Modern Engineering Thermodynamics

530 CHAPTER 13: Vapor and Gas Power Cycles
36. Steam enters the high-pressure turbine of a Rankine cycle power
plant at 1200. psia and 700.°F and exits as a saturated vapor.
It is then reheated to 600.°F before it enters the low-pressure
turbine, which exhausts to a condenser at 1.00 psia. The
isentropic efficiencies of the high- and low-pressure turbines
and the boiler feed pump are 88.0%, 79.0%, and 65.0%,
respectively. Determine the thermal efficiency and the net power
per unit mass flow rate of steam for this plant.
37.* Consider a steam turbine with a constant inlet temperature of
500.°C connected to a constant pressure condenser at 1.00 kPa.
When the steam expands to a saturated vapor in the turbine, it
is removed and reheated in the boiler to 500.°C then returned
to the turbine to continue to expand until it reaches the
condenser pressure. The turbine isentropic efficiency is constant
at 80.0%. Ignoring the boiler feed pump power, plot
a. The Rankine cycle thermal efficiency.
b. The percent moisture in the turbine exhaust vs. the boiler
pressure over a boiler pressure range of 1.00 to 20.0 MPa.
Computerized steam tables are recommended for this
problem.
38. The first steam turbine used in an American electrical power
plant was a Westinghouse reaction turbine of the Parson’s type
installed at the Hartford, Connecticut, Electric Light Company in
1902. The turbine inlet state was 200. psig and 400.°F, the
generator produced 2.00 MW, and the plant had a heat rate of
35.0 × 10 3 Btu/(kW · h). Determine its thermal efficiency.
39. In 1903, a General Electric Curtis impulse steam turbine was
installed at the Fisk Street Station of the Commonwealth Electric
Company in Chicago, Illinois, and was at that time the most
powerful steam turbine in the world. 13 The turbine inlet state
was 175 psig with 150.°F of superheat, and the condenser
pressure was 1.50 in of mercury. When the generator produced a
net 5000. kW, the steam flow rate per unit of electrical power
produced ( _m / _W elect: ) was 22.5 lbm/(kW · h). For this unit,
determine
a. The isentropic power output of the turbine.
b. The isentropic efficiency of the turbine-generator unit.
c. The isentropic Rankine cycle thermal efficiency of the power
plant, assuming saturated liquid exits the condenser and
neglecting pump work.
40. In 1939, the Port Washington, Wisconsin, power plant of the
Milwaukee Electric Railway and Light Company 14 had an
unusually high heat rate of 10,800 Btu/(kW · h). Determine its
thermal efficiency.
41. Refrigerant-22 is used as the working fluid in a 1.00 MW
Rankine bottoming cycle for a steam power plant. The
bottoming cycle turbine inlet state is saturated vapor at 210.°F,
and the condenser outlet is saturated liquid at 70.0°F. The
turbine and pump isentropic efficiencies are 85.0% and 70.0%,
respectively. Determine
a. The thermal efficiency of the bottoming cycle.
b. The ratio of the pump to turbine power.
c. The required mass flow rate of refrigerant.
42. It is common to model hot ASC performance with the same
formula used in cold ASC analysis except that a specific heat
ratio (k) typical of high-temperature gas is used. Determine the
Carnot ASC thermal efficiency of an engine with an 8.00 to 1
compression ratio, using
a. A cold ASC analysis with k = 1.40.
b. A hot ASC analysis with k = 1.30.
c. Determine the percent decrease in the Carnot thermal
efficiency between the cold and hot ASC analysis.
43. Air enters an engine at 40.0°F and is compressed isentropically
in a 9.00 to 1 compression ratio. Determine the Carnot ASC
thermal efficiency of this engine, using
a. A cold ASC analysis with k = 1.40.
b. A hot ASC analysis using the gas tables (Table C.16a in
Thermodynamic Tables to accompany Modern Engineering
Thermodynamics).
c. Determine the percent decrease in the Carnot thermal
efficiency between the cold and hot ASC analysis.
44.* Air enters an engine at atmospheric pressure and 17.0°C and is
isentropically compressed to 871.4 kPa. Determine the Carnot
ASC thermal efficiency of the engine, using
a. A cold ASC analysis with k = 1.40.
b. A hot ASC analysis using the gas tables (Table C.16b).
c. Determine the percent decrease in the Carnot thermal
efficiency between the cold and hot ASC analysis.
45. Determine the mechanical efficiency of a Stirling cycle engine
operating with a 1300.°F heater and a 100.°F cooler. The
engine produces a net 10.0 hp output with a heat input of
80.0 × 10 3 Btu/h.
46. In 1964, an experimental Stirling engine was installed in a
modified Chevrolet Corvair at the General Motors Research
Laboratory. Alumina (aluminum oxide) heated to 1200.°F served
as the heat source for the engine, while the atmosphere at 100.°F
served as the heat sink (because of the use of alumina in the
engine, the car was dubbed the Calvair by GM researchers).
Assuming a mechanical efficiency of 67.0%, determine the actual
thermal efficiency of the engine based on a cold ASC analysis.
47. A Stirling cycle engine uses 0.0800 lbm of air as the working
fluid. Heat is added to this air isothermally at 1500.°F and is
rejected isothermally at 200.°F. The initial volume of the air
before the heat addition (V 4 in Figure 13.38) is 0.750 ft 3 and
the final volume after the heat addition (V 1 in Figure 13.38)
is 1.00 ft 3 . For the cold ASC, determine
a. The air pressure at the beginning and end of the expansion
stroke (p 4 and p 1 in Figure 13.38).
b. The air pressure at the beginning and end of the
compression stroke (p 2 and p 3 in Figure 13.38).
c. The cold ASC thermal efficiency of the engine.
d. The net reversible work produced inside the engine per cycle
of operation.
48. In 1853, John Ericsson constructed a huge 300. hp hot air
engine that ran on the Ericsson cycle. It had pistons 14.0 ft
in diameter and it consumed 2.00 lbm of coal per indicated
13 On May 28, 1975, this turbine-generator unit was designated as the seventh National Historic Mechanical Engineering Landmark by the American
Society of Mechanical engineers.
14 In 1980, this power plant was designated as the 48th National Historic Mechanical Engineering Landmark by the American Society of Mechanical
Engineers.