5.1. A steam power plant operates on the Rankine cycle according to the specified conditions below. Using stream numbering from Fig. 5.2 on page 201, for each of the options below, determine:
a. The work output of the turbine per kg of steam;
b. The work input of the feedwater pump per kg of circulated water;
c. The flowrate of steam required;
d. The heat input required in the boiler/superheater;
e. The thermal efficiency
5.2. A steam power plant operates on the Rankine cycle with reheat, using the specified conditions below. Using stream numbering from Fig. 5.3 on page 203, for each of the options below, determine
a. The work output of each turbine per kg of steam;
b. The work input of the feedwater pump per kg of circulated water;
c. The flowrate of steam required;
d. The heat input required in the boiler/superheater and reheater;
e. The thermal efficiency.
5.3. A modified Rankine cycle using a single feedwater preheater as shown in Fig. 5.7 on page 206 has the following characteristics.
a. The inlet to the first turbine is at 500°C and 0.8 MPa.
b. The feedwater preheater reheats the recirculated water so that stream 7 is 140°C, and steam at 0.4 MPa is withdrawn from the outlet of the first turbine to perform the heating.
c. The efficiency of each turbine and pump is 79%.
d. The output of the plant is to be 1 MW.
e. The output of the second turbine is to be 0.025 MPa.
Determine the flow rates of streams 1 and 8 and the quality of stream 9 entering the condenser (after the throttle valve). Use the stream numbers from Fig. 5.7 on page 206 to label streams in your solution.
5.4. A modified Rankine cycle uses reheat and one closed feedwater preheater. The schematic is a modification of Fig. 5.7 on page 206 obtained by adding a reheater between the T-joint and turbine II. Letting stream 3 denote the inlet to the reheater, and stream 3a denote the inlet to the turbine, the conditions are given below. The plant capacity is to be 80 MW. Other constraints are as follows: The efficiency of each turbine stage is 85%; the pump efficiency is 80%; and the feedwater leaving the closed preheater is 5°C below the temperature of the condensate draining from the bottom of the closed preheater. For the options below, calculate:
a. The flowrate of stream 1;
b. The thermal efficiency of the plant;
c. The size of the feedwater pump (kW);
Options:
i. T1 = 500°C, P1 = 4 MPa, P2 = 0.8 MPa, T3a = 500°C, P4 = 0.01 MPa.
ii. T1 = 600°C, P1 = 4 MPa, P2 = 1.2 MPa, T3a = 600°C, P4 = 0.01 MPa.
5.5. A regenerative Rankine cycle uses one open feedwater preheater and one closed feedwater preheater. Using the stream numbering from Fig. 5.6 on page 206, and the specified conditions below, the plant capacity is to be 75 MW. Other constraints are as follows: The efficiency of each turbine stage is 85%; the pump efficiencies are 80%; and the feedwater leaving the closed preheater is 5°C below the temperature of the condensate draining from the bottom of the closed preheater. For the options below, calculate
a. The flowrate of stream 1.
b. The thermal efficiency of the plant.
c. The size of the feedwater pumps (kW).
Options:
i. The conditions are T1 = 500°C, P1 = 4 MPa, P2 = 0.7 MPa, P3 = 0.12 MPa, and P4 = 0.02 MPa.
ii. The conditions are T1 = 600°C, P1 = 4 MPa, P2 = 1.6 MPa, P3 = 0.8 MPa, and P4 = 0.01 MPa.
5.6. A regenerative Rankine cycle utilized the schematic of Fig. 5.6 on page 206. Conditions are as follows: stream 1, 450°C, 3 MPa; stream 2, 250°C, 0.4 MPa; stream 3, 150°C, 0.1 MPa; stream 4, 0.01 MPa; stream 9, 140°C, H = 592 kJ/kg.
a. Determine the pressures for streams 5, 6, 8, 9, and 10.
b. Determine 
.
c. Determine the enthalpies of streams 5 and 6 if the pump is 80% efficient.
d. Determine the efficiency of turbine stage I.
e. Determine the output of turbine stage III per kg of stream 4 if the turbine is 80% efficient.
f. Determine 
.
g. Determine the work output of the system per kg of stream 1 circulated.
5.7. A regenerative Rankine cycle uses three closed feedwater preheaters. Using the stream numbering from Fig. 5.5 on page 205, and the specified conditions below, the plant capacity is to be 80 MW. Other constraints are as follows: The efficiency of each turbine stage is 88%; the pump efficiency is 80%; and the feedwater leaving each preheater is 5°C below the temperature of the condensate draining from the bottom of each preheater. For the options below, calculate:
a. The flowrate of stream 1
b. The thermal efficiency of the plant
c. The size of the feedwater pump (kW)
Options:
i. The conditions are T1 = 700°C, P1 = 4 MPa, P2 = 1 MPa, P3 = 0.3 MPa, P4 = 0.075 MPa, and P5 = 0.01 MPa.
ii. The conditions are T1 = 750°C, P1 = 4.5 MPa, P2 = 1.2 MPa, P3 = 0.4 MPa, P4 = 0.05 MPa, and P5 = 0.01 MPa.
5.8. An ordinary vapor compression refrigerator is to operate on refrigerant R134a with evaporator and condenser temperatures at –20°C and 35°C. Assume the compressor is reversible.
a. Make a table summarizing the nature (e.g., saturated, superheated, temperature, pressure, and H) of each point in the process.
b. Compute the coefficient of performance for this cycle and compare it to the Carnot cycle value.
c. If the compressor in the cycle were driven by a 1 hp motor, what would be the tonnage rating of the refrigerator? Neglect losses in the motor.
5.9. An ordinary vapor compression refrigeration cycle using R134a is to operate with a condenser at 45°C and an evaporator at –10°C. The compressor is 80% efficient.
a. Determine the amount of cooling per kg of R134a circulated.
b. Determine the amount of heat rejected per kg of R134a circulated.
c. Determine the work required per kg of R134a circulated, and the COP.
5.10. An ordinary vapor compression cycle using propane operates at temperatures of 240 K in the cold heat exchanger, and 280 K in the hot heat exchanger. How much work is required per kg of propane circulated if the compressor is 80% efficient? What cooling capacity is provided per kg of propane circulated? How is the cooling capacity per kg of propane affected by lowering the pressure of the hot heat exchanger, while keeping the cold heat exchanger pressure the same?
5.11. The low-temperature condenser of a distillation column is to be operated using a propane refrigeration unit. The evaporator is to operate at –20°C. The cooling duty is to be 10,000,000 kJ/hr. The compressor is to be a two-stage compressor with an adiabatic efficiency of 80% (each stage). The compression ratio (Pout/Pin) for each stage is to be the same. The condenser outlet is to be at 50°C. Refer to Fig. 5.8 on page 208 for stream numbers.
a. Find the condenser, evaporator, and compressor interstage pressures.
b. Find the refrigerant flowrate through each compressor.
c. Find the work input required for each compressor.
d. Find the cooling rate needed in the condenser.
5.12. Solve problem 5.11 using an economizer at the intermediate pressure and referring to Fig. 5.10 on page 211 for stream numbers.
5.13. A refrigeration process with interstage cooling uses refrigerant R134a. The outlet of the condenser is to be saturated liquid at 40°C. The evaporator is to operate at –20°C, and the outlet is saturated vapor. The economizer is to operate at 10°C. Refer to Fig. 5.10 on page 211 for stream numbers in your solution.
a. Determine the required flowrate of stream 1 if the cooling capacity of the unit is to be 8250 kJ/h.
b. Determine the pressure of stream 3, and the work required by the first compressor if it has an efficiency of 85%.
c. What are the flowrates of streams 7 and 6?
d. What is the enthalpy of stream 4?
e. Determine the work required by the second compressor (85% efficient) and the COP.
5.14. A refrigeration process with interstage cooling uses refrigerant R134a, and the outlet of the condenser is to be saturated liquid at 40°C. Refer to Fig. 5.10 on page 211 for stream numbers in your solution. The pressure of the flash chamber and the intermediate pressure between compressors is to be 290 kPa. The evaporator is to operate at –20°C and the outlet is to be saturated vapor. The flow rate of stream 1 is 23 kg/h. The flash chamber may be considered adiabatic. The compressors may be considered to be 80% efficient. Attach the P-H chart with your solution.
a. What is the work input required to the first compressor in kJ/h?
b. What are the flow rates of streams 7 and 6?
c. What is the enthalpy of stream 4?
5.15. The Claude liquefaction process is to be applied to methane. Using the schematic of Fig. 5.13 on page 214 for stream numbering, the key variables depend on the fraction of stream 3 that is liquefied, 
, and the fraction of stream 3 that is fed through the expander, 
. Create a table listing all streams from low to high stream numbers. Fill in the table as you complete the problem sections. Attach a P–H diagram with your solution.
a. Write a mass balance for the system boundary encompassing all equipment except the compressor and precooler.
b. Write an energy balance for the same boundary described in part (a), and show
c. Stream 3 is to be 300 K and 3 MPa, stream 4 is to be 280 K and 3 MPa, stream 12 is to be 290 K and 0.1 MPa, and the flash drum is to operate at 0.1 MPa. The expander has an efficiency of 91%. The fraction liquefied is to be 
. Determine how much flow to direct through the expander, .
d. Find the enthalpies of streams 3–12, and the temperatures and pressures.
5.16. A Brayton gas turbine typically operates with only a small amount of fuel added so that the inlet temperatures of the turbine are kept relatively low because of material degradation at higher temperatures, thus the flowing streams can be modeled as only air. Refer to the online supplement for stream labels. Consider a Brayton cycle modeled with air under the following conditions: TA = 298 K, PA = PD = 0.1 MPa, PB = 0.6 MPa, and TC = 973 K. The efficiencies of the turbine and compressor are to be 85%. Consider air as an ideal gas stream with CP = 0.79·CP,N2 + 0.21·CP,O2. Determine the thermal efficiency, heat required, and net work output per mole of air assuming
a. The heat capacities are temperature-independent at the values at 298 K.
b. The heat capacities are given by the polynomials in Appendix E.
This problem references an online supplement at the URL given in the front flap.
5.17. The thermal efficiency of a Brayton cycle can be increased by adding a regenerator as shown in the schematic below. Consider a Brayton cycle using air under the following conditions: TA = 298 K, PA = PE = PF = 0.1 MPa, PB = 0.6 MPa, TD = 973 K, TF = 563 K. The efficiency of the turbine and compressor are to be 85%. Consider air as an ideal gas stream with CP = 0.79·CP,N2 + 0.21·CP,O2, and assume the molar flows of B and E are equal. Determine the thermal efficiency, heat required, and net work output per mole of air, assuming
This problem references an online supplement at the URL given in the front flap.
a. The heat capacities are temperature-independent at the values at 298 K.
b. The heat capacities are given by the polynomials in Appendix E.
5.18. Consider the air-standard Otto cycle explained in the online supplement. At the beginning of the compression stroke, P1 = 95 kPa, T1 = 298 K. Consider air as an ideal gas stream with CP = 0.79·CP,N2 + 0.21·CP,O2. If the compression ratio is 6, determine T2, T4, and the thermal efficiency, if T3 = 1200 K and the following are true
a. The heat capacities are temperature-independent at the values at 298 K.
b. The heat capacities are given by the polynomials in Appendix E.
This problem references an online supplement at the URL given in the front flap.
5.19. A hexane (ρ ≈ 0.66 kg/L, μ = 3.2 E-3 g/(cm-s)) storage tank in the chemical plant tank farm is 250 m from the 200 L solvent tank that is to be filled in 3 min. A pump is located at the base of the storage tank at ground level. The storage tank is large enough so that the liquid height doesn’t change significantly when 200 L are removed. The bends and fittings in the pipe contribute lost work equivalent to 15 m of additional pipe. The pump and motor are to be sized based on a storage tank liquid level of 0.3 m above ground level to ensure adequate flow rate when the storage tank is nearly empty. Find the required power input to the pump and motor.
a. The pipe is to be 2.5 cm in diameter and the outlet is to be 10 m above ground level. The pump efficiency is 85%, the motor efficiency is 90%.
b. The pipe is to be 3.0 cm in diameter and the outlet is to be 8.5 m above ground level. The pump efficiency is 87%, the motor efficiency is 92%.
c. Determine the time required to fill the solvent tank using the pump and motor sized in part (a) if the storage tank liquid level is 6.5 m above ground.
d. Answer part (c) except determine the filling time for part (b).
This problem references an online supplement at the URL given in the front flap.
5.20. Consider problem 5.16(a). Determine the amount of fuel required per mole of air if the fuel is modeled as isooctane and combustion is complete.
5.21. Consider problem 5.18(a). Determine the amount of fuel required per mole of air if the fuel is modeled as isooctane and combustion is complete.
5.22. In the event of an explosive combustion of vapor at atmospheric pressure, the vapor cloud can be modeled as adiabatic because the combustion occurs so rapidly. The vapor cloud expands rapidly due to the increase in moles due to combustion, but also due to the adiabatic temperature rise. Estimate the volume increase of a 22°C, 1 m3 mixture of propane and a stoichiometric quantity of air that burns explosively to completion. Estimate the temperature rise.
a. Derive the energy balance for a closed, constant-volume, adiabatic-system vapor phase chemical reaction, neglecting the energy of mixing for reactants and products, and assuming the ideal gas law.
b. Suppose that a 200 L propane tank is at 0.09 MPa pressure and, due to an air leak, contains the propane with a stoichiometric quantity of air. If a source of spark is present, the system will burn so rapidly that it may be considered adiabatic, and there will not be time for any flow out of the vessel. If ignited at 20°C, what pressure and temperature are generated assuming this is a constant volume system and the reaction goes to completion?CopycopyHighlighthighlightAdd NotenoteGet Linklink
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