Читать книгу Geochemistry - William M. White - Страница 52

Recall that the first law states:

If we restrict work to P–V work, this may be rewritten as:

If the heating is carried out at constant volume (i.e., dV= 0), then dU = dQ (all energy change takes the form of heat) and:

(2.67)

In an ideal gas, each atom has three degrees of translational freedom. A mole of such gas will have N_A such atoms and 3N_A degrees of freedom. According to the kinetic theory of gases, the energy, U, of this gas is ³/₂N_AkT. Thus (dU/dT)_V = ³/₂N_Ak, or ³/₂R where R is the gas constant. Molecular gases, however, are not ideal. Vibrational and rotational modes also come into play, and heat capacity of real gases, as well as solids and liquids, is a function of temperature.

For solids, motion is vibrational and heat capacities depend on vibrational frequencies, which in turn depend on temperature and bond strength (for stronger bonds there is less energy stored as potential energy, hence less energy is required to raise temperature), for reasons discussed below. For nearly incompressible substances such as solids, the difference between C_V and C_P is generally small.