Modern Engineering Thermodynamics

Problems 277
46. a. Determine a formula for the final pressure (p 2 )thatresults
when two volumes of the same constant specific heat ideal
gas initially at p a , T a and p b , T b are mixed isentropically.
b. Does this mixture pressure represent an upper or lower
bound when this mixing is done adiabatically but not
isentropically?
47. Determine the entropy produced as 5.0 × 10 –3 lbm of human
saliva at 98.6°F is adiabatically mixed with 3.00 × 10 –3 lbm of
human saliva at 103.2°F in a passionate and infectious kiss. The
specific heat of the saliva is 0.950 Btu/(lbm·R).
48.* Determine the entropy produced as 10.0 kg of liquid water at
10.0°C is adiabatically mixed with 20.0 kg of liquid water at
80.0°C. The specific heat of the water is 4.20 kJ/(kg·K).
49. Here is the complete classical coffee and cream problem. Which
of the following processes produces less entropy:
a. Mixing cream with hot coffee and letting the mixture cool to
the drinking temperature.
b. Letting the coffee cool to a temperature such that, when the
cream is added, the mixture will be at the drinking
temperature? Do not ignore the cooling heat transfer entropy
production.
Design Problems
The following are elementary, 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.
50.* Carry out a preliminary thermodynamic design of a system that
heats 20.0 kg of liquid water from 20.0 to 80.0°C in 15.0 min
at atmospheric pressure in a closed vessel. Use an electrical
heating system and determine the electrical power and current
requirements (assume standard line voltage values). Include a
means of relieving any pressure buildup, and discuss safety
considerations.
51. Carry out a preliminary thermodynamic design of a single
piston-cylinder apparatus that produces 25.0 hp as it moves
through a mechanical cycle in 10.0 s. The piston is to be
drawn into the cylinder by condensing steam that enters the
apparatusasasaturatedvaporat212°F. No work is done
during the return stroke of the piston, during which time a
fresh charge of steam is drawn into the apparatus. Continuous
motion of this type can be accomplished through the use of a
flywheel.
52.* Carry out a preliminary thermodynamic design of a system that
mixes by only diffusive processes 5.00 kg of gaseous CO 2 with
10.0 kg of air in a maximum of 6.00 min in a closed, rigid
vessel. Specify the vessel material, size, and internal geometry
and discuss any relevant safety considerations.
Computer Problems
The following computer assignments are designed to be carried out
on a personal computer using a spreadsheet or equation solver. They
are meant to be exercises using some of the basic formulae of
this chapter. They may be used as part of a weekly homework
assignment.
53. Develop a program that determines the power output from
a reversible solar power plant similar to that discussed in
Example 8.2. Input all the relevant variables (in proper units),
and output the net reversible electrical power produced. At
your instructor’s discretion, add screen graphics depicting
a diagram of the power plant and the input and output
variables. Allow the choice of working in either Engineering
English or SI units.
54. Develop a program that performs an energy and entropy
balance on a closed system with an isothermal boundary. The
system contains an incompressible substance (either a liquid
or a solid) that is undergoing an irreversible process. Input (in
proper units) the heat and work transports of energy, the
system volume, the initial internal temperature and the
isothermal boundary temperature of the system, and the
density and specific heat of the incompressible material
contained in the system. Output to the screen the system
mass, final temperature, and entropy production. Note that, if
the entropy production becomes negative (an impossible
physical situation), then the system boundary temperature was
not properly specified. Check for this possibility and prompt
the user for another boundary temperature if it occurs.
Allow the choice of working in either Engineering English
or SI units.
55. Develop a program that performs an energy and an entropy
balance on a closed system with an isothermal boundary. The
system contains an ideal gas with constant specific heats that is
undergoing an irreversible process. Input (in proper units): the
heat and work transports of energy, the system volume, the
initial temperature and pressure of the system, and the
constant volume specific heat and gas constant of the gas
contained in the system. Output to the screen the system mass,
the final pressure and temperature, and the entropy production
for the process. Check to make sure the entropy production is
positive and prompt the user for corrected input if it is not. Allow
the choice of working in either Engineering English or SI units.
56. Repeat Problem 55, except allow the user to choose the system
ideal gas from a screen menu and omit the prompts for gas
properties. Use the data in Table C.13 of Thermodynamic Tables to
accompany Modern Engineering Thermodynamics for the properties
of the gases in your menu.
57.* Develop a program that allows you to plot the entropy
production rate due to the heat transfer from the fin in
Example 8.12 vs. the base temperature of the fin T f .Allow
the T f to range from 20.0 to 200.°C. Keep all the remaining
variables constant.
58.* The temperature profile for the fin discussed in Example 8.12 is
for a “very long” (i.e., infinite) fin. A more accurate equation for
a finite fin of length L is
cosh½mðL − xÞŠ + ½h/ðmkÞŠ sinh½mðL − xÞŠ
TðxÞ = T ∞ + ðT f − T ∞ Þ
coshðmLÞ + ½h/ðmkÞŠ sinhðmLÞ
where the remaining variables are defined in Example 8.12.
Using this temperature profile, rework Example 8.12 and
Problem 57 to produce a new plot of entropy production rate vs.
fin base temperature (you may wish to use a numerical