Modern Engineering Thermodynamics

Problems 403
Design Problems
The following are open-ended design problems. The objective is to
carry out a preliminary thermal design as indicated. A detailed design
with working drawings is not expected unless otherwise specified.
These problems do not have specific answers, so each student’s
design is unique.
70. Design a system to liquefy nitrogen by repeatedly expanding it
until it reaches the saturation temperature. (Hint: Consult your
library about the Linde gas liquefaction process.)
71. Design a system to cut ice into various two-dimensional shapes
using localized pressure to produce a phase change and thus
locally “melting” out the desired shape. (Suggestion: Try a highpressure
“cookie-cutter” technique.)
72.* Design a fire extinguisher system that expands liquid carbon
dioxide under a suitable pressure at ambient temperature
(which can vary by ±50.0°C) and produce a fine spray of solid
carbon dioxide particles at high velocity and low temperature.
73. Design a 3.00 ft 3 cylindrical tank that safely contains oxygen gas
at 2500. psia under ambient temperature conditions (which can
vary by ±100.°F). (Suggestion: Consult the ASME Pressure
Vessel Design Codes in your library.)
74.* Design an experiment that illustrates and accurately measures
the difference in p-v-T behavior between water vapor and a
suitable ideal gas (such as air) over the temperature range from
0.00 to 150.°C.
Computer Problems
The following computer assignments are designed to be carried out
on a personal computer using a spreadsheet or equation solver. They
may be used as part of a weekly homework assignment.
75.* Develop a computer program, spreadsheet, equation solver, or
the like to determine the percent error in the pressure predicted
by the van der Waals equation of state for water along the T =
500°C isotherm, p = RT/(v – b) – a/v 2 . Use Table C.3b or other
appropriate tables for the actual values of p for various values of
v at T = 500.°C. The van der Waals coefficients for water vapor
can be found in Table C.15b.
76.* Develop a computer program, spreadsheet, equation solver, or
the like to determine the percent error in the pressure predicted
by the Beattie-Bridgeman equation of state for water along the
T = 500.°C isotherm, p = [(1 – ε)(v + B)RT – A]/v 2 , where
A =A o (1 – a/v), B = B o (1 – b/v), and ε = c/(vT 3 ). Use Table C.3b
or other appropriate tables for the actual values of p for various
values of v at T = 500.°C. The Beattie-Bridgeman coefficients for
water vapor can be found in Table C.15b.
77.* Develop a computer program, spreadsheet, equation solver, or the
like to determine the percent error in the pressure predicted by the
Redlich-Kwong equation of state for water along the T =500.°C
isotherm, p = RT/(v – b) – a/[v (v + b)T 1/2 ]. Use Table C.3b or other
appropriate tables for the actual values of p for various values of v
at T =500.°C. The Redlich-Kwong coefficients for water vapor can
be found in Table C.15b.
78. Plot a minimum of 100 points along the T = 500. R isotherm
on p-v coordinates for air using
a. The ideal gas equation of state.
b. The Clausius equation of state (use the van der Waals value
for b).
79. Plot a minimum of 100 points along the T = 500. R isotherm
on p-v coordinates for hydrogen using
a. The ideal gas equation of state.
b. The van der Waals equation of state.
80. Plot a minimum of 100 points along the T = 500. R isotherm
on p-v coordinates for methane using
a. The ideal gas equation of state.
b. The Beattie-Bridgeman equation of state.
81. Using the steam tables as a guide, find the regions on a Mollier
diagram or a p-v diagram where the ideal gas equations with
constant specific heats are accurate to within ±1.00% for
a. Specific volume v.
b. Enthalpy h.
c. Entropy s.
82. Expand Problem 81 by adding temperature-dependent ideal gas
specific heats.
83. Expand Problem 81 by using the van der Waals equation of
state in place of the ideal gas equation of state.
84. Develop an interactive computer program for ammonia using
the Beattie-Bridgeman equation of state to produce the
following results from responses to appropriate screen prompts:
a. Output p when v and T are input.
b. Output T when p and v are input.
c. Output v when p and T are input.
85. Develop an interactive computer program that replaces the gas
tables Tables C.16a and C.16b. Do this in two steps:
a. First have the program return u, h, ϕ, p r , and v r when T is
input by assuming constant specific heats.
b. Modify the program developed in step a to include the
temperature-dependent specific heats given in Table C.14
in Thermodynamic Tables to accompany Modern Engineering
Thermodynamics.
86.* The purpose of this assignment is to investigate the accuracy of
several historically important p-T relations for saturated water
vapor. Using the tables in the tables book or some other source
for accurate saturation p-T data, calculate, tabulate, and plot the
percent error in saturation pressure for each of the following
cases using % error = (CP – TP)/TP, where CP is the calculated
saturation pressure and TP is the saturation pressure found in
the steam tables.
a. By 1847, Henri Regnault had developed an equation from
his experimental p sat – T sat results for saturated steam. It was
valid in the range of −33.0 to 232°C and had the form
where p sat is in mm Hg and
log 10 p sat = A − BD n − CE n
A = 6:2640348 log 10 D = 9:994049292 − 10
log 10 B = 0:1397743 log 10 E = 9:998343862 − 10
log 10 C = 0:6924351
n = T sat + 20:0°C
Make your % error calculations every 20.0°C between 20.0
and 220.°C.
b. In 1849 Williams Rankine fit his own equation to
Regnault’s data and came up with the following relation:
log 10 p sat = A − B/T sat − C/Tsat
2
where p sat is in psia and T sat = T sat (in °F) + 461.2 (–461.2°F
was Rankine’s best estimate of absolute zero), and
A = 6:1007 log 10 B = 3:43642 log 10 C = 5:59873