Modern Engineering Thermodynamics

76 CHAPTER 3: Thermodynamic Properties
EXAMPLE 3.5 (Continued )
state (the critical state), and we are asked to determine a thermodynamic property (the mass) at the initial state. In Table 3.4
or Table C.12a of Thermodynamic Tables to accompany Modern Engineering Thermodynamics, we find for water that p c = 3203.8
psia, T c = 1165.1R, and v c = 0.05053 ft 3 /lbm. Also, since both the volume and mass are constant here, v 2 = v 1 = v c .This
process can then be diagrammed as follows:
Constant volume
Initial state !
process
p 1 = 14:696 psia
T 1 = 212°F ðsaturatedÞ
v 1 = v 2 ðfrom the process pathÞ
Final state
p 2 = p c
T 2 = T c
v 2 = v c
Therefore,
m = V v 1
= V v 2
= V v c
=
0:500 ft 3
0:05053 ft 3 = 9:90 lbm
/lbm
We can now find the quality in the initial state by using Eq. (3.26) and the data given in Example 3.2 as
x 1 = v − v f 1
v fg1
= v c − v f 1
v g1 − v f 1
=
ð 0:05053 − 0:01672 Þft3 /lbm
ð26:8 − 0:01672Þft 3 /lbm = 1:26 × 10−3 = 0:126% vapor
Final state (critical point)
x = 1.00
p
x = 0.00
Process
path
14.696
psia
v 1 = v 2 = v c
Initial state
v
p-v diagram
FIGURE 3.19
Example 3.5. Note that, since the quality is not defined at the critical state (quality is one of the properties that has a discontinuity
there), no value for x 2 = x c can be given.
3.9 THERMODYNAMIC EQUATIONS OF STATE
In this section, we discuss some of the basic p-v-T equations of state for various substances. These equations can
be easily typed into a computer spreadsheet, which greatly simplifies the calculations and allows for studying
the effect of varying individual terms and plotting of the results. All engineering students today have access to a
computer, and numerous computer programs can be found on the Internet that calculate the thermodynamic
properties of water, refrigerants, and various other substances.
WHO WAS EMMY NOETHER?
PART 3
From 1908 to 1915, Emmy Noether taught at the University of Erlangen’s Mathematical Institute without pay, occasionally
substituting for her father when he was too ill to lecture. In the spring of 1915, she was invited to return to the University
of Göttingen by David Hilbert and Felix Klein. Their effort to recruit her, however, was blocked by the faculty: Women,
they insisted, should not become faculty. One faculty member protested: “What will our soldiers think when they return to
the university and find that they are required to learn at the feet of a woman?” Hilbert responded with indignation, stating,
“I do not see that the sex of the candidate is an argument against her admission as faculty. 3 After all, we are a university,
not a bath house.”