Modern Engineering Thermodynamics

CHAPTER 9
Second Law Open System Applications
CONTENTS
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
9.2 Mass Flow Transport of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
9.3 Mass Flow Production of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
9.4 Open System Entropy Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
9.5 Nozzles, Diffusers, and Throttles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
9.6 Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
9.7 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
9.8 Shaft Work Machines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
9.9 Unsteady State Processes in Open Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
Final Comments on the Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
9.1 INTRODUCTION
This chapter is an extension of Chapter 6, except here we use both the first and second laws of thermodynamics
to analyze open systems. As in Chapter 8, we have two types of system processes to consider, reversible and
irreversible. A reversible process is easier to analyze, because its entropy production is always equal to zero.
However, reversible process models are often unrealistic in actual engineering applications because they require
that the system have no losses (i.e., no friction or no heat transfer through a finite temperature difference etc.).
On the other hand, irreversible process models are very realistic, because they take into account all the losses
within the system, but they are often very difficult to analyze because of the complex entropy production terms
that must be evaluated. We are therefore faced with the choice of carrying out a quick but possibly inaccurate
analysis based on hypothetical reversible processes or a more complex but accurate analysis based on real
irreversible processes. The material presented in this chapter focuses primarily on the latter by utilizing the
appropriate entropy production formulae developed in Chapter 7.
Since we have not yet considered the impact of flow streams on the general entropy balance, we must now
introduce the mass flow transport and production of entropy characteristic of open systems.
9.2 MASS FLOW TRANSPORT OF ENTROPY
Mass flow transport of entropy occurs every time mass crosses the system boundary. Every element of mass dm
is assumed to be in local equilibrium and hence has a well-defined specific entropy s. Therefore, dm transports
an amount of entropy sdm when it crosses a system boundary, and we can set
ðdS T Þ m
= sdm
Modern Engineering Thermodynamics. DOI: 10.1016/B978-0-12-374996-3.00009-9
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