Page 78 - Modern physical chemistry

4.6 Isochoric and Isobaric Heats 67

Whenever Pex differs only infinitesimally fromP, (4.14) reduces to

[4.15]

When the pressure P is plotted against the volume V, this integral is represented by the
area under the curve. See Figure 4.3.
For a process in which the pressure is kept constant (an isobaric process), (4.15) inte-
grates without trouble:
Wp = _pf~2 dV =-P(V 2 - Vl) = -Pi1V. [4.16]

Processes in the laboratory are often carried out in this manner.
When the system is an ideal gas, equation (4.15) becomes

[4.17]

In general, the temperature is not determined by the volume alone. So this integral depends
on the path, on how T does vary between the initial and the final states. When the change
in volume occurs at a given temperature, isothermally, we have

V2 dV V 2 P 2
WT = -nRT f - = -nRTln- = nRTln-. [4.18]
VI V V l P l
Results (4.16), (4.17), and (4.18) require that
[4.19]

Example 4.1
How much heat is absorbed by n moles of an ideal gas undergoing a reversible, isother-
mal process?
When an ideal gas absorbs heat, it may use the energy to do work against an exter-
nal pressure and to increase the thermal agitation of its molecules. None is used to do
work against intermolecular attraction as the volume increases, because this attraction
is negligible.
As the temperature is kept constant, we have
L1ET = 0
for the ideal gas, and

Substituting for wr with (4.18) yields

4.6 Isochoric and Isobaric Heats
Similarly, the heat absorbed by a given system depends not only on the initial and
final states but also on the path followed between the states.
Consider a uniform system for which all work is compressional. Then