Eng3901 - Quiz 2 Sample Questions Eng3901 – Thermodynamics I 1 Quiz 2 Sample Questions The second quiz in Eng3901 - Thermodynamics I is designed to test your skills in the application of the 1st Law of Thermodynamics to open systems operating under steady state conditions. A quiz consists of two questions, one using water (or refrigerant) and the other using an ideal gas. Appropriate tables are supplied for water (or refrigerant), no tables are supplied for the ideal gas, and one formula sheet is provided. Below are some sample questions (with answers) from previous quizzes. Solutions are available in a separate document. Enjoy. 1. A two-stage steam turbine with reheat is shown below. The steam enters the high pressure (HP) turbine at state 1 (m ˙ 1 = 50 kg/s, p1 = 6 MPa, T1 = 600o C). A portion of the steam is bled from the HP turbine at state 2 (p2 = 1 MPa, T2 = 360o C), and the remainder exits the HP turbine at state 3 (p3 = 500 kPa, T3 = 270o C). The steam is reheated before it enters the low pressure (LP) turbine at state 4. The steam exits the LP turbine at state 5 (p5 = 10 kPa, x5 = 0.98). The rate at which heat is transferred to the steam in the reheater is 19.054 MW, and the LP turbine generates 37.67 MW of power. State all assumptions when answering the following questions. (a) What is the mass flow rate of the steam that enters the LP turbine? (40 kg/s) (b) How much power is generated by the two stages of the turbine? (68.714 MW) 2. Air enters a water-cooled air compressor at 100 kPa, 300K, at a rate of 10 kg/s. The compressor is designed to deliver two compressed air streams: stream 2 exits the compressor at 500 kPa, 392.3K; and stream 3 exits the compressor at 1 MPa. The power input to the compressor is 2 MW. The cooling water mass flow rate is 16.42 kg/s, and it rises in temperature by 10o C as it passes through the compressor. Assume the compression process is polytropic. Use the properties given below when answering the following questions. State all assumptions. (a) What is the temperature of the air at state 3? (440.3 K) (b) What are the mass flow rates of the two exiting air streams? (m ˙ 2 = 2 kg/s, m ˙3 = 8 kg/s) Air properties: cp = 1005 J/kg/K, R = 287 J/kg/K, Tcrit = 133 K, pcrit = 3.76 MPa Water properties: cp = 4181 J/kg/K Eng3901 - Quiz 2 Sample Questions 2 3. A throttling valve, direct contact heat exchanger and compressor used in a refrigeration cycle are shown below. The working fluid in the cycle is R-134a. The refrigerant enters the throttling valve at state 1 (saturated vapour at 240 kPa) and the heat exchanger at state 3 (saturated vapour at 140 kPa); it exits the compressor at state 5 (1 MPa, 50o C). The power input to the compressor is 85.08 kW and the mass flow rate exiting the compressor is 2 kg/s. State all assumptions when answering the following questions. (a) What are the mass flow rates of R-134a entering the heat exchanger? (m ˙ 2 = 0.4 kg/s, m ˙ 3 = 1.6 kg/s) (b) What is the temperature of the R-134a at the entrance to the compressor? (−16.88o C) 4. A two-stage turbine with reheat uses air as the working fluid. The air enters the high pressure (HP) turbine at state 1 (1 MPa, 1400 K) and expands to 300 kPa. The air then enters a heat exchanger where it is reheated to 1100 K before entering the low presure (LP) turbine. The air expands to exit conditions 860 K and 100 kPa in the LP turbine. The power output of the LP turbine is 1.206 MW. Use the air properties given below and state all assumptions when answering the following questions. (a) What is the maximum power output of the HP turbine? Hint: Assume the process in the HP turbine is reversible and adiabatic. (2047.7 kW) (b) What is the required rate of heat transfer to the air in the reheater? (540.2 kW) Air properties: cp = 1.005 kJ/kg/K, cv = 0.718 kJ/kg/K, R = 0.287 kJ/kg/K, Tcrit = 133 K, pcrit = 3.76 MPa Eng3901 - Quiz 2 Sample Questions 3 5. Water enters the waste heat recovery steam generator at state 1 (p1 = 300 kPa, T1 = 100o C) and exits at state 2 where it enters the turbine. The steam exits the turbine at state 3 (p3 = 10 kPa, x3 = 0.9). Exhaust gases (modelled as air) enter the steam generator at state 4 (T4 = 500o C) and exit at state 5 (T5 = 300o C). If the turbine is producing 1040 kW when m ˙ 3 = 2 kg/s, what is the required exhaust gas mass flow rate? State all assumptions and use the air properties given below to model the exhaust gas properties. (24.34 kg/s) (Note: No solution available.) Air properties: cp = 1005 J/kg/K, cv = 718 J/kg/K, R = 287 J/kg/K 6. A two-stage air compressor with an intercooler, used to cool the air between the two stages, is shown below. The compressor is designed to compress air (m ˙ 1 = 10 kg/s, p1 = 100 kPa (abs), T1 = 300 K) and deliver two exit air streams, 2 (p2 = 200 kPa), and 5 (p5 = 1.6 MPa, T5 = 450 K). The air is cooled at a constant pressure of 400 kPa in between the two stages. The power input to the low pressure compressor is 1304.3 kW. Assume the processes in both stages of the compressor are reversible and adiabatic. State all assumptions when answering the following questions. (Note: No solution available.) (a) What is the mass flow rate of the air through the high pressure stage of the compressor? (8 kg/s) (b) What is the power requirement for the compressor? (2487.8 kW) (c) What is the rate of heat transfer from the air in the intercooler? (1149.7 kW) Air properties: cp = 1005 J/kg/K, cv = 718 J/kg/K, R = 287 J/kg/K, Tcrit = 133 K, pcrit = 3.76 MPa