Such relationships are particularly useful for systems where, for example, it
might be impossible to keep the volume of the system constant. The constant-
volume derivative can be expressed in terms of derivatives at constant temper-
ature and constant pressure, two conditions that are easy to control in any lab-
oratory setting.
1.9 Summary
Gases are introduced first in a detailed study of thermodynamics because their
behavior is simple. Boyle enunciated his gas law about the relationship between
pressure and volume in 1662, making it one of the oldest of modern chemical
principles. Although it is certain that not all of the “simple” ideas have been
discovered, in the history of science the more straightforward ideas were de-
veloped first. Because the behavior of gases was so easy to understand, even
with more complicated equations of state, they became the systems of choice
for studying other state variables. Also, the calculus tool of partial derivatives
is easy to apply to the behavior of gases. As such, a discussion of the proper-
ties of gases is a fitting introductory topic for the subject of thermodynamics.
A desire to understand the state of a system of interest, which includes state
variables not yet introduced and uses some of the tools of calculus, is at the
heart of thermodynamics. We will proceed to develop such an understanding
in the next seven chapters.
1.9 Summary 21