Modern Engineering Thermodynamics

84 CHAPTER 3: Thermodynamic Properties
EXAMPLE 3.8 (Continued )
Solution
Since the temperature is very high, we can ignore the intermolecular forces in the propellant gases and use the Clausius
equation of state (this equation is known as the Noble-Abel equation in ballistics literature): p(v − b) =RT, where R = R/M
and R = 8314:3N . m/ ðkgmole . KÞ is the universal gas constant. Then,
where v =1/ρ = 1/(200. kg/m 3 ) = 5.00 × 10 –3 m 3 /kg; and
p max =
RT max
Mðv − bÞ
p max =
RT max
Mðv − bÞ = ½8314:3 Ngm/ðkgmolegKÞŠð2830 + 273:15 KÞ
ð23:26 kg/kgmoleÞð5:00 × 10 −3 − 0:960 × 10 −3 m 3 /kgÞ
= 2:7456 × 10 8 N/m 2 = ð2:7456 × 10 8 N/m 2 1 lbf/in 2
Þ
6894:76 N/m 2
= 39,800 lbf/in 2 absolute = 39,800 psia
Exercises
13. Determine the breech temperature in Example 3.8 if the breech pressure is 60.0 × 10 3 psia and all the remaining
variables are as given in the example. Answer: T breech = 4400°C.
14. Use the van der Waals equation of state to determine the pressure of water vapor at 100°C when the specific volume is
57.79 m 3 /kg. Answer: p = 2.98 kPa. (Hint: The values of a and b for water vapor can be found in Table C.15.)
WHO WAS EMMY NOETHER?
PART 4
When Adolf Hitler became chancellor of Germany in January 1933, one of the first actions of his administration was to
remove all Jews from government positions (including university professors). In April 1933, Noether received a notice that
her right to teach at the University of Göttingen had been withdrawn.
She joined the ranks of dozens of newly unemployed German professors who were searching for positions outside of Germany.
Albert Einstein and Hermann Weyl were subsequently moved to the Institute for Advanced Study in Princeton, and
late in 1933, Emmy Noether accepted a position at Bryn Mawr College, which is located ten miles west of Philadelphia,
Pennsylvania.
In 1934, Noether began lecturing at the Institute for Advanced Study in Princeton (then an all-male university), but she felt
that she was not welcome at the “men’s university, where nothing female is admitted.”
Emmy Noether once said, “If one proves the equality of two numbers a and b by showing first that a is less than or equal
to b, and then a is greater than or equal to b, it is unfair, one should instead show that they are really equal by disclosing
the inner ground for their equality.”
On April 14, 1934, Emmy Noether died suddenly after an operation for a pelvic tumor. Her body was cremated and her
ashes interred under the walkway around the cloisters of the M. Carey Thomas Library at Bryn Mawr College.
3.10 THERMODYNAMIC TABLES
Thermodynamic tables are generated from complex equations of state, which in turn were developed from
accurate experimental data. These tables are quick and easy to use, but they are not available for all materials of
engineering interest. Tables C.1 through C.13 in the Thermodynamic Tables to accompany Modern Engineering Thermodynamics
give the thermodynamic properties of a variety of substances. Basically, only three types of tables are
given there: pressure and temperature entry saturation tables, superheated vapor tables, and compressed or subcooled
liquid tables. The saturation tables contain properties only along the saturation curve (x = 0 and x =1)and
no property values of liquid-vapor mixtures. These mixture properties must be calculated from the saturation
values and the quality using Eq. (3.27). The superheated vapor and compressed liquid tables provide values
throughout their regions of definition. Figure 3.24 illustrates the range of applicability of these tables.