Modern Engineering Thermodynamics

126 CHAPTER 4: The First Law of Thermodynamics and Energy Transport Mechanisms
EXAMPLE 4.11 (Continued )
Exercises
24. If the energy conversion efficiency in Example 4.11 were 15.5%, what would be the power output of the engine
measured on the test stand for the same fuel flow rate? Answer: _W actual = 80:4 hp.
25. An engineer designs a pump that requires 1.30 kW of reversible power to operate. A prototype pump is made and taken
to the test laboratory. The actual power required to operate the prototype pump is measured at 1.50 kW. Determine the
work (or mechanical) efficiency of this pump. Answer: η W = 86.7%.
26. A refrigeration system is powered by a 5.0 kW electric motor. It removes 18 × 10 3 J/s from the cold storage space. What
is the coefficient of performance of this refrigeration system? Answer: COP = 3.6.
Because of the many irreversibilities that occur within a system, we cannot calculate actual work absorbed or
produced from a theoretical formula. All efficiency values are determined from laboratory or field measurements
on the actual work of real operating systems. When energy conversion efficiencies are to be taken into account
in textbook problems, the efficiency values usually are provided within the problem statement. Experienced
engineers often have a “feel” for what the efficiencies of certain devices should be, and they can use these efficiency
estimations in their design calculations. Student engineers, however, are not presumed to be innately
blessed with this knowledge.
The general form of Eq. (4.70) allows the creation of many different types of efficiencies. There are thermal,
mechanical, volumetric, thermodynamic, and total efficiencies (to name just a few) in today’s engineering
literature. One should always be sure to understand the type of efficiency being used in any
calculation.
4.10 THE LOCAL EQUILIBRIUM POSTULATE
Surprisingly, there is no adequate definition for the thermodynamic properties of a system that is not in an
equilibrium state. Some extension of classical equilibrium thermodynamics is necessary for us to be able to
analyze nonequilibrium (or irreversible) processes. We do this by subdividing a nonequilibrium system into
many small but finite volume elements, each of which is larger than the local molecular mean free path, so
that the continuum hypothesis holds. We then assume that each of these small volume elements is in local
equilibrium. Thus, a nonequilibrium system can be broken down into a very large number of very small systems,
each of which is at a different equilibrium state. This technique is similar to the continuum hypothesis,
wherein continuum equations are used to describe the results of the motion of discrete molecules (see
Chapter 2).
The differential time quantity dt used in nonequilibrium thermodynamic analysis cannot be allowed to go to
zero as in normal calculus. We require that dt > σ s , where σ is the time it takes for one of the volume elements
of the subdivided nonequilibrium system just described to “relax” from its current nonequilibrium state to an
appropriate equilibrium state. This is analogous to not allowing the physical size of the element to be less than
its local molecular mean free path, as required by the continuum hypothesis. The error incurred by these postulates
is really quite small, because they are the result of second-order variations of the thermodynamic variables
from their equilibrium values. However, just as the continuum hypothesis can be violated by systems such as
rarefied gases, the local equilibrium postulate can also be violated by highly nonequilibrium systems such as
explosive chemical reactions. In the case of such violations, the analysis must be carried forward with techniques
of statistical thermodynamics.
Because of the similarity between the local equilibrium postulate and the continuum hypothesis, it is clear that
the local equilibrium postulate could as well be called the continuum thermodynamics hypothesis.
SIMPLE SYSTEM
Any two independent intensive property values are sufficient to determine (or “fix”) the local equilibrium state of a simple
system.