Modern Engineering Thermodynamics

130 CHAPTER 4: The First Law of Thermodynamics and Energy Transport Mechanisms
Table 4.9 Typical Emissivity Values for Various Materials
Material Temperature (°C/°F) Emissivity ε (dimensionless)
Aluminum 100/212 0.09
Iron (oxidized) 100/212 0.74
Iron (molten) 1650/3000 0.28
Concrete 21/70 0.88
Flat black paint 21/70 0.90
Flat white paint 21/70 0.88
Aluminum paint 21/70 0.39
Water 0–100/32–212 0.96
ThesignconventionintheStefan-BoltzmannlawhasbeenchosentobepositivewhenT 2 > T 1 ; therefore, the
“system” should be object 1 to achieve the correct thermodynamic sign convention. Also note that this equation contains
the temperature raised to the fourth power. This means that absolute temperature units must always be used.
4.14 A THERMODYNAMIC PROBLEM SOLVING TECHNIQUE
The previous 11 example problems have been relatively straightforward, mainly illustrating the use of specific
energy and work mode equations. However, most thermodynamics problems are not so straightforward, and
now we are ready to introduce a comprehensive thermodynamic problem solving technique that allows you to
set up and solve even the most complex thermodynamics problems.
Thermodynamic problem statements sometimes have the appearance of being stories full of technical jargon,
liberally sprinkled with numbers. All too often, your first instinct on being faced with such a situation is to calculate
something—anything—because the act of calculation brings about the euphoria of apparent progress
toward a solution. However, this approach is quickly stalled by the inability to reach the final answer, followed
by long frustrating periods of shoe shuffling and window staring until either enlightenment, discouragement, or
sleep occurs. This is definitely the wrong problem solving technique. A good technique must have definite starting
and ending points, and it must contain clear and logical steps that carry you toward a solution.
As a prelude to discussing the details of the problem solving technique, you should realize that the general
structure of a thermodynamic word problem usually contains the following three features.
1. A thermodynamic problem statement is usually a small “story” that is too long to be completely and
accurately memorized no matter how many times you read it. So simply reading the problem statement
once is usually not enough; you must translate it into your own personal environment by adding a
schematic drawing, writing down relevant assumptions, and beginning a structured solution.
2. To completely understand the problem statement, you must first “decode” it. That is, you must dissect and
rearrange the problem statement until it fits into a familiar pattern. Any problem solving technique is, of
course, based on the premise that the problem has a solution. Curiously, it is very easy to construct problem
statements that are not solvable without the introduction of extraneous material (judiciously called
assumptions).
3. Thermodynamic problem statements tend to be very wide ranging. They can be written about virtually any
type of system and can deal with virtually any form of technology. To give the problem statements a
pragmatic engineering flavor, they are usually written as tiny stories that are designed to reflect what you
will encounter as a working engineer.
Unfortunately, many students facing thermodynamics for the first time are overwhelmed by these factors. How
are you supposed to know anything about how a nuclear power plant operates, how the combustion chamber
of a turbojet engine functions, or how a boiler feed pump works if you have never actually seen one in operation?
The key is that you really do not have to know that much about how these things work to carry out a
good thermodynamic analysis of them. But, you do have to understand how problem statements are written
and how to analyze them correctly. This is the core of the problem solving technique.
In fact, it would be possible to write a computer program that could solve any thermodynamic word problem.
What we are going to do is to show you how to solve thermodynamic problems by using a computerlike flowchart
approach, as in Figure 4.21.
The technique is really very simple. First, you must learn to formulate a general starting point. Then you must
learn to identify the key logical decisions that have to be made as the solution progresses. Finally, when all the