WORKSHOP HEAT ENGINES

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__________________ PROBLEMS

1. An air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2. At the beginning
of the compression process, air is at 95 kPa and 27°C. Accounting for the variation of specific
heats with temperature, determine (a) the temperature after the heat-addition process, (b) the
thermal efficiency, and (c) the mean effective pressure.

2. An air-standard Diesel cycle has a compression ratio of 18.2. Air is at 120°F and 14.7 psia at the
beginning of the compression process and at 3200 R at the end of the heat addition process.
Accounting for the variation of specific heats with temperature, determine (a) the cutoff ratio, (b)
the heat rejection per unit mass, and (c) the thermal efficiency.

3. A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air enters
the compressor at 520 R and the turbine at 2000 R. Accounting for the variation of specific heats
with temperature, determine (a) the air temperature at the compressor exit, (b) the back work
ratio, and (c) the thermal efficiency.

4. Consider a simple Brayton cycle using air as the working fluid; has a pressure ratio of 12; has a
maximum cycle temperature of 600°C; and operates the compressor inlet at 100 kPa and 15°C.
Which will have the greatest impact on the back-work ratio: ¿a compressor isentropic efficiency
of 80 percent or a turbine isentropic efficiency of 80 percent? Use constant specific heats at room
temperature.

5. A gas turbine for an automobile is designed with a regenerator. Air enters the compressor of this
engine at 100 kPa and 30°C. The compressor pressure ratio is 10; the maximum cycle
temperature is 800°C; and the cold air stream leaves the regenerator 10°C cooler than the hot
air stream at the inlet of the regenerator. Assuming both the compressor and the turbine to be
isentropic, determine the rates of heat addition and rejection for this cycle when it produces 115
kW. Use constant specific heats at room temperature.

6. Air enters a gas turbine with two stages of compression and two stages of expansion at 100 kPa
and 17°C. This system uses a regenerator as well as reheating and intercooling. The pressure ratio
across each compressor is 4; 300 kJ/kg of heat are added to the air in each combustion chamber;
and the regenerator operates perfectly while increasing the temperature of the cold air by 20°C.
Determine this system’s thermal efficiency. Assume isentropic operations for all compressor and
 the turbine stages and use constant specific heats at room temperatura.

7. Consider a regenerative gas-turbine power plant with two stages of compression and two stages
of expansion. The overall pressure ratio of the cycle is 9. The air enters each stage of the
compressor at 300 K and each stage of the turbine at 1200 K. Accounting for the variation of
specific heats with temperature, determine the minimum mass flow rate of air needed to
develop a net power output of 110 MW.

8. A simple ideal Rankine cycle which uses water as the working fluid operates its condenser at 40°C
and its boiler at 300°C. Calculate the work produced by the turbine, the heat supplied in the
boiler, and the thermal efficiency of this cycle when the steam enters the turbine without any
superheating.

9. A simple ideal Rankine cycle with water as the working fluid operates between the pressure limits
of 2500 psia in the boiler and 5 psia in the condenser. What is the minimum temperature
required at the turbine inlet such that the quality of the steam leaving the turbine is not below
80 percent. When operated at this temperature, what is the thermal efficiency of this cycle?

10. Consider a steam power plant that operates on the ideal reheat Rankine cycle. The plant
maintains the boiler at 5000 kPa, the reheat section at 1200 kPa, and the condenser at 20 kPa.
The mixture quality at the exit of both turbines is 96 percent. Determine the temperature at the
inlet of each turbine and the cycle’s thermal efficiency.

11. A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine
at 6 MPa and 450°C and is condensed in the condenser at 20 kPa. Steam is extracted from the
turbine at 0.4 MPa to heat the feedwater in an open feedwater heater. Water leaves the
feedwater heater as a saturated liquid. Show the cycle on a T-s diagram, and determine (a) the
net work output per kilogram of steam flowing through the boiler and (b) the thermal efficiency
of the cycle.
12. Consider a steam power plant that operates on the ideal regenerative Rankine cycle with a closed
feedwater heater as shown in the figure. The plant maintains the turbine inlet at 3000 kPa and
3508C; and operates the condenser at 20 kPa. Steam is extracted at 1000 kPa to serve the closed
feedwater heater, which discharges into the condenser after being throttled to condenser
pressure. Calculate the work produced by the turbine, the work consumed by the pump, and the
heat supply in the boiler for this cycle per unit of boiler flow rate.

13. A large food-processing plant requires 1.5 lbm/s of saturated or slightly superheated steam at
140 psia, which is extracted from the turbine of a cogeneration plant. The boiler generates
steam at 800 psia and 1000°F at a rate of 10 lbm/s, and the condenser pressure is 2 psia. Steam
leaves the process heater as a saturated liquid. It is then mixed with the feedwater at the same
pressure and this mixture is pumped to the boiler pressure. Assuming both the pumps and the
turbine have isentropic efficiencies of 86 percent, determine (a) the rate of heat transfer to the
boiler and (b) the power output of the cogeneration plant.

14. Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at 9
MPa and 400°C and expands to a pressure of 1.6 MPa. At this pressure, 35 percent of the steam is
extracted from the turbine, and the remainder expands to 10 kPa. Part of the extracted steam is
used to heat the feedwater in an open feedwater heater. The rest of the extracted steam is used
for process heating and leaves the process heater as a saturated liquid at 1.6 MPa. It is
subsequently mixed with the feedwater leaving the feedwater heater, and the mixture is pumped
to the boiler pressure. Assuming the turbines and the pumps to be isentropic, show the cycle on
a T-s diagram with respect to saturation lines, and determine the mass flow rate of steam
through the boiler for a net power output of 25 MW.

15. The gas-turbine portion of a combined gas–steam power plant has a pressure ratio of 16. Air
enters the compressor at 300 K at a rate of 14 kg/s and is heated to 1500 K in the combustion
chamber. The combustion gases leaving the gas turbine are used to heat the steam to 400°C at
 10 MPa in a
heat exchanger. The combustion gases leave the heat exchanger at 420 K. The steam leaving the
turbine is condensed at 15 kPa. Assuming all the compression and expansion processes to be
isentropic, determine (a) the mass flow rate of the steam, (b) the net power output, and (c) the
thermal efficiency of the combined cycle. For air, assume constant specific heats at room
temperatura.

16. Propane fuel (C3H8) is burned in the presence of air. Assuming that the combustion is theoretical
—that is, only nitrogen (N2), water vapor (H2O), and carbon dioxide (CO2) are present in the
products—determine (a) the mass fraction of carbon dioxide and (b) the mole and mass fractions
of the water vapor in the products.

17. Propal alcohol (C3H7OH) is burned with 50 percent excess air. Write the balanced reaction
equation for complete combustion and determine the air-to-fuel ratio.

18. Calculate the higher and lower heating values of a coal from Illinois which has an ultimate analysis
(by mass) as 67.40 percent C, 5.31 percent H2, 15.11 percent O2, 1.44 percent N2, 2.36 percent
S, and 8.38 percent ash (non-combustibles). The enthalpy of formation of SO2 is 2297,100
kJ/kmol.

19. Diesel fuel (C12H26) at 25°C is burned in a steady flow combustion chamber with 20 percent
excess air that also enters at 25°C. The products leave the combustion chamber at 500 K.
Assuming combustion is complete, determine the required mass flow rate of the diesel fuel to
supply heat at a rate of 2000 kJ/s.

20. Liquid ethyl alcohol (C2H5OH(l)) at 25°C is burned in a steady-flow combustion chamber with 40
percent excess air that also enters at 25°C. The products leave the combustion chamber at 600 K.
Assuming combustion is complete, determine the required volume flow rate of the liquid ethyl
alcohol, to supply heat at a rate of 2000 kJ/s. At 258C the density of liquid ethyl alcohol is 790
kg/m3 , the specific heat at a constant pressure is 114.08 kJ/kmol*K, and the enthalpy of
vaporization is 42,340 kJ/kmol.