The pressure ratio across each turbine stage is the same. The
high-pressure turbine exhaust gas enters the regenerator and
then enters the low-pressure turbine for expansion to the
compressor inlet pressure. Determine the thermal efficiency
of this cycle as a function of the compressor pressure ratio
and the high-pressure turbine to compressor inlet temperature
ratio. Compare your result with the efficiency of the standard
regenerative cycle.
9–155 A four-cylinder, four-stroke spark-ignition engine
operates on the ideal Otto cycle with a compression ratio of
11 and a total displacement volume of 1.8 liter. The air is at
90 kPa and 50°C at the beginning of the compression
process. The heat input is 1.5 kJ per cycle per cylinder.
Accounting for the variation of specific heats of air with tem-
perature, determine (a) the maximum temperature and pres-
sure that occur during the cycle, (b) the net work per cycle
per cyclinder and the thermal efficiency of the cycle, (c) the
mean effective pressure, and (d) the power output for an
engine speed of 3000 rpm.
9–156 A gas-turbine plant operates on the regenerative
Brayton cycle with two stages of reheating and two-stages of
intercooling between the pressure limits of 100 and
1200 kPa. The working fluid is air. The air enters the first and
the second stages of the compressor at 300 K and 350 K,
respectively, and the first and the second stages of the turbine
at 1400 K and 1300 K, respectively. Assuming both the com-
pressor and the turbine have an isentropic efficiency of
80 percent and the regenerator has an effectiveness of 75 per-
cent and using variable specific heats, determine (a) the back
work ratio and the net work output, (b) the thermal efficiency,
and (c) the second-law efficiency of the cycle. Also deter-
mine (d) the exergies at the exits of the combustion chamber
(state 6) and the regenerator (state 10) (See Figure 9–43 in
the text). Answers:(a) 0.523, 317 kJ/kg, (b) 0.553, (c) 0.704,
(d) 931 kJ/kg, 129 kJ/kg
9–157 Electricity and process heat requirements of a manu-
facturing facility are to be met by a cogeneration plant consist-
ing of a gas turbine and a heat exchanger for steam production.
548 | Thermodynamics
500 °C350 °C 25 °CHeat
Combustion exchanger
chamberCompressor Turbine100 kPa
30 °C123
1.2 MPa Sat. vapor
200 °C4FIGURE P9–157The plant operates on the simple Brayton cycle between the
pressure limits of 100 and 1200 kPa with air as the working
fluid. Air enters the compressor at 30°C. Combustion gases
leave the turbine and enter the heat exchanger at 500°C, and
leave the heat exchanger of 350°C, while the liquid water
enters the heat exchanger at 25°C and leaves at 200°C as a sat-
urated vapor. The net power produced by the gas-turbine cycle
is 800 kW. Assuming a compressor isentropic efficiency of
82 percent and a turbine isentropic efficiency of 88 percent and
using variable specific heats, determine (a) the mass flow rate
of air, (b) the back work ratio and the thermal efficiency, and
(c) the rate at which steam is produced in the heat exchanger.
Also determine (d) the utilization efficiency of the cogenera-
tion plant, defined as the ratio of the total energy utilized to the
energy supplied to the plant.
9–158 A turbojet aircraft flies with a velocity of 900 km/h
at an altitude where the air temperature and pressure are
35°C and 40 kPa. Air leaves the diffuser at 50 kPa with a
velocity of 15 m/s, and combustion gases enter the turbine at
450 kPa and 950°C. The turbine produces 500 kW of power,
all of which is used to drive the compressor. Assuming an
isentropic efficiency of 83 percent for the compressor, tur-
bine, and nozzle, and using variable specific heats, determine
(a) the pressure of combustion gases at the turbine exit,
(b) the mass flow rate of air through the compressor, (c) the
velocity of the gases at the nozzle exit, and (d) the propulsive
power and the propulsive efficiency for this engine. Answers:
(a) 147 kPa, (b) 1.76 kg/s, (c) 719 m/s, (d) 206 kW, 0.156
9–159 Using EES (or other) software, study the effect
of variable specific heats on the thermal effi-
ciency of the ideal Otto cycle using air as the working fluid.
At the beginning of the compression process, air is at 100
kPa and 300 K. Determine the percentage of error involved in
using constant specific heat values at room temperature for
the following combinations of compression ratios and maxi-
mum cycle temperatures:r6, 8, 10, 12, and Tmax1000,
1500, 2000, 2500 K.
9–160 Using EES (or other) software, determine the
effects of compression ratio on the net work
output and the thermal efficiency of the Otto cycle for a maxi-
mum cycle temperature of 2000 K. Take the working fluid to
be air that is at 100 kPa and 300 K at the beginning of the
compression process, and assume variable specific heats. Vary
the compression ratio from 6 to 15 with an increment of 1.
Tabulate and plot your results against the compression ratio.
9–161 Using EES (or other) software, determine the
effects of pressure ratio on the net work output
and the thermal efficiency of a simple Brayton cycle for a
maximum cycle temperature of 1800 K. Take the working
fluid to be air that is at 100 kPa and 300 K at the beginning
of the compression process, and assume variable specific
heats. Vary the pressure ratio from 5 to 24 with an increment
of 1. Tabulate and plot your results against the pressure ratio.
At what pressure ratio does the net work output become a