Modern Engineering Thermodynamics

1.9 Modern Units Systems 15
where M is the molecular mass 7 of the substance, it is clear that the molecular mass must have units of mass/
mass-mole. Therefore, we can write the molecular mass of water as
M H2 O = 18 g/gmole = 18 lbm/lbmole = 18 kg/kgmole = :::
The numerical value of the molecular mass is constant, but it has units that must be taken into account whenever
it is used in an equation.
EXAMPLE 1.5
A cylindrical drinking glass, 0.07 m in diameter and 0.15 m high, is three-quarters full of water
(Figure 1.12). Determine the number of kilogram moles of water in the glass. The density of
liquid water is exactly 1000 kg/m 3 .
Solution
The mass of water in the glass is equal to the volume of water present multiplied by the density of
water, or
m = πR 2 L × ρ = πð0:035 mÞ 2 ð0:75 × 0:15 mÞ 1000 kg/m 3 = 0:433 kg
3/4 full
0.15 m
The molecular mass of water is 18 kg/kgmole, and Eq. (1.9) gives the number of moles present as
n = m M = 0:433 kg
= 0:024 kgmole
kg
18
kgmole
Exercises
13. Determine the number of lbmole in a cubic foot of air whose mass is 0.075 lbm. The molecular mass
of air is 28.97 lbm/lbmole. Answer: n = 0.00259 lbmole.
14. How many kilograms are contained in 1 kgmole of a polymer with a molecular mass of
2.5 × 10 6 kg/kgmole? Answer: m = 2.5 × 10 6 kg.
15. Exactly 2 kgmole of xenon has a mass of 262.6 kg. What is the molecular mass of xenon?
Answer: M = 131.3 kg/kgmole.
0.07 m
FIGURE 1.12
Example 1.5.
1.9 MODERN UNITS SYSTEMS
The units systems commonly used in thermodynamics today are the traditional Engineering English system and
the metric SI system. Table 1.4 lists various common derived secondary units of the SI system, and Table 1.5
shows the approved SI prefixes, along with their names and symbols.
You need to understand the difference between the units of absolute pressure and gauge pressure. In the Engineering
English units system, we add the letter a or g to the psi (pounds per square inch) pressure units to
make this distinction. Thus, atmospheric pressure can be written as 14.7 psia or as 0 psig. In the SI units system,
we add the word that applies (and not the letter a or g) immediately after the unit name or symbol. For example,
atmospheric pressure in the SI system is 101,325 Pa absolute or 0 Pa gauge. When the words absolute or gauge
do not appear on a pressure unit, assume it is absolute pressure.
In 1967, the degree symbol (°) was officially dropped from the absolute temperature unit, and the notational
scheme was introduced wherein all unit names were to be written without capitalization (unless, of course, they
HOW DO I KNOW WHETHER IT IS ABSOLUTE OR GAUGE PRESSURE?
When the clarifying term absolute or gauge is not present in a pressure unit in the textbook, assume that pressure unit is
absolute. For example, the pressure 15.2 kPa is interpreted to mean 15.2 kPa absolute.
7 Most texts call M the molecular weight, probably out of historical tradition. However, M clearly has units of mass, not weight, and
therefore is more appropriately named molecular mass.