2-1)

Now, E is, except for an arbitrary constant, determined uniquely by the temperature and volume of the system. Hence

$$$$

and (2-1) may be rewritten in the form

$$$$

(2-2)

The specific heat in general is defined by dQ/dT, and unless stated otherwise, will be assumed to refer to 1 gram molecule of the solid. However, unless one specifies in which way the increase in temperature takes place, the specific beat is undetermined; in particular one must specify the corresponding change in volume, as is evident from (2-2). Thus there exist an infinite number of specific heats, but in general one is interested in only two: the specific heat at constant volume C _V and the specific heat at constant pressure C _p . According to (2-2), the former is given by

$$$$

(2-3)

Theoretically speaking, this is the most interesting quantity, as it is obtained immediately from the energy of the system; most of the following discussions will therefore refer to C _V . From the experimental point of view, however, it is much more convenient to measure the specific heat of a solid at constant pressure than at constant volume.