Page 80 - Modern physical chemistry

4.7 Energy Capacities 69

As a result, term PV may be called the external energy of the system.

Example 4.3
Calculate D.E and MI for the vaporization of 1 mole water at 372.778 K and 1 bar pres-
sure, where the heat of vaporization is 40,893 J mol-I.
Since the vaporization occurs at constant pressure, the heat absorbed in the process is

qp = (1.0000 mOlX 40,893 J mOl-I) = 40,893 J.

Also, the work done on the system is

Wp = -Pf..V = -p(V g - VI)
where Vg is the volume of the final gas and VI the volume of the initial liquid.
Neglect the volume of the liquid and approximate the volume of the gas with the ideal
gas equation:
RT
V=V g =-.
P
The work done reduces to

I
Wp = -P e:; = -RT =-(8.3145 J K- X372.778 K)= -3099 J.
Substituting into equation (4.13) yields

!lE = q + W = 40,893 - 3099 J = 37,794 J;
and into equation (4.27),
MI = qp = 40,893 J.

4.7 Energy Capacities

Any energy added to a system goes to increase the internal energy and the external
energy. Varying with the former in a given phase is the average translational energy and
the average kinetic energy in a degree of freedom. But the latter is proportional to the
Kelvin temperature by section 3.3.
Let us consider a given uniform system at temperature T. Suppose that energy is
added to the system in the form of heat q. Dividing this by the resulting temperature rise
f..T yields the energy capacity C:
~=C. [4.31 ]
f..T
Besides varying with the substance and its amount, C varies with the path followed and
with the temperature. Because of the variation with T, one generally employs the ratio
of differentials,
dq =C [4.32]
dT '
for each chosen temperature. Also by convention, determinations are made along paths
with the volume constant or with the pressure constant. In any case, energy capacity C
is an extensive property.