Page 48 - Physical chemistry eng

2.5 HEAT CAPACITY 25

of the atom. However, the discrete energy level structure influences how the system can
take up energy. This will become clearer in the next section when we consider how
molecules can take up energy through rotation and vibration.

2.5 Heat Capacity

The process shown in Figure 2.4b provides a way to quantify heat flow in terms of the
easily measured electrical work done on the heating coil, w = Ift . The response of a
single-phase system of constant composition to heat input is an increase in T as long as
the system does not undergo a phase change such as the vaporization of a liquid.
The thermal response of the system to heat flow is described by a very important
thermodynamic property called the heat capacity, which is a measure of energy
needed to change the temperature of a substance by a given amount. The name heat
capacity is unfortunate because it implies that a substance has the capacity to take up
heat. A much better name would be energy capacity.
Heat capacity is a material-dependent property, as will be discussed later.
Mathematically, heat capacity is defined by the relation
q dq
C = lim = (2.9)
¢T:0 T - T i dT
f
–1
where C is in the SI unit of J K . It is an extensive quantity that doubles as the mass of
the system is doubled. Often, the molar heat capacity C is used in calculations. It is an
m
–1
intensive quantity with the units of J K –1 mol . Experimentally, the heat capacity of
fluids is measured by immersing a heating coil in the gas or liquid and equating the
electrical work done on the coil with the heat flow into the sample. For solids, the heat-
ing coil is wrapped around the solid. The significance of the notation dq for an incre-
mental amount of heat is explained in the next section.
The value of the heat capacity depends on the experimental conditions under which
it is determined. The most common conditions are constant V or P, for which the heat
capacity is denoted C and C , respectively. Values of C P,m at 298.15 K for pure sub-
P
V
stances are tabulated in Tables 2.2 and 2.3 (see Appendix B, Data Tables), and formulas
for calculating C P,m at other temperatures for gases and solids are listed in Tables 2.4
and 2.5, respectively.
We next discuss heat capacities using a molecular level model, beginning with
gases. Figure 2.7 illustrates the energy level structure for a molecular gas. Molecules
can take up energy by moving faster, by rotating in three-dimensional space, by peri-
odic oscillations (known as vibrations) of the atoms around their equilibrium structure,
and by electronic excitations. These energetic degrees of freedom are referred to as

E electronic
E vibration E rotation E translation

Rotational Translational FIGURE 2.7
Vibrational energy energy Energy levels are shown schematically for
energy levels levels each degree of freedom. The gray area
levels
between electronic energy levels on the
left indicates what appear to be a continu-
ous range of allowed energies. However,
Electronic as the energy scale is magnified stepwise,
energy discrete energy levels for vibration, rota-
levels tion, and translation can be resolved.