Modern Engineering Thermodynamics

14 CHAPTER 1: The Beginning
EXAMPLE 1.4 (Continued )
Solution
a. From the text, we see that g c is always a constant. It does not depend on the local acceleration of gravity. From Eq. (1.6)
and Table 1.2, we find that in the Engineering English units system g c = 32.174 lbm·ft/lbf·s 2 .
b. Since weight is force due to gravity, we have W = F = mg/g c , and the mass can be computed from m = Wg c /g, or
m =
ð25,000 lbfÞ 32:174 lbm
.ft
lbf .s 2
32:174 ft = 25,000 lbm
s 2
Then the weight in Earth orbit is
W orbit = mg orbit
g c
= ð25,000 lbmÞð2:50 ft/s2 Þ
32:174 lbm .ft
lbf .s 2
= 1940 lbf
Exercises
10. Suppose you use the SI units system in Example 1.4. What is the value of g c in the orbit? Answer: 1.0 and dimensionless
(see Table 1.2).
11. Suppose the orbit in Example 1.4 changes so that the local acceleration of gravity is decreased from 2.50 ft/s 2 to 1.75 ft/s 2 .
Determine the new weight of the telescope in orbit. Answer: W orbit = 1360 lbf.
12. If the telescope in Example 1.4 weighs 112 kN on the surface of the Earth, how much does it weigh on the surface of
the Moon, where the local gravity is only 1.60 m/s 2 ? Answer: W moon = 18.3 kN.
1.8 CHEMICAL UNITS
A good deal of energy conversion technology comes from converting the chemical energy of fuels into thermal
energy. Therefore, we need to be aware of the nature of units used in chemical reactions.
A chemical reaction equation is essentially a molecular mass balance equation. For example, the equation
A + B = C tells us that one molecule of A reacts with one molecule of B to yield one molecule of C. Since
the molecular mass of substance A, M A , contains the same number of molecules (6.022 × 10 23 , Avogadro’s
constant) as the molecular masses M B and M C of substances B and C, the coefficients in their chemical
reaction equation are also equal to the number of molecular masses involved in the reaction as well as the
number of molecules.
Chemists find it convenient to use a mass unit that is proportional to the molecular masses of the substances
involved in a reaction. Since chemists use only small amounts of chemicals in laboratory experiments, the
centimeter-gram-second (CGS) units system has proven to be ideal for their work. Therefore, chemists defined
their molecular mass unit as the amount of any chemical substance that has a mass in grams numerically equal to the
molecular mass of the substance and gave it the name mole.
However, the chemists’ mole unit is problematic, in that most of the other physical sciences do not use the
CGS units system and the actual size of the molar mass unit depends on the size of the mass unit in the
units system being used. Strictly speaking, the molar mass unit used by chemists should be called a gram
mole, becausethewordmole by itself does not convey the type of mass unit used in the units system. Consequently,
we call the molar mass of a substance in the SI system a kilogram mole; in the Absolute and Engineering
English systems it is a pound mole; and in the Technical English system it is a slug mole. Inthistext,
we abbreviate gram mole as gmole, kilogram mole as kgmole, and pound mole as lbmole. Clearly, these are all
different amounts of mass, since 1 gmole ≠1 kgmole≠ 1 lbmole ≠ 1 slug mole. For example, 1 pound mole
of water would have a mass of 18 lbm, whereas 1 gram mole would have a mass of only 18 g (0.04 lbm),
so that there is an enormous difference in the molar masses of a substance depending on the units system
being used.
Since the molar amount n of a substance having a mass m is given by
n = m M
(1.9)