Modern Engineering Thermodynamics

358 CHAPTER 10: Availability Analysis
70. The turbine of a large power plant receives 1.00 × 10 8 Btu/h of
heat from the boiler at 900.°F and rejects 5.50 × 10 6 Btu/h of
heat to the condenser at 60.0°F while producing 22.0 × 10 3 kW
of electrical power. The local environment (ground state) is at
14.7 psia and 50.0°F. Determine
a. The first law thermal efficiency.
b. The rate at which available energy enters the boiler.
c. The rate at which available energy enters the condenser.
d. The second law availability efficiency of the power plant.
71. The Heat-Master is a new heat pump design that has a Carnot
COP (coefficient of performance) of 15.5. However, its actual
coefficient of performance is only 6.90. Determine the second
law availability efficiency of this heat pump.
72.* A heat pump is designed to provide 9.00 kW of heat to a
small house at 20.0°C when the outside temperature is 5.00°C.
The electric motor driving the heat pump draws 1.20 kW.
Determine:
a. The first law thermal efficiency (i.e., COP) of the heat pump.
b. The second law availability efficiency of the heat pump.
73. The Cool-Master is a new window air conditioner design that
has a Carnot coefficient of performance (COP) of 18.9.
However, its actual coefficient of performance is only 3.30.
Determine the second law availability efficiency of this air
conditioner.
74. A common window air conditioner has an actual COP of
7.88. If the inside temperature is T 0 = T L = 75.0°F andthe
outside temperature is 95.0°F, then determine the second
law availability efficiency of this air conditioner.
75. Liquid water is to be heated in a nonmixing heat exchanger
with waste steam. The liquid water (an incompressible liquid)
flows through the heat exchanger at 15.0 lbm/s with an inlet
temperature of 50.0°F and an exit temperature of 75.0°F. The
steam flows through the heat exchanger at 3.00 lbm/s with an
inlet state of 600.°F and 60.0 psia and an exit state of 400.°F
and 40.0 psia. Determine the second law availability efficiency
of this heat exchanger. Neglect all kinetic and potential energy
effects, and use saturated liquid water at 50.0°F as the local
environment (ground state).
76. The inlet air to a gas turbine engine is preheated with the
engine’s exhaust gases. The preheater is insulated so that all
heat transfer is internal. The engine’s exhaust gas enters the
preheater at 800.°F and 1.30 atm pressure and exits at 500.°F
and 1.00 atm. The inlet air enters the preheater at 70.0°F and
1.40 atm and exits at 1.30 atm. The mass flow rates of the
inlet air and the exiting exhaust are approximately the same at
2.10 lbm/s. Both gases can be treated as constant specific heat
ideal gases. The specific heat and gas constant of the exhaust
gas are (c p ) exh. = 0.238 Btu/(lbm·R) and R exh. = 0.0640 Btu/
(lbm·R). Neglecting all kinetic and potential energies, and
taking the local environment (ground state) as p 0 = 1.00 atm,
and T 0 = 70.0°F, determine:
a. The exit temperature of the inlet air.
b. The second law availability efficiency of the preheater.
77.* Can you believe that 0.800 kg/s of air at 60.0°C and1.50
MPa is mixed in an open heat exchanger with 1.50 kg/s of
air at 20.0°C and 1.50 MPa to produce an outlet mixture at
30.0°C at 1.50 MPa? Determine the second law availability
efficiency of this heat exchanger. Neglect all kinetic and
potential energy effects, and take the local environment
(ground state) to be 0.101 MPa and 20.0°C.
78.* A student is using a bathtub with separate hot and cold water
faucets. The student turns on both faucets and adjusts them to
create a pool of warm water in the tub. The tub’s drain is
open, so the faucets must be kept running to maintain the
pool of water. The hot water faucet provides 40.0°C water at
0.100 kg/s, and the cold water faucet provides 15.0°C water at
0.250 kg/s. The local environment (ground state) is at 0.101
MPa and 18.0°C. Neglecting all flow stream kinetic and
potential energy and assuming the tub itself is insulated,
determine
a. The temperature of the mixed water in the tub.
b. The second law availability efficiency of the tub as a
mixing type heat exchanger.
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 required unless otherwise specified by
your instructor. These problems do not have specific answers, so each
student’s design is unique.
79.* Carry out the preliminary design of a closed domestic hot
water heater that has a first law efficiency of at least 95.0%
and a second law efficiency of at least 10.0%. The inlet water
temperature is fixed at 10.0°C. The remaining variables
(including the ground state) are unrestrained and can be
chosen to fit the needs of the designer.
80. You are to prepare the preliminary design of a commercial,
open, liquid water heater that has a first law efficiency of at
least 88.0% and a second law efficiency of at least 15.0%. The
inlet water temperature is fixed at 50.0°F. The remaining
variables (including the ground state) are unrestrained and can
be chosen to fit the needs of the designer.
81.* As chief engineer of a large heat exchanger company, you are
to prepare the preliminary design of a nonmixing heat
exchanger that has a second law availability efficiency of at
least 15.0%. The two flow streams are to be liquid water,
with one flow stream having a mass flow rate of 10 kg/s,
entering at 10.0°C and leaving at 30.0°C. The remaining
variables (including the ground state) are not specified and
are left to the discretion of the designer.
82. Design a benchtop apparatus that illustrates the basic
principles of a mixing heat exchanger. You may use either
liquids or gases or a combination of liquids and gases as the
flow streams. Determine the measurements that must be made
to compute the second law availability of the heat exchanger.
83. Carry out the preliminary design of an instrument that
provides a readout of the specific availability of any fluid
(liquid or gas) in which it is immersed. Determine the
necessary sensors and any calibration procedure required.
Computer Problems
The following open-ended computer problems are designed to be
done on a personal computer using a spreadsheet or equation solver.
84. Plot the specific availability of the air in the tank in Example
10.2 as a function of air pressure. Assume all the remaining
variables are constant.