Modern Engineering Thermodynamics

10 CHAPTER 1: The Beginning
EXAMPLE 1.2 (Continued )
Solution
(a) From Table 1.1, we find that both 0°N and 32°F correspond to the freezing point of water, and body heat (temperature)
corresponds to 12°N and 98.6°F (on the modern Fahrenheit scale) on these scales. Since both these scales are linear
temperature scales, we can construct a simple proportional relation between the two scales as
98:6 − 55
98:6 − 32 = 12 − x
12 − 0
where x is the temperature on the Newton scale that corresponds to 55°F. Solving for x gives
98:6 − 55
x = 12 1 − = 4:14°N⁡
98:6 − 32
(b) Since the Reaumur scale is also a linear scale with 0°Re and 80°Re corresponding to 32°F and 212°F, respectively, we
can establish the following proportion for the Reaumur temperature y that corresponds to 55°F:
from which we can solve for
212 − 55
212 − 32 = 80 − y
80 − 0
212 − 55
y = 80 1 −
212 − 32
= 10:2°Re⁡
(c) Here we have 273.15 K and 373.15 K corresponding to 32°F and 212°F, respectively. The proportionality between these
scales is then
212 − 55
212 − 32 = 373:15 − z
373:15 − 273:15
from which we can compute the Kelvin temperature z that corresponds to 55°F as
212 − 55
z = 373:15 − ð373:15 − 273:15Þ = 285:9K⁡
212 − 32
Notice that we do not use the degree symbol (°) with either the Kelvin or the Rankine absolute temperature scale symbols.
The reason for this is by international agreement as explained later in this chapter.
Exercises
4. Convert 20.0°C into Kelvin and Rankine. Answer: 293.2 K and 527.7 R.
5. Convert 30°C into degrees Newton and degrees Reaumur. Answer: 9.7°N and 24°Re.
6. Convert 500. K into Rankine, degrees Celsius, and degrees Fahrenheit. Answer: 900 R, 226.9°C, and 440.3°F.
1.7 CLASSICAL MECHANICAL AND ELECTRICAL UNITS SYSTEMS
The establishment of a stable system of units requires the identification of certain measures that must be taken
as absolutely fundamental and indefinable. For example, one cannot define length, time, or mass in terms of
more fundamental dimensions. They all seem to be fundamental quantities. Since we have so many quantities
that can be taken as fundamental, we have no single unique system of units. Instead, there are many equivalent
units systems, built on different fundamental dimensions. However, all the existing units systems today have
one thing in common—they have all been developed from the same set of fundamental equations of physics,
equations more or less arbitrarily chosen for this task.
It turns out that all the equations of physics are mere proportionalities into which one must always introduce a
“constant of proportionality” to obtain an equality. These proportionality constants are intimately related to the
system of units used in producing the numerical calculations. Consequently, three basic decisions must be made
in establishing a consistent system of units:
1. The choice of the fundamental quantities on which the system of units is to be based.
2. The choice of the fundamental equations that serve to define the secondary quantities of the system of units.
3. The choice of the magnitude and dimensions of the inherent constants of proportionality that appear in the
fundamental equations.
With this degree of flexibility, it is easy to see why such a large number of measurement units systems have
evolved throughout history.