Modern Engineering Thermodynamics

CHAPTER 8
Second Law Closed System Applications
CONTENTS
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
8.1.1 Closed System Indirect Method ...................................................250
8.1.2 Closed System Direct Method .....................................................250
8.2 Systems Undergoing Reversible Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
8.3 Systems Undergoing Irreversible Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
8.4 Diffusional Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
8.1 INTRODUCTION
Chapters 8 and 9 provide closed and open system applications of the second law of thermodynamics in the
same way that Chapters 5 and 6 dealt with closed and open system applications of the first law of thermodynamics.
In this chapter, we present a series of applications of the closed system entropy balance and entropy
production equations developed in Chapter 7. This material is organized into two major subdivisions: applications
involving reversible processes and applications involving irreversible processes. Because the second law is
seldom used alone, most of these examples also involve the application of the energy balance.
Our discussion of the applications involving reversible processes is similar to the way the second law is treated
in many classical thermodynamics textbooks. Restricting consideration to reversible processes significantly simplifies
the analysis, because the entropy production is zero and the second law is reduced to a simple conservation
of entropy law. However, few real processes are truly reversible, so that any analysis that requires (or
specifies) that a reversible process be assumed to get a solution always is somewhat in error. It should be
remembered that a “reversible” process is just an idealization (a model) of some real irreversible process, much
in the same way that we often model complex real gas behavior with the simple ideal gas equation of state. On
the other hand, the study of reversible processes does provide an easy introduction to the use of the second law
and the entropy balance equations, and they are accurate approximations to real processes in systems that have
low entropy production values.
The section dealing with purely irreversible processes begins by expanding the closed system energy balance (first
law) examples presented in Chapter 5 to include an entropy balance (second law) analysis. In Chapter 7, we
introduce two methods for determining entropy production, the direct and the indirect methods. In the direct
method, the amount of entropy produced for a process is calculated from its defining equations (e.g., Eqs. (7.65)
and (7.66)); and in the indirect method, the amount of entropy production for a process is calculated from an
entropy balance on the system.
The indirect method requires detailed temperature and heat flow information evaluated at the boundary of the
system plus specific information about changes in system entropy, whereas the direct method requires detailed
information about temperature, heat flow, and work mode irreversibilities spread throughout the interior of the
system. The examples presented in this chapter illustrate the use of both methods. The following entropy
production formulae correspond to these definitions.
Modern Engineering Thermodynamics. DOI: 10.1016/B978-0-12-374996-3.00008-7
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