Page 15 - Physical Chemistry

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Preface

This textbook is for the standard undergraduate course in physical chemistry.
In writing this book, I have kept in mind the goals of clarity, accuracy, and depth.
To make the presentation easy to follow, the book gives careful definitions and expla-
nations of concepts, full details of most derivations, and reviews of relevant topics in
mathematics and physics. I have avoided a superficial treatment, which would leave
students with little real understanding of physical chemistry. Instead, I have aimed at
a treatment that is as accurate, as fundamental, and as up-to-date as can readily be pre-
sented at the undergraduate level.

LEARNING AIDS

Physical chemistry is a challenging course for many students. To help students, this
book has many learning aids:
• Each chapter has a summary of the key points. The summaries list the specific
kinds of calculations that students are expected to learn how to do.

3.9 SUMMARY
We assumed the truth of the Kelvin–Planck statement of the second law of ther-
modynamics, which asserts the impossibility of the complete conversion of heat to
work in a cyclic process. From the second law, we proved that dq rev /T is the differ-
ential of a state function, which we called the entropy S. The entropy change in a
2
process from state 1 to state 2 is S 1 dq rev /T, where the integral must be eval-
uated using a reversible path from 1 to 2. Methods for calculating S were dis-
cussed in Sec. 3.4.
We used the second law to prove that the entropy of an isolated system must
increase in an irreversible process. It follows that thermodynamic equilibrium in an
isolated system is reached when the system’s entropy is maximized. Since isolated
systems spontaneously change to more probable states, increasing entropy corre-
sponds to increasing probability p. We found that S k ln p a, where the Boltzmann
constant k is k R/N A and a is a constant.
Important kinds of calculations dealt with in this chapter include:
• Calculation of S for a reversible process using dS dq rev /T.
• Calculation of S for an irreversible process by finding a reversible path between
the initial and final states (Sec. 3.4, paragraphs 5, 7, and 9).
• Calculation of S for a reversible phase change using S H/T.
• Calculation of S for constant-pressure heating using dS dq rev /T (C P /T) dT.
• Calculation of S for a change of state of a perfect gas using Eq. (3.30).
• Calculation of S for mixing perfect gases at constant T and P using Eq. (3.33).
Since the integral of dq rev /T around any reversible cycle is zero, it follows
2
(Sec. 2.10) that the value of the line integral 1 dq rev /T is independent of the path be-
tween states 1 and 2 and depends only on the initial and final states. Hence dq rev /T is
the differential of a state function. This state function is called the entropy S:
dq rev
dS K closed syst., rev. proc. (3.20)* • Equations that students should memorize
T
are marked with an asterisk. These are the
The entropy change on going from state 1 to state 2 equals the integral of (3.20):
fundamental equations and students are cau-
2 dq rev tioned against blindly memorizing unstarred
¢S S 2 S 1 closed syst., rev. proc. (3.21)*
1 T equations.
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