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Modern Engineering Thermodynamics

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CHAPTER 8<br />

Second Law Closed System Applications<br />

CONTENTS<br />

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249<br />

8.1.1 Closed System Indirect Method ...................................................250<br />

8.1.2 Closed System Direct Method .....................................................250<br />

8.2 Systems Undergoing Reversible Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250<br />

8.3 Systems Undergoing Irreversible Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256<br />

8.4 Diffusional Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271<br />

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273<br />

8.1 INTRODUCTION<br />

Chapters 8 and 9 provide closed and open system applications of the second law of thermodynamics in the<br />

same way that Chapters 5 and 6 dealt with closed and open system applications of the first law of thermodynamics.<br />

In this chapter, we present a series of applications of the closed system entropy balance and entropy<br />

production equations developed in Chapter 7. This material is organized into two major subdivisions: applications<br />

involving reversible processes and applications involving irreversible processes. Because the second law is<br />

seldom used alone, most of these examples also involve the application of the energy balance.<br />

Our discussion of the applications involving reversible processes is similar to the way the second law is treated<br />

in many classical thermodynamics textbooks. Restricting consideration to reversible processes significantly simplifies<br />

the analysis, because the entropy production is zero and the second law is reduced to a simple conservation<br />

of entropy law. However, few real processes are truly reversible, so that any analysis that requires (or<br />

specifies) that a reversible process be assumed to get a solution always is somewhat in error. It should be<br />

remembered that a “reversible” process is just an idealization (a model) of some real irreversible process, much<br />

in the same way that we often model complex real gas behavior with the simple ideal gas equation of state. On<br />

the other hand, the study of reversible processes does provide an easy introduction to the use of the second law<br />

and the entropy balance equations, and they are accurate approximations to real processes in systems that have<br />

low entropy production values.<br />

The section dealing with purely irreversible processes begins by expanding the closed system energy balance (first<br />

law) examples presented in Chapter 5 to include an entropy balance (second law) analysis. In Chapter 7, we<br />

introduce two methods for determining entropy production, the direct and the indirect methods. In the direct<br />

method, the amount of entropy produced for a process is calculated from its defining equations (e.g., Eqs. (7.65)<br />

and (7.66)); and in the indirect method, the amount of entropy production for a process is calculated from an<br />

entropy balance on the system.<br />

The indirect method requires detailed temperature and heat flow information evaluated at the boundary of the<br />

system plus specific information about changes in system entropy, whereas the direct method requires detailed<br />

information about temperature, heat flow, and work mode irreversibilities spread throughout the interior of the<br />

system. The examples presented in this chapter illustrate the use of both methods. The following entropy<br />

production formulae correspond to these definitions.<br />

<strong>Modern</strong> <strong>Engineering</strong> <strong>Thermodynamics</strong>. DOI: 10.1016/B978-0-12-374996-3.00008-7<br />

© 2011 Elsevier Inc. All rights reserved. 249

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