Modern Engineering Thermodynamics

6 CHAPTER 1: The Beginning
EXAMPLE 1.1 (Continued )
Then, the acceleration becomes
a =
Remember, the answer is not correct if the units are not correct.
176 − 125 feet
second
= 10:3 feet
5 seconds
second 2 = 10:3ft/s2
Following most of the Example problems in this text are a few Exercises, complete with answers, that are based on the
Example. These exercises are designed to allow you to build your problem solving skills and develop self-confidence. The
exercises are to be solved by following the solution structure of the preceding example problem. Here are typical exercise
problems based on Example 1.1.
Exercises
1. Determine the acceleration of the race car in Example 1.1 if its final velocity is 130. mph instead of 120. mph.
Answer: a = 13.2 feet/second 2 .
2. If the racecar in Example 1.1 has a constant acceleration of 10.0 ft/s 2 , determine its velocity after 6.00 s.
Answer: V = 126 mph.
3. A dragster travels a straight level 1 4 mile drag strip in 6.00 s from a standing start (i.e., X initial = V initial = 0). Determine the
average constant acceleration of the dragster. Hint: The basic physics equation you need here is X final = V initial × t +( 1 2 )at2 .
Answer: a = 73.3 ft/s 2 .
3 You may be wondering why there are decimal points and extra zeros added to some of these numbers. This is because we are indicating the number of
significant figures represented by these values. The subject of significant figures is covered later in this chapter.
4 For future reference, there are “exactly” 5280 feet in one mile and “exactly” 3600 seconds in one hour.
1.4 UNITS AND DIMENSIONS
In thermodynamics, you determine the energy of a system in its many forms and master the mechanisms by
which the energy can be converted from one form to another. A key element in this process is the use of a consistent
set of dimensions and units. A calculated engineering quantity always has two parts, the numerical value
and the associated units. The result of any analysis must be correct in both categories: It must have the correct
numerical value and it must have the correct units.
Engineering students should understand the origins of and relationships among the several units systems
currently in use within the profession. Earlier measurements were carried out with elementary and often inconsistently
defined units. In the material that follows, the development of measurement and units systems is presented
in some detail. The most important part of this material is that covering modern units systems.
1.5 HOW DO WE MEASURE THINGS?
Metrology is the study of measurement, the source of reproducible quantification in science and engineering. It deals
with the dimensions, units, and numbers necessary to make meaningful measurements and calculations. It does not
deal with the technology of measurement, so it is not concerned with how measurements are actually made.
We call each measurable characteristic of a quantity a dimension of that quantity. If the quantity exists in the
material world, then it automatically has three spatial dimensions (length, width, and height), all of which are
called length (L) dimensions. If the quantity changes in time, then it also has a temporal dimension called time (t).
Some dimensions are not unique because they are made up of other dimensions. For example, an area (A) isa
measurable characteristic of an object and therefore one of its dimensions. However, the area dimension is the
same as the length dimension squared (A = L 2 ). On the other hand, we could say that the length dimension is the
same as the square root of the area dimension.
Even though there seems to be a lack of distinguishing characteristics that allow one dimension to be recognized
as more fundamental than some other dimension, we easily recognize an apparent utilitarian hierarchy within a
set of similar dimensions. We therefore choose to call some dimensions fundamental and all other dimensions
related to the chosen fundamental dimensions secondary or derived. It is important to understand that not all systems
of dimensional analysis have the same set of fundamental dimensions.
Units provide us with a numerical scale whereby we can carry out a measurement of a quantity. They are established
quite arbitrarily and are codified by civil law or cultural custom. How the dimension of length ends up