Eng Thermodynamics I: Sample Final Exam Questions 1

Transcription

1 Eng Thermodynamics I: Sample Final Exam Questions 1 The final exam in Eng Thermodynamics I consists of four questions: (1) 1st Law analysis of a steam power cycle, or a vapour compression refrigeration cycle operating at steady state; (2) 2nd Law analysis of a simple cycle or closed system (includes 1st Law); (3) steady state 2nd Law analysis of an open system (includes 1st and 2nd Law); and (4) an is something possible question. Appropriate tables, constants and one formula sheet are provided. Below are some sample questions (with answers) from previous final exams. Solutions are not available for these questions. The formula sheet is available in a separate document. Enjoy! 1. The working fluid in the refrigeration system shown below is R-22. The refrigerant exits the evaporator at 150 kpa, and it exits the condenser as a saturated liquid at 1.4 MPa. Some of the refrigerant is bled off at state 3 and throttled to state 6 before it enters a heat exchanger. The refrigerant exits the heat exchanger at states 4 and 7. The heat exchanger is used to subcool the refrigerant before it is throttled to the evaporator pressure. Determine the coefficient of performance for the refrigeration cycle. State all assumptions. (β = 2.34) ṁ 2 + ṁ 8 = 10 kg/s x 3 = 0 p 7 = 400 kpa p 1 = 150 kpa p 4 = 1.4 MPa x 7 = 1 p 2 = 1.4 MPa T 4 = 6 C p 8 = 1.4 MPa T 2 = 90 C p 5 = 150 kpa T 8 = 65 C p 3 = 1.4 MPa p 6 = 400 kpa ẆC,1 = kw

2 Eng Thermodynamics I: Sample Final Exam Questions 2 2. It is proposed that an air compressor be designed to operate in a polytropic process with n = 1.2. The compressor would intake 10 kg/s of air at 100 kpa (abs) and 300 K, and produce two exit streams: 2 kg/s at 400 kpa and 8kg/s at 800 kpa. The proposed power input is 1.4 MW. The compressor will not be well-insulated but the outer casing temperature should not exceed 350 K. Is it possible to construct the compressor? Why? Use the air properties given below and state all assumptions. (No. σ < 0) Air Properties: c p = kj/kg K, c v = kj/kg K, R = kj/kg K 3. A simple refrigeration plant consists of an evaporator, condenser, compressor, three throttling valves, a heat exchanger and a direct contact heat exchanger, as shown below. The working fluid in the system is R-134a. The refrigerant exits the compressor at state 3 and enters the condenser. At the exit of the condenser, state 4, some of the refrigerant is bled off, throttled to state 7, enters the heat exchanger where it is heated to state 8, and is then throttled to state 9. The remaining refrigerant enters the heat exchanger, is cooled to exit state 5, throttled to state 6 and then flows through the evaporator, emerging at state 1. The two fluid streams, 1 and 9, mix in the well-insulated direct contact heat exchanger and exit at state 2. The refrigerant at state 2 is compressed to state 3 in the compressor. Given the information below, determine the coefficient of performance for the refrigeration cycle. State all assumptions. (β = 2.78) ṁ 1 = 4 kg/s T 3 = 55 C p 6 = 140 kpa p 1 = 140 kpa p 4 = 1 MPa p 7 = 320 kpa x 1 = 1 x 4 = 0 p 8 = 320 MPa p 2 = 140 kpa p 5 = 1 MPa x 8 = 1 p 3 = 1 MPa T 5 = 20 C p 9 = 140 kpa

3 Eng Thermodynamics I: Sample Final Exam Questions 3 4. The specifications of a steam turbine with one inlet and two exits suggest that it can generate 23 MW. The turbine is well insulated and requires inlet flow conditions ṁ 1 = 20 kg/s, p 1 = 5 MPa, T 1 = 500 C. The turbine allows 15% of the inlet mass flow rate to be bled from the turbine at p 2 = 2 MPa and T 2 = 350 C, to be used in another process. The remainder of the steam exits the turbine at a pressure of 10 kpa. Are these specifications possible? Why? State all assumptions. (No. σ < 0 or η t > 1) 5. A simple steam power plant consists of a boiler, a turbine, a condenser, an open feedwater heater, and two pumps as shown below. The steam enters the turbine at state 1. Some of the steam is bled from the turbine at state 2 to be used in the open feedwater heater. The remaining steam exits the turbine at state 3 and enters the condenser. The water exits the condenser at state 4, is pressurized by the low pressure pump, and enters the open feedwater heater at state 5. The preheated water exits the feedwater heater at state 6, is pressurized to state 7 in the high pressure pump and enters the boiler. The turbine is producing power Ẇ T = MW. Heat is added to the steam at the rate of MW in the boiler. The power requirement of the low pressure pump is 7 kw. Determine the thermal efficiency of the power plant. State all assumptions. (η th = 0.268) m 1 = 12 kg/s p 3 = 10 kpa p 6 = 500 kpa p 1 = 3 MPa x 3 = 0.95 p 7 = 3 MPa T 1 = 400 C p 4 = 10 kpa Q B = MW p 2 = 500 kpa p 5 = 500 kpa Ẇ T = MW T 2 = 180 C T 5 = 36 C ẆLP = 7 kw

4 Eng Thermodynamics I: Sample Final Exam Questions 4 6. You are faced with the prospect of replacing a gas turbine. Two sales reps visit. Rep A has a turbine that for a mass flow rate of ṁ A = 20 kg/s, inlet conditions p 1A = 1 MPa and T 1A = 650 K, and exit pressure p 2A = 200 kpa produces 4 MW of power. Rep B has a turbine that for a mass flow rate of ṁ B = 20.5 kg/s, inlet conditions of p 1B = 1 MPa and T 1B = 640 K, and exit pressure p 2B = 210 kpa produces 4 MW of power. You require a turbine that will produce at least 3.9 MW. You will not have any difficulty (or extra expense) in meeting the inlet conditions of the two turbines. Which is the better turbine? Why (i.e. justify your choice)? State all assumptions. Use air properties for the gas (Table A-22) and R = kj/kg/k. (Turbine B. η t,b > η t,a ) 7. A simple steam power plant consists of a boiler, a turbine, a condenser, two pumps, a closed feedwater heater, and a mixing chamber as shown below. Steam enters the turbine at state 1. Some of the steam is bled from the turbine at state 2 to be used in the closed feedwater heater. This stream exits the feedwater heater at state 8, is pressurized by pump 2 (P2) to state 9 where it enters a well-insulated mixing chamber. The remaining steam exits the turbine at state 3 and enters the condenser. The water that exits the condenser at state 4 is pressurized to state 5 in pump 1 (P1), and then it enters the closed feedwater heater. The preheated feedwater exits the heater at state 6 where it enters the mixing chamber and mixes with stream 9. The mixtures exits the chamber at state 7, and then enters the boiler. The power requirements of pumps 1 and 2 are ẆP 1 = 127 kw, and ẆP 2 = 11 kw, respectively. Determine the thermal efficiency of the power plant. State all assumptions. (η th = 0.275) m 1 = 20 kg/s x 3 = 0.9 p 7 = 5 MPa p 1 = 5 MPa p 4 = 10 kpa p 8 = 1 MPa T 1 = 400 C T 4 = 10 C x 8 = 0 p 2 = 1 MPa p 5 = 5 MPa p 9 = 5 MPa T 2 = 240 C p 6 = 5 MPa ẆP 1 = 127 kw p 3 = 10 kpa T 6 = 68 C ẆP 2 = 11 kw

5 Eng Thermodynamics I: Sample Final Exam Questions 5 8. An air compressor is proposed to compress 10 kg/s of air from inlet conditions p 1 = 100 kpa, T 1 = 300 K and v 1 = 100 m/s, to exit conditions p 2 = 2 MPa, T 2 = 350 K and v 2 = 10 m/s, with a power requirement of 600 kw. The surface temperature of the compressor is uniform and constant at T b = 310 K. Is this proposal feasible? Why? State all assumptions. (Note: Use Table A-22 for air properties and R = kj/kg/k) (No. σ < 0) 9. A two-stage air compressor with intercooling between the stages is shown below. Air enters the low pressure (LP) compressor at state 1 (p 1 = 100 kpa, T 1 = 300 K) and is compressed to state 2 ( p 2 = 500 kpa). The air is then cooled in a constant pressure heat transfer process to state 3 by cooling water in the intercooler. The exit from the high pressure compressor is state 4 (p 4 = 2 MPa, T 4 = 550 K). The power requirement of the HP compressor is (ẆHP /ṁ) = kj/kg. (a) If the isentropic efficiency of the LP compressor is η c = 0.8, determine the total power requirement, Ẇ cp /ṁ air, of the two-stage compressor. Assume constant specific heats: c p = kj/kg K, c v = kj/kg K. (b) Determine the isentropic efficiency of the HP compressor. properties. Use tabular data for air (c) Sketch a (neat) T -s diagram for the process through the complete two-stage compressor and intercooler (i.e. one diagram). 10. An inventor tells you he has a device that can intake saturated water vapour at state 1 (ṁ 1 = 1 kg/s, p 1 = 100 kpa) and air at state 3 (ṁ 3 = 5 kg/s, p 3 = 100 kpa, T 3 = 300 K), and output saturated liquid water at state 2 (p 2 = 100 kpa) and air at state 4 (p 4 = 400 kpa, T 4 = 400 K). Typical of inventors, his device is inside a black box and it is top-secret. The only other information available is that the air and water streams do not mix, the device has no power requirements, and the temperature of the outer casing of the black box does not exceed 50 C. Using tabular data for the water, and the air properties given below, determine if the device is possible. Justify your answer. Air properties: c p = kj/kg K, c v = kj/kg K, R = kj/kg K

6 Eng Thermodynamics I: Sample Final Exam Questions A simple steam power cycle (shown below) consists of a boiler, turbine, condenser and pump. Steam exits the boiler at 1 MPa, 400 C, and it exits the turbine at 10 kpa. Saturated liquid water exits the condenser at 10 kpa. The work input to the pump is 1.2 kj/kg. If the isentropic efficiency of the turbine is 0.85, what is the thermal efficiency for the cycle? State all assumptions. (η th = 0.248)