Modern Engineering Thermodynamics

Problems 531
horsepower hour. Assuming a heating value for coal of
13.0 × 10 3 Btu/lbm and that the engine was reversible,
determine the thermal efficiency of this engine.
49. The air standard Ericsson cycle (see Figure 13.40) is made up of
an isothermal compressor (T 2 =T 3 =T L ), an isothermal prime
mover (T 1 =T 4 =T H ), and an isobaric regenerator (p 1 = p 2 and
p 3 = p 4 ). Show that the compressor and prime mover must have
identical pressure ratios, that is, p 2 /p 3 =p 1 /p 4 , and show that this
also requires that v 3 /v 2 =v 4 /v 1 .
50.* An Ericsson cycle operates with a compressor inlet pressure and
volume of 1.00 MPa, 0.0200 m 3 and a turbine inlet pressure and
volume of 5.00 MPa, 0.0400 m 3 . For a reversible cycle, determine
a. The heat added.
b. The heat rejected.
c. The work done.
d. The thermal efficiency of the cycle.
51.* An inventor claims to have developed a Lenoir engine with an
isentropic compression ratio of 8.00 to 1 that produces a
combustion temperature of 1500.°C when the intake temperature
is 20.0°C. Assuming k = 1.40 and that the engine operates on a
cold ASC, show whether or not the inventor’s claim is possible.
52.* A World War II Lenoir cycle “buzz bomb” has an air intake at
10.0°C, a combustion temperature of 1000.°C, and a compression
ratio of 2.30. Determine its cold ASC thermal efficiency.
53.* Plot the cold ASC thermal efficiency of a Lenoir engine having an
air intake at 15.0°C and a combustion temperature of 2000.°C vs.
the isentropic compression ratio over the range 1.01 ≤ CR ≤ 5.50.
54. A Brayton cold ASC has a turbine isentropic efficiency of 92.0%
and a compressor isentropic pressure ratio of 13.37. The
compressor and turbine inlet temperatures are 500. and 2200. R,
respectively. Determine the value of the compressor isentropic
efficiency that causes the overall thermodynamic thermal
efficiency of this system to be exactly zero.
55. A Brayton cold ASC has a turbine that is 80.0% isentropically
efficient and a compressor with an isentropic pressure ratio of
7.00. The compressor inlet temperature is 530. R and the
turbine inlet temperature is 2460 R. Determine the compressor
isentropic efficiency that causes the entire cycle thermal
efficiency to become exactly zero. Assume k=1.40.
56. Show that the product of the compressor and turbine isentropic
efficiencies must be greater than (T L /T H ) 1/2 if a Brayton cycle gas
turbine unit is to operate at its maximum power output.
57. A test on an open loop Brayton cycle gas turbine produced the
following results:
Net power output = 180:5hp
Air mass flow rate = 20:0 × 10 3 lbm/h
Inlet air temperature = 80:0°F
Inlet air pressure = 14:5 psia
Compressor exit pressure = 195 psia
Compressor isentropic efficiency = 85:0%
Combustion chamber heat addition = 4:00 × 10 6 Btu/h
Using a cold ASC analysis and assuming k = 1.40, determine
a. The cycle thermal efficiency.
b. The isentropic efficiency of the turbine.
58. On July 29, 1949, the first gas turbine installed in the
United States for generating electric power went into service at
the Belle Isle station of the Oklahoma Gas and Electric
Company. 15 It had a 15-stage compressor with an isentropic
pressure ratio of 6 to 1, a 2-stage turbine with overall entrance
and exit temperatures of 1400°F and 780°F, respectively, and the
turbine-generator unit was rated at 3500 kW. Assuming a
Brayton cold ASC, determine
a. The isentropic efficiency of the turbine.
b. The Brayton cold ASC thermal efficiency of the entire
turbine-compressor unit.
59.* The regenerator in a Brayton cycle is simply a heat exchanger
designed to transfer heat from hot exhaust gas to cool inlet
gas. In an “ideal” regenerator, the exit temperature of the
inlet (heated) gas is equal to the entrance temperature of the
exhaust (cooled) gas. Since this is not normally the case in
practice, regenerator (or heat exchanger) efficiency can be
defined as
η regeneration =
ð _Q regeneration Þ actual ðh out − h in Þ
=
heated
ð _Q regeneration Þ ðh in Þ maximum
cooled
− ðh in Þ heated
possible
and, for constant specific heats, this reduces to
ðT out − T in Þ
η regeneration =
heated
ðT in Þ coo1ed − ðT in Þ heated
Note that regeneration is practical only when the engine
exhaust temperature is greater than the compressor exhaust
temperature. Therefore, as the compression and expansion
ratios of the compressor and prime mover increase, the
effectiveness of regeneration decreases. Determine an expression
for the limiting isentropic pressure ratio (PR) in terms of T 1 , T 3 ,
and k for which regeneration is no longer useful in the Brayton
ASC with regeneration as shown in Figure 13.69. Evaluate this
expression to find the limiting pressure ratio when T 1 = 1500.°C,
T 3 = 10.0°C, and k=1.40.
60.* An aircraft gas turbine engine operating on a Brayton cycle has a
cold ASC thermal efficiency of 25.0% when the intake air is at
20.0°C and the combustion chamber outlet temperature is at
1200.°C. Assuming k=1.40, determine
a. The isentropic pressure ratio of the engine.
b. The isentropic compression ratio of the engine.
c. The isentropic outlet temperature of the engine’s
compressor.
d. The optimum isentropic pressure ratio for maximum
isentropic power output from the engine.
e. The optimum isentropic compression ratio for maximum
isentropic power output from the engine.
f. The engine’s thermal efficiency when operated at the
maximum isentropic power output.
61. In Professor John L. Krohn’s laboratory at Arkansas Tech
University, air enters the compressor of an ideal Brayton cycle
at p 1 = 14.5 psi, T 1 = 70.0°F with a volumetric flow rate of
20.0 × 10 3 ft 3 /min. The compressor pressure ratio is 12.0
15 On November 8, 1984, the Belle Isle gas turbine was designated as the 73rd National Historic Mechanical Engineering Landmark by the American
Society of Mechanical Engineers.