1.1 IDEAS, DIMENSIONS, AND PROPERTIES
The seemingly distinct engineering disciplines, mechanical engineering, electrical engineering, chemical engineering and all others have in common that their respective devices and processes involve energy transfer as work or heat (either in operation or in their construction). In addition, engineering designs must be made safe for the range of temperatures they will experience. Heat, work and the manner of property change with temperatiurenge. are three of the many topics of thermodynamics. A partial list of systems understood in terms of thermodynamic perspectives and principles includes:
Combustion engines that burn gasoline or diesel fuel, jets engines, rockets, fossil and nuclear power plants, mechanical transmissions, gear trains, belts, pumps, compressors, propellers, ... electric motors and generators, transformers, batteries, brakes, shock absorbers, heat exchangers, stove burners, welding torches... windmills, ship design, weather, muscle action, smart-prothesis design... and many others.
Although Engineering Thermodynamics is scarcely 300 years old, its methods and discoveries have proven very beneficial to progress and industrialization. The purpose of this writing is to explain the begging topics, the foundations of Engineering Thermodynamics. Previous reading and familiarity with mathematics, algebra, a little calculus (the sweetest part) and some physics is assumed but is also repeated as needed in this coverage.
BASIC IDEASOur observations of the physical world form the basis of science and engineering studies. Our primal perceptions of existence, co-existence and change are at the root of our understandings of physical reality. The study of thermodynamics needs but a narrow perspective of these ideas:
- System: To engineering thermodynamics existence means matter. All that exists is matter and what is not matter, does not exist. The first step of every instance of thermodynamic inquiry is (directly or in effect) to select specific matter. This matter is called the system.
- Surroundings: Space, or extent, encompasses the idea of co-existence. Matter is said to occupy space and to coexist with other matter in all of space - the universe. All matter not selected at the initiation of a study is called surroundings.
- Event: Time is our abstract of change. We are aware that we live, grow and change in time. We and everything on Earth exists in a continuation of time. We are involved in rate processes. Time is the measure of those events and processes.
With these general ideas or perspectives, Engineering Thermodynamics uses both analysis and experimentation in its studies of physical reality. Experimentation is time-consuming and often prohibitively expensive. Analysis, the use of pencil and paper (or computer) with theories of physical behavior is less costly. Analysis however, always requires great approximation such that its results, or answers, are distorted from reality to the point that they provide only bounds or extremums of behaviors of actual events. This writing focuses on the analytic techniques and methods of thermodynamics.
DIMENSIONS AND UNITS Dimensions which are the engineer's "coordinates of perception" of physical reality, are categorized as primary (some say "base" or "fundamental") dimensions and secondary (some say "derived") dimensions.
Primary Dimensions: Primary dimensions are unique. It is agreed that nine primary, (some say "base" or "fundamental") dimensions are sufficient to describe physical reality. Here, to begin, we need understand only three of the nine.
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Mass:
is both a dimension and a property of any system. As a property it is given the symbol, "m." The notation, [ m ], means, "has the dimension mass." Boxed dimensions are used to check and assure the dimensional consistency of equations. Standardized units for mass are known: The SI (or metric) system uses the kilogram (kg). The Engilish Engineering syatem uses the pound mass.(lbm). The equivalence is: 1 kg = 2.2 lbm.
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Length:
The simplest quantitative idea of space is the "length of a straight line that extends from some point to another." The dimension, length, has the symbol, [L]. An important aspect of length, "area," is a vector property with dimension, length squared ~ [ L ]2. Standardized units for length are: SI (or metric) ~ meter (m), Engineering ~ foot (ft). The equivalence is: m = 3.28 ft.
- Time: The measure of periodicity or duration of an event is time. Brackets placed left and tight of t, [ t ], means "has the dimension, time. Both unit systems use the base unit second ~ s.
Secondary Dimensions Dimensions of many physical quantities are expressed as combinations of the base dimensions. To name just a few physical quantities whose dimensions are secondary:
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Density, (with symbol ~ ρ): Quantity of matter, defined by Newton is today called mass. Mass can be expressed as the product of its density times its volume, m = ρ V. is sometimes written as its reciprocal, v = 1/ρ where lower case V is called specific volume and has the dimension [ L3/m]. A useful equivalence with water as the basis is: 1000 kg/m3 = 62.4 lbm/ft3
. - Energy: with dimension written as [E] or [m][L/t]2
. - Power: which is change of energy with time. Dimensionally, power is [E/t] or [FL/t].
Dimensions and measurement are the tools of science and likewise thermodynamics. Comprehension of physical reality (how events happen, or are caused, and how they proceed) are the understandings we seek. Little calculus or physics is needed to start; that will accrue as we go.
ABOUT PRESENTATION
This writing aims to teach its readers how to apply basic analytic methods of Engineering Thermodynamics. The narration is descriptive TEXT (kept short) with many, thoroughly worked illustrative EXAMPLES. Coverage begins at a high school level with simple, review-type examples. Advance to material of your interest. Simply browse directly through the EXAMPLES until you find something of interest.
Eratosthenes Some 2000 years ago, Eratosthenes, having seen eclipses of the moon, assumed that Earth was spherical and that sunlight arrived to Earth in parallel rays. In a famous experiment, he used these assumptions to measure the circumference of Earth. Use the data of the image. Repeat the calculation Eratosthenes made.
Prove: ( A - B )2 = A2 - 2 AB + B2: Let's take a break from reading to review geometry as it relates to algebra.
LNG Tanker
If you are given a scale drawing along with some "full-size" dimensions of a tanker, there are other dimensions or properties that you can calculate. The volume of cargo of this tanker is 128,000 cubic meters. Calculate the length and beam of the tanker.
Perhaps you understand Eratosthene's experiment and calculation and also the manner of estimation of the length of the LNG Tanker. Those tasks, mensuration and use of physical properties are topics of high school physics. These examples and all examples of thermodynamics have a commonality. Every case or investigation involves a system and its physical properties.
Physical Properties
A physical property of an amount of matter consists of a name, a technical description and at least one process of measurement by which the property can be made quantitative. A measurement of temperature by a calibrated device called a thermometer (or by a thermocouple, can be easy, resulting in a single number. Position (and other vectors) requires the setup of a basis and the determination of three numbers. With regard to numbers, physical properties are tensors and are classed by rank as rank zero, rank one, two or some larger integer.
There are (3)RANK numbers with appropriate dimensions, vector basis and so, associated with a physical tensor or system property. The "numbers" of physical properties must be established by some measurement process.
| RANK | NUMBERS | NAME | EXAMPLES |
| 0 | (3)0 = 1 | scalar | mass, density, length... |
| 1 | (3)1 = 3 | vector | position, velocity, momentum, area. Force and heat are vectors but are not properties. |
| 2 | (3)2 = 9 | tensor | moment of inertial and material stress |
The table shows that only the simplest properties are scalars. Some call position, ("where you are") and velocity, ("the speed and direction you are now moving") "system characteristics" rarther than properties. Area, force and heat are vectors. To understand thermodyanamics requires competence witch generally are ignored by educators, for the most part, by cherry-picking degenerate problems. Geometry, algebra and vectors are needed in engineering analysis. Some refresher-type problems are presented below.
It is likely that the number system, arithmetic, geometry and then algebra were the first sciences. All modern sciences use results from those studies. The next example uses the idea, "The whole area equals the sum of its parts' to obtain a common algebraic formula.
Prove: (-1) x (-1) = 1 Mathematics is essential to science. Calculus (which we will use later) has algebra and geometry as its basis. Can you prove that (-1) times (-1) equals 1?
Sphere, Tank, and Water Geometry, algebra and Calculus are valuable tools. Geometry of the simple, regular shapes etc, might seem trivial but sometimes it gets interesting. Give this problem about the additivity of volumes a try.