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CHAPTER
3 The Second Law of

Thermodynamics

CHAPTER OUTLINE

3.1 The Second Law of
Thermodynamics
3.2 Heat Engines A major application of thermodynamics to chemistry is to provide information about
equilibrium in chemical systems. If we mix nitrogen and hydrogen gases together with
3.3 Entropy
a catalyst, portions of each gas react to form ammonia. The first law assures us that
3.4 Calculation of Entropy the total energy of system plus surroundings remains constant during the reaction, but
Changes the first law cannot say what the final equilibrium concentrations will be. We shall see
that the second law provides such information. The second law leads to the existence
3.5 Entropy, Reversibility, and of the state function entropy S, which possesses the property that for an isolated sys-
Irreversibility tem the equilibrium position corresponds to maximum entropy. The second law of
thermodynamics is stated in Sec. 3.1. The deduction of the existence of the state func-
3.6 The Thermodynamic tion S from the second law is carried out in Secs. 3.2 and 3.3. The rest of this chapter
Temperature Scale shows how to calculate entropy changes in processes (Sec. 3.4), shows the relation be-
tween entropy and equilibrium (Sec. 3.5), defines the thermodynamic temperature
3.7 What Is Entropy?
scale (Sec. 3.6), and discusses the molecular interpretation of entropy in terms of prob-
3.8 Entropy, Time, and ability and the dispersion of energy (Sec. 3.7). The details of the derivation of the state
Cosmology function S in Secs. 3.1, 3.2, and 3.3 are not important. What is important is the final
results, Eqs. (3.20) and (3.21), and the use of these equations to calculate entropy
3.9 Summary changes in processes.
Energy is both a molecular and a macroscopic property and plays a key role in
both quantum chemistry and thermodynamics. Entropy is a macroscopic property but
is not a molecular property. A single molecule does not have an entropy. Only a col-
lection of a large number of molecules can be assigned an entropy. Entropy is a less
intuitively obvious property than energy. The concept of entropy has been applied and
perhaps misapplied in many fields outside the physical sciences as evidenced by books
with titles such as Entropy and Art, Social Entropy Theory, Entropy in Urban and
Regional Modeling, and Economics, Entropy and the Environment.

3.1 THE SECOND LAW OF THERMODYNAMICS

In 1824 a French engineer named Sadi Carnot published a study on the theoretical ef-
ficiency of steam engines. This book (Reflections on the Motive Power of Fire) pointed
out that, for a heat engine to produce continuous mechanical work, it must exchange
heat with two bodies at different temperatures, absorbing heat from the hot body and
discarding heat to the cold body. Without a cold body for the discard of heat, the en-
gine cannot function continuously. This is the essential idea of one form of the second
law of thermodynamics. Carnot’s work had little influence at the time of its publica-
tion. Carnot worked when the caloric theory of heat held sway, and his book used
this theory, incorrectly setting the heat discarded to the cold body equal to the heat
absorbed from the hot body. When Carnot’s book was rediscovered in the 1840s, it
caused confusion for a while, since Joule’s work had overthrown the caloric theory.