HW-1: Due Friday 25 August 2017 by 4:30:00 pm EDT To Your Division s GradeScope Site

Transcription

1 HW-1: Due Friday 25 August 2017 by 4:30:00 pm EDT To Your Division s GradeScope Site A washing machine agitator is shown below. Its purpose is to mix soiled clothing with the water-detergent mixture. Draw a system sketch and identify all energy transfer processes that cross the system boundary.

2 HW-2: Due Friday 25 August 2017 by 4:30:00 pm EDT To Your Division s GradeScope Site With all the construction in WL and on campus, it s likely that you ve seen a cement pumper truck. An example is provided below. The yellow pumper truck receives cement from the orange truck and then distributes it to the brown forms in the lower right. Treat the pumper truck as your system, draw a system diagram and on it include all mass and energy transport processes.

3 HW3 Due by 4:30 pm EST on Friday 1 September 2017 on Gradescope site. (i) A 10 m 3 rigid tank has two sections separated by a membrane. Each section contains nitrogen gas. The nitrogen gas in section A has an initial density of 1.6 kg/m 3 and the nitrogen gas in section B has a mass of 6 kg. At a certain time, the membrane is punctured. The final density of the nitrogen gas in the tank is found to be 1.8 kg/m 3. Determine the initial density (kg/m 3 ) of nitrogen gas that existed in section B. Answer: Not attached (ii) A thermodynamics professor always insists that students should use correct units. On a particular quiz, however, students who did the problem correctly arrived at the same numerical value of temperature irrespective of using C or F units. (a) What was the numerical value of the temperature ( C and F)? (b) Determine the corresponding absolute temperature (K and R). Answers: Not attached

4 HW4 Due by 4:30 pm EST on Friday 1 September 2017 on Gradescope site. A body initially at rest is accelerated to a velocity of 200 m/s along a surface inclined at 30 relative to the horizontal. The body travels up by a distance of 10 m along the inclined surface. The work required during this time is 200 kj. Assume acceleration due to gravity is 9.81 m/s 2. Calculate mass (kg) of the body. Answer: Not attached

5 HW5 Due by 4:30 pm EST on Friday 1 September 2017 on Gradescope site. The pressure of a gas inside a piston-cylinder device is initially balanced by atmospheric pressure of 100 kpa (absolute) outside it. The initial volume of the gas in the cylinder is 32 cm 3. A spring attached to the outside of the piston is initially uncompressed and exerts no force on the piston. The area of the weightless piston is m 2. Heat transfer to the gas causes the piston to move upwards by a distance of 2 cm. The spring constant is 10 N/cm. (a) Determine the final absolute pressure (kpa) of the gas. (b) Calculate the final volume (cm 3 ) of the gas. (c) Show the expansion process on a P-V diagram. (d) Calculate the work (J) for the gas during the process. Indicate whether the work is done by the gas or on the gas. Answers: (a) 150 kpa (absolute); (d) 1 J

6 HW-6: Due by 4:30 pm EDT on Friday 8 September 2017 to GradeScope (i) An unknown fluid is heated within a rigid, closed container from a hot source while being stirred with a paddle wheel device, as shown in the accompanying figure. During a period of time, 30 kj of heat transfer occurs to the fluid from the source, 5 kj of heat transfer occurs to the surrounding air, and the paddle wheel work is 500 N-m. Determine the final energy of the system (kj) if its initial energy is 10 kj. (ii) An electric motor is being used with a pulley to raise a 100-kg weight a distance of 50 m during a construction project. (a) What is the minimum electrical energy (kj) required to raise the weight in the absence of drag, frictional effects, and motor losses? (b) If the object is being raised at a constant rate of 5 m/s, then what is the required electrical input power (kw) to the motor? (iii) A classroom is being maintained at a constant temperature during the winter using a heater. At a particular time, the class is occupied by 50 students who are each losing energy via heat transfer at a rate of 50 W. The lights and projection system are operating with a total electrical power input of 1000 W. It is a cold day and the net heat transfer rate through the walls and windows to the outside is estimated to be 6000 W. Estimate the rate of heat transfer (kw) required from the heater at these conditions. Note: Assume that there is no inflow or outflow of air to the room during the class period.

7 HW-7: Due by 4:30 pm EDT on Friday 8 September 2017 on GradeScope (i) A closed stationary cycle involves four separate processes with the given energy transfers and changes in internal energy shown in the table below. (a) Fill in all the blanks. Process i à j Q i-j (kj) W i-j (kj) DU= U j - U i (kj) 1 à à à à Net Cycle Total (b) Comment on whether this is a power or refrigeration/heat pump cycle. Explain the reason for your answer. (c) Determine an appropriate efficiency for the cycle. Note: Follow the formal solution process but it is only necessary to show an energy flow diagram (EFD) for the cycle as a whole. (ii) Consider that the heater for HW-6 (iii) is an electrically-driven heat pump that extracts energy from the outdoors and provides heat transfer to the classroom. The heat pump COP for heating is 2.5. (a) Determine the electrical power input to the heat pump (kw)? (b) Calculate the heat transfer rate from the ambient to the heat pump (kw).

8 HW-8: Due by 4:30 pm EDT on Friday 15 September 2017 to GradeScope. (i) A rigid, closed vessel contains pure R-134a at its critical point (374.2 K and MPa). If there is heat transfer from the container to the surroundings (at 300 K), the refrigerant in the vessel will become: (a) No change (b) Superheated vapor (c) Subcooled liquid (d) Saturated liquid/vapor mixture (e) Saturated liquid (f) Saturated vapor Depict this process with initial and final states on appropriately labeled P-v and T-v diagrams. (ii) A home gas grill typically employs a tank containing a 2-phase mixture of propane as the fuel source. The tank is sitting outside at a temperature of 20 C. At this temperature, the saturation pressure for propane is kpa. There is a pressure gauge on the tank that measures gage pressure. Assume standard atmospheric pressure. For each of the following two pressure measurements, indicate whether there is any liquid in the tank (yes, no, can t tell) and provide an explanation for your answer in each case. (a) P = 600 kpa (gage) (b) P = 750 kpa (gage) (c) What would be the expected gage pressure measurement if the tank were half filled with liquid? Note: Use properties from tables found on the ME 200 website reference section (

9 HW-9: Due by 4:30 pm EDT on Friday 15 September 2017 to GradeScope. (i) A 0.5 m 3 rigid vessel initially contains a saturated liquid-vapor mixture of water at 100 C. The water is heated until it reaches its critical point. (a) Indicate the process on a P-v diagram. (b) What is the mass of liquid water (kg) at the initial state? (c) Determine the volume occupied by vapor (m 3 ) at the initial state. (ii) R-134a vapor initially at 3.2 bar and 40 C (State 1) is contained within a piston-cylinder device. The refrigerant is cooled at constant volume until its temperature reaches -8 C (State 2) and then undergoes an isothermal process to a pressure of 3 bar (State 3). (a) Locate all three states on appropriately labeled P-v and T-v diagrams. (b) Determine specific volume (m 3 /kg), specific internal energy (kj/kg) and specific enthalpy (kj/kg) at all three states. Note: Use properties from tables found on the ME 200 website reference section (

10 HW-10: Due by 4:30 pm EDT on Friday 15 September 2017 to GradeScope. A pressure cooker is a device that boils water at an elevated pressure in order to cook food faster. It maintains a constant pressure using a regulator valve that discharges steam vaporized by an energy source. The cooker shown in the accompanying figure operates at a pressure of 0.15 MPa once it comes up to temperature and has an internal volume of 0.01 m 3. Assume that it initially contains 5 kg of water/steam. Pressure Cooker (a) What is the quality of the saturated mixture in the cooker when steam just begins to escape? (b) What is the quality of the saturated mixture in the cooker after 4.5 kg of steam has escaped? (c) If the cooker were initially open to the atmosphere at a temperature of 20 C and then were closed and placed on the stove, then determine the heat transfer (kj) to the water between the time the stove is turned on and when the pressure valve begins to release steam. Note: Use properties from tables found on the ME 200 website reference section (

11 HW-11: Due by 4:30 pm EDT on Monday 25 September 2017 to GradeScope. (i) Using the ideal gas tables provided on the ME 200 course website, find: (a) cv (kj/kmol-k) for N2 at 300 and 1500 K. (b) cv (kj/kmol-k) for CO2 at 300 and 1500 K. (c) Provide physical reasoning for the differences observed between the specific heats at two temperatures and the differences observed between N2 and CO2. (ii) You are hiking in the wilderness with a camp stove and with a limited supply of fuel. You exclusively use this stove to heat and boil water. With a full tank of fuel your camp stove can provide a heat transfer of 1 MJ to your water pot. Assume the atmospheric pressure is 1 bar and the specific heat of liquid water is 4.18 kj/kg-k. Using a full tank of fuel, find: (a) The mass of liquid water (kg) that you can heat from 10 C to 99.6 C. Assume the liquid water is incompressible with a constant specific heat capacity. (b) Repeat (a), but do not use specific heats in your solution. Hint: you will need to use a thermodynamic property table. (c) The mass of liquid water (kg) that you can boil, starting from an initial temperature of 10 C. Assume the liquid water is incompressible with a constant specific heat capacity Note: Use properties from tables found on the ME 200 website reference section (

12 HW-12: Due by 4:30 pm EDT on Monday 25 September 2017 to GradeScope. The Air Balloon Company has a helium balloon that will be used in an attempted crossing of the Atlantic Ocean. The helium in the balloon is initially at 20 C and 500 kpa and cv = 3.12 kj/kg-k for helium. The balloon can be considered to be a rigid sphere with a radius of 25 m. (a) Determine the mass of helium (kg) in the balloon. (b) As the balloon rises, the helium is heated by solar radiation to 300 C. The balloon will burst if the absolute pressure in the balloon is greater than 1 MPa. Will the balloon burst? (c) What is the heat transfer to the balloon (MJ) due to solar heating? (d) The Air Balloon Company wants to reduce the weight of the balloon to 26,690 kg. What gas can they use instead of helium to achieve this goal?

13 HW-13: Due by 4:30 pm EDT on Monday 25 September 2017 to GradeScope. A piston-cylinder assembly is used to compress air from State 1 (v1 = 0.75 m 3 /kg, T1 = 300 K) to State 2 (v2 = m 3 /kg). At State 2, the piston is locked in place and then 750 kj/kg of heat transfer occurs to the air at constant volume, which heats the air to State 3. Next, the piston is released and allowed to expand the air to State 4 (v4 = v1). The compression and expansion processes are polytropic with Pv 1.3 = constant. Assume constant specific heats for air (cv = kj/kg-k) unless indicated otherwise. (a) Find the temperature (K) of air at State 2. (b) Determine the temperature (K) of air at State 3. (c) What would be the temperature (K) of the air at State 3 be if the variation of specific heat of air were considered? Do not interpolate between table values in your analysis (i.e., round to the nearest value that is tabulated). (d) Find the absolute pressure (kpa) of air at State 3 using the temperature calculated in (c). (e) Calculate the specific work (kj/kg) during the expansion process. If your solution approach requires a value for the temperature at State 3, use the value you found in (c). Note: Use properties from tables found on the ME 200 website reference section (

14 HW-14: Due by 4:30 pm EDT on Friday 29 September 2017 to GradeScope. The air in a D = m inner diameter pipe has a mass flow rate of 1 kg/s and is heated from T1 = 300 K to T2 = 450 K from the inlet to the outlet, respectively. The operating pressure of the air in the pipe is a constant 5 bar. Use a gas constant of R = 287 J/kgK for the air and assume the pipe has a constant cross section as well as 1 inlet and 1 outlet. (a) (b) (c) Find the pipe inlet and outlet velocities V1 and V2, respectively (m/s) Find the heat transfer to the air in the pipe (kw) Find how the heat transfer to the air in the pipe would change if the pipe inner diameter is changed to 0.05 m instead of m (still being a constant diameter). What percentage error would be incurred by ignoring the kinetic energy terms for the case of D = 0.05 m? Is this error significant?

15 HW-15: Due by 4:30 pm EDT on Friday 29 September 2017 to GradeScope. A laboratory mixing chamber at Purdue propulsion laboratories is to be designed to achieve an air flow at the outlet of 2 kg/s with a temperature of T3 = 600 K and a pressure of P3 = 10 bar. To achieve these conditions, an undergraduate research assistant must design the mixing system to utilize an available supply of T1 = 800 K heated air at P1 = 10 bar and mix this with a supply of T2 = 300 K unheated air at P2 = 10 bar and determine the mass flow rates of each inlet supply to achieve the desired outlet conditions. Assume that the mixing chamber is well insulated (i.e., negligible heat losses). Use a gas constant of R = 287 J/kgK for the air. (a) (b) (c) Find the mass flow rates of the two air supplies (kg/s) at States 1 and 2 (hint: assume that changes in kinetic energy are negligible in the energy equation). To complete the design, the supervising graduate student instructs the undergraduate research assistant to make sure that the inlet and outlet pipe inner diameters are designed such that none of the inlet or outlet velocities exceeds 0.3 of the sound speed, c, to avoid compressible flow conditions. I.e., the maximum velocity at 1 should not exceed V1 = 0.3c1, and so forth. Assuming that the sound speeds are c1 = 567 m/s, c2 = 347 m/s, and c3 = 491 m/s, corresponding to T1 = 800 K, T2 = 300 K, and T3 = 600 K for air, respectively, determine the minimum pipe inner diameters needed. While you assumed that changes in kinetic energy were negligible in part (a), given the maximum velocities in part (b), corresponding to 0.3 of the sound speeds, recompute the energy balance from part (a) so as to include the kinetic energy terms and determine if these terms make a significant change to the mass flow rates you computed in part (a).

16 HW-16: Due by 4:30 pm EDT on Friday 6 Oct 2017 to GradeScope. Steam expands through an adiabatic nozzle from the inlet at P1 = 1.5 MPa, T1 = 240 C, and V1 = 10 m/s to the exit at P2 = 1 MPa and T1 = 200 C. (a) (b) (c) Find the velocity at the exit, V2 (m/s) Find the area ratio A1/A2 and the diameter ratio D1/D2 assuming a round nozzle. Sketch the process on a T-v diagram. Include the vapor dome, label the axes with units, label the states with values on the axes, show the process path with an arrow, and draw lines of constant pressure that go through the vapor dome and pass through States 1 and 2. Make sure that the locations of States 1 and 2 are not randomly drawn but are drawn accurately relative to (i.e., above or below) the critical temperature Tc = K, as well as accurately relative to (i.e., above or below) Tsat,1 and Tsat,2. Also make sure that the process path (i.e., up/down, right/left) accurately reflects the changes in T and v from State 1 to 2.

17 HW-17: Due by 4:30 pm EDT on Friday 6 Oct 2017 to GradeScope. A steam turbine is designed to operate at a mass flow rate of 1.5 kg/s. The inlet conditions are P1 = 2 MPa, T1 = 400 C, and V1 = 60 m/s. The exit is at P2 = 0.1 MPa, x2 = 0.98, and V2 = 150 m/s. The change in elevation from inlet to exit is a drop of 1 m, and the heat loss to the surroundings is 50 kw. (a) (b) (c) Evaluate the power output of the turbine (kw) without neglecting the kinetic and potential energy terms. What are the contributions of the kinetic and potential energy terms (kw) to the power output, and what are their fractions relative to the total power output? What are the diameters of the inlet and outlet pipes (cm)?

18 HW-18: Due by 4:30 pm EDT on Friday 6 Oct 2017 to GradeScope. Saturated steam flows through an insulated pipe, as shown to the right, at P1 = 1 MPa. A small amount of the main flow steam is extracted and passed through a throttling valve to a superheated vapor state at P2 = 200 kpa and T2 = 150 C. The chamber at State 2 is kept at a constant pressure by a bleed flow or exhaust line. This device, encompassed by the dashed lines to the right, is called a throttling calorimeter as it is used to determine the quality of steam, x1, in the steam supply lines with just a simple measurement of P1, P2, and T2. Pressures P1 and P2 listed above are absolute. (a) (b) What is the quality of the steam, x1, in the steam line? Sketch the process on a P-h diagram. Label the axes with units. Include the vapor dome. Include in the diagram a line of constant temperature for T1, the starting State 1 at P1 = 1 MPa and ending at State 2 at P2 = 200 kpa. Label P1, P2, h1, and h2. Be sure that the initial and final states end up in the correct part of the diagram (under the dome is saturated vapor-liquid mixture and to the right is the superheated vapor region). Can steam with low quality, x1, be measured with a throttling calorimeter? Use the P-h diagram to justify your answer. Hint: P-h diagrams can be found in the same ME200 website where you found the property tables.

19 HW-19: Due by 4:30 pm EDT on Friday 13 October 2017 to GradeScope. Air at 0.25 bar absolute pressure, 220 K temperature, and velocity 300 m/s (State 1) steadily enters the diffuser of a turbojet engine. Air exits from the diffuser at an absolute pressure of 0.48 bar and negligible velocity (State 2). Air exiting the diffuser then enters a low-pressure compressor (LPC) where it is compressed to 2.63 bar absolute pressure and 400 K temperature (State 3). Air leaving from the LPC flows into a heat exchanger which cools the air to a temperature equal to that at the exit of the diffuser (T 4 = T 2 ). Heat transfer occurs at the rate of 6805 kw from the heat exchanger to its surroundings. Air leaving from the heat exchanger enters a high-pressure compressor (HPC) and it is compressed to 14.4 bar absolute pressure and 400 K temperature (State 5). (a) Calculate the temperature (K) of air at the exit of the diffuser. (b) Determine the mass flow rate (kg/s) of air through the engine. (c) Find the total power input (kw) for the LPC and HPC. (d) What is the area (m 2 ) and the corresponding diameter (ft) of the diffuser inlet section?

20 HW-20: Due by 4:30 pm EDT on Friday 13 October 2017 to GradeScope. Consider a steadily operating power cycle shown in the figure below. The boiler (a heat exchanger to boil liquid water) produces steam at 80 bar absolute pressure and 520 C temperature (State 1) with a mass flow rate of 30 kg/s. Steam leaving the boiler enters a highpressure turbine (HPT) and expands to an absolute pressure of 7 bar and temperature of 180 C (State 2). A fraction of the steam (y) is extracted at State 2 and the remaining fraction of the steam (1 y) expands in a low-pressure turbine (LPT) to 0.08 bar absolute pressure and 81% quality (State 3). Steam leaving the LPT is cooled in a condenser and exits as saturated liquid at 0.08 bar absolute pressure (State 4). Saturated liquid water leaving from the condenser is pumped to an absolute pressure of 7 bar and temperature of 43 C (State 5) in a low-pressure pump (LPP). Liquid leaving the LPP (State 5) is mixed with the extracted steam (State 2) in a rigid, insulated mixing chamber. The mixed stream exits the mixing chamber as saturated liquid at 7 bar absolute pressure (State 6). Saturated liquid water leaving from the mixing chamber is pumped to an absolute pressure of 80 bar and temperature of 167 C (State 7) in a high-pressure pump (HPP) and is supplied to the boiler to heat it back to State 1 in the boiler. Assume that both turbines and pumps have negligible heat transfer. kg m steam 30 s p 1 = 80 bar T 1 = 520 C HPT p 2 = 7 bar T 2 = 180 C LPT Remaining Steam y m 1 steam Extracted Steam = ym steam p 3 = 0.08 bar x 3 = 0.81 Boiler Mixing Chamber p 9 = 1 bar T 9 = 30 C Cooling Water Exit p 7 = 80 bar T 7 = 167 C HPP p 6 = 7 bar sat. liquid p 5 = 7 bar T 5 = 43 C LPP p 4 = 0.08 bar sat. liquid p 8 = 1 bar T 8 = 20 C Cooling Water Inlet

21 (a) Determine the fraction of steam (y) extracted at State 2. (b) Calculate the total power output (kw) for the HPT and LPT. (c) Find the total power input (kw) for the LPP and HPP. (d) What is the rate of heat transfer (kw) for water in the boiler? (e) What is the rate of heat transfer (kw) for steam in the condenser? (f) Determine thermal efficiency (%) of the cycle using only your answers in (b), (c), and (d). Re-calculate the value of thermal efficiency (%) using only your answers in (d) and (e). Suppose steam passing through the condenser is cooled by liquid water entering at 1 bar absolute pressure and 20 C temperature (State 8) and exiting at 1 bar absolute pressure and 30 C temperature (State 9). (g) Calculate the mass flow rate (kg/s) of the cooling water.

22 HW-21: Due by 4:30 pm EDT on Monday 23 Oct 2017 to GradeScope. An ordinary household refrigerator operating in steady state receives electrical work while discharging net energy by heat transfer to its surroundings (e.g., the kitchen). a. Is this a violation of the Kelvin-Planck statement of the Second Law of Thermodynamics? Explain your answer. b. Consider the same question, but now consider an electric motor operating in steady state.

23 HW-22: Due by 4:30 pm EDT on Monday 23 Oct 2017 to GradeScope. A heat pump cycle is used to maintain the interior of a building at 21 C. At steady state, the heat pump receives energy by heat transfer from well water at 9 C and discharges energy by heat transfer to the building at a rate of 120,000 kj/h. Over a period of 14 days, an electric meter records that 1490 kwh of electricity is provided to the heat pump. Determine: a. the amount of energy that the heat pump receives over the 14-day period from the well water by heat transfer, in kj. b. the heat pump s coefficient of performance. c. the coefficient of performance of a reversible heat pump cycle operating between hot and cold reservoirs at 21 C and 9 C.

24 HW-23: Due by 4:30 pm EDT on Monday 23 Oct 2017 to GradeScope. A Carnot power cycle is executed on 1 kg of water. The cycle consists of isobaric expansion of saturated liquid at 160 C to a volume of 0.3 m 3 followed by a reversible adiabatic expansion to 20 C and a quality of 76.0%. The water is then compressed isothermally to a quality of 19.7% and, finally, compressed reversibly and adiabatically back to the original state. a. Sketch the cycle on a p-v plot. b. Determine the heat transferred and net work, each in kj. c. Evaluate the thermal efficiency of this power cycle using the values found in part (b) and compare this value with the value based on the maximum possible value for a reversible cycle operating between the absolute temperatures of the thermal reservoirs.

25 HW-24: Due by 4:30 pm EDT on Friday 27 October 2017 to GradeScope. List the Given and Find, but in your solution the EFD, assumptions, and basic equations are not needed in this problem. (a) Return to HW-20 and find the specific entropy (kj/kg K) for the steam and water at the inlets and outlet of the mixer. (b) Determine the change in specific entropy (kj/kg K) between states 1 and 2 of the fluids given below: (i) Propane. State 1: T1 60 C, p1 30 bar, State 2: T2 85 C, p2 4.0 bar (ii) Ammonia. State 1: T1 50 C, x1 0.0, State 2: T2 48 C, p2 0.4 bar (iii) Water. State 1: T1 70 C, x1 0.6, State 2: T2 400 C, p bar

26 HW-25: Due by 4:30 pm EDT on Friday 27 October 2017 to GradeScope. ISO 100 quenching oil is used to cool an ingot of EN 18 steel. The oil is originally at 25 C and has a final temperature of 300 C. The steel is initially at 855 C and ends up in thermal equilibrium with the oil. The steel and oil physical properties are listed in the following table. Substance C, kj/kg-k, kg/m3 ISO 100 oil EN 18 steel a) Calculate the number of liters of oil required to cool 1 kg of 855 C EN 18 steel to the 300 C target temperature. b) Calculate the entropy change (kj/k) for the oil, for the steel, and for the system of oil and steel.

27 HW-26: Due by 4:30 pm EDT on Friday 3 November 2017 to GradeScope. Four (4.00) kg of N2 are contained in a piston-cylinder system. The N2 is initially at T1 = 280 K and p1 = 135 kpa. The N2 undergoes the following two processes: Process 1-2: adiabatic compression from state 1 to state 2 with T2 = 520K and p2 = 1100 kpa Process 2-3: an internally reversible isothermal expansion from state 2 to state 3 with p3 = 340 kpa Assume that the pressure values are absolute. (a) (b) Calculate the change in entropy (kj/k) for the N2 during each process. Comment on whether or not process 1-2 is possible for an adiabatic system. Calculate the work and heat transfer (kj) for each process.

28 HW-27: Due by 4:30 pm EDT on Friday 3 November 2017 to GradeScope. Two insulated tanks both contain air and are connected by a line with a closed valve. The volume of tank A is 2.0 m 3 and the volume of tank B is 5.0 m 3. Initially, tank A contains air at 500 K and 600 kpa while tank B contains air at 900 K and 200 kpa. The valve is opened and air from both the tanks mixes and eventually the combined system reaches equilibrium at a temperature of T2 and pressure p2. Assume that the volume of the connecting line is negligible compared to the volume of the tanks, and also that the connecting line is well-insulated, and that the pressure values are absolute. (a) (b) (c) Determine the final temperature T2 (K) and absolute pressure p2 (kpa). Calculate the entropy generation (kj/k) during the mixing process. Which physical processes are responsible for the entropy generation?

29 HW-28: Due by 4:30 pm EDT on Friday 3 November 2017 to GradeScope. Two valves (one at the turbine inlet and one at the turbine outlet) are used to control an adiabatic turbine operating at steady state. Air enters the first valve at P1 = 1000 kpa and T1 = 800 K, and exits at P2 = 900 kpa. The turbine outlet pressure is P3 = 140 kpa. Downstream of the second valve, the air is at P4 = 100 kpa and T4 = 500 K. You may assume that the air behaves as an ideal gas. Assume that the pressure values are absolute. Find: (a) The work per unit mass (kj/kg) of air produced by the turbine. (b) The entropy generated per unit mass (kj/kg-k) for the process 1 4. (c) (d) The entropy generated per unit mass (kj/kg-k) by the turbine only (i.e. process 2 3). Which device(s) is (are) responsible for generating the majority of the entropy (valves or turbine)?

30 HW-29: Due by 4:30 pm EDT on Friday, 10 November 2017 to GradeScope. A non-adiabatic steam turbine operating steadily and producing power of 2700 kw has inlet conditions of p1 = 60 bar and T1 = 813 K and outlet conditions of p2 = 0.2 bar and x2 = 0.9. The steam mass flow rate is 2.5 kg/s. Assuming that heat losses occur at a boundary temperature Tb = 350 K, that kinetic and potential energy changes are negligible, and that given pressures are absolute, find: (a) (b) The rate of heat transfer to the surroundings [kw]. The entropy generation rate [kw/k].

31 HW-30: Due by 4:30 pm EDT on Friday, 10 November 2017 to GradeScope. As an idealization, it is assumed that air in a diesel engine cylinder with a volume of 1 liter is compressed isentropically from p1 = 1 bar and T1 = 300 K to p2 = 10 bar (to compress and heat the air prior to fuel injection). Assuming that the given pressures are absolute and that the molecular weight of air is 28.9 kg/kmol, find: (a) (b) (c) T2 [K] and V2 [L] using relative pressure, pr, and relative volume, vr, respectively. T2 [K] and V2 [L] using constant specific heats and specific heat ratio k = 1.4. Indicate the percent difference in each as compared with the answers from part (a). Work of the compression process [kj] using values calculated in (a). Is it harder or easier to compress the air if it starts out at a higher temperature? Assume that the pressures at States 1 and 2 are still p1 = 1 bar and p2 = 10 bar, respectively.

32 HW-31: Due by 4:30 pm EDT on Friday, 10 November 2017 to GradeScope. An adiabatic steam turbine has an isentropic turbine efficiency of t = 0.92, inlet conditions of p1 = 60 bar and T1 = 813 K, and outlet pressure of p2 = 0.2 bar. The steam mass flow rate is 2.5 kg/s. Assuming that potential and kinetic energy changes are negligible and that given pressures are absolute, find: (a) (b) (c) (d) The power output of the turbine [kw]. The isentropic power output [kw] and power lost to irreversibilities [kw]. The actual enthalpy at State 2, h2 [kj/kg K]. State whether h2 > h2s and explain why or why not. Draw the T-s diagram. Label States 1, 2, and 2s and indicate the isentropic process path and the non-isentropic process path. Draw lines of constant pressure and label the values of T1 and T2 on the diagram. The critical pressure and temperature of water are 221 bar and 374 C, respectively. (e) The entropy generation [kw/k] (Hint: Find the actual quality from h2 and then actual s2)

33 HW-32: Due by 4:30 pm EDT on Monday, 20 November 2017 to GradeScope. A homeowner wishes to design a pump and pipe system for watering her lawn. She connects the pipes and pump so that she can fill a tank from a nearby pond as shown in the following sketch. You may assume the system operates adiabatically. a. Determine the minimum power per unit mass flow rate, in units of kj/kg, required to operate the pump at steady state. b. Prove that if irreversibilities are present, the temperature of the water in the tank will be larger than the water temperature in the pond. c. Prove that if irreversibilities are present, the power per unit mass flow rate required to operate the pump will have a larger magnitude than the result found in part (a). g = 9.81 m/s 2 tank 1 m pond pump 1 m 10 m 5 m

34 HW-33: Due by 4:30 pm EDT on Monday, 20 November 2017 to GradeScope. Consider a steam-power plant cycle in which saturated water vapor enters the turbine at 12.0 MPa (abs) and saturated liquid exits the condenser at a pressure of MPa (abs). The net power output of the cycle is 122 MW. a. Assuming that the isentropic efficiencies of the turbine and pump are 80%, determine the following: i. the mass flow rate of the water, in kg/h, ii. the rate of heat transfer into the boiler, in MW iii. the rate of heat transfer from the condenser, in MW, and iv. the thermal efficiency of the power plant cycle. b. Draw a T-s diagram for the cycle, clearly indicating the process paths, states, and isobar values. pump 4 boiler turbine 1 3 condenser 2

35 HW-34: Due by 4:30 pm EDT on Friday, 01 December 2017 to GradeScope. Consider a vapor power cycle with reheat where the working fluid is water. The pump and turbines operate adiabatically. At the exit of both turbines, the water exits as saturated water vapor. The mass flow rate through the system is 2.1 kg/s. a. Determine the net power developed by the cycle, in kw. b. Determine the thermal efficiency of the power cycle. c. Sketch the cycle on a T-s plot, indicating states, paths, and isobars. You needn t in include numerical values for the properties. pump 6 5 boiler 1 condenser turbines State p [bar (abs)] h [kj/kg] x

36 HW-35: Due by 4:30 pm EDT on Friday, 1 December 2017 to GradeScope. A refrigeration system is used to cool a freezer that is at a temperature of -20 C. Ammonia is the refrigerant within the vapor compression cycle and the following conditions are known for the ammonia: compressor inlet is superheated vapor with p 1 = 1.50 bar and T 1 = -22 C; compressor pressure ratio p 2 /p 1 is 10.67; condenser exit is a saturated liquid; and the refrigerant mass flow rate is 0.8 kg/sec. Heat transfer from the condenser occurs to surroundings at 35ºC. The isentropic efficiency of the compressor is Assume that the pressure drops in the evaporator and condenser are negligible. (a) Plot the cycle for the refrigerant on a T-s diagram, labeling the states 1, 2, 2s, 3, and 4, and indicate all process paths. (b) Calculate the quality x 4 at state 4. (c) Calculate the coefficient of performance for the refrigeration cycle. (d) Calculate the rate of heat rejection from the condenser. (e) Calculate the rates of entropy production in each of the four system components. Assume that the boundary temperature for heat transfer into the evaporator is -20 C. Assume that the boundary temperature for heat transfer out of the condenser is 35ºC.

37 HW-36: Due by 4:30 pm EDT on Friday, 1 December 2017 to GradeScope. A house is heated using a heat pump that employs refrigerant-134a. At a particular time, the rate of heat loss from the house is 20 kw for an indoor air temperature of 20 o C. The heat pump uses the ground as a heat source that is at a temperature of 8 o C. The refrigerant enters the compressor as saturated vapor at 280 kpa, and leaves at 1 MPa and 60 o C. The compression process is adiabatic. The refrigerant exits the expansion valve with a specific enthalpy of kj/kg. (a) Draw the cycle on a T-s diagram and label the states. (1 = compressor inlet, 2 = compressor exit, 3 = condenser exit, 4 = evaporator inlet) (b) Complete the table below. (c) Find the refrigerant flow rate, in kg/s. (d) Calculate the power input to the heat pump, in kw. (e) Find the rate of entropy production of the evaporator in kw/k. (f) Compute the coefficient of performance of the heat pump. State points p (kpa) T ( o C) Region or quality h (kj/kg) s (kj/kg K) , ,

38 HW-37: Due by 4:30 pm EDT on Friday, 01 December 2017 to GradeScope. An air-standard Otto cycle has a compression ratio of 10. At the beginning of compression, the pressure is 100 kpa (abs) and temperature is 27 ºC. The mass of air is 5 g and the maximum temperature in the cycle is 727 ºC. Determine: a. the heat rejections, in kj, b. the net work, in kj, c. the thermal efficiency of the cycle, d. the mean effective pressure, in kpa (abs), and e. sketch the process on a T-s plot, clearly indicating states, paths, and lines of constant specific volume.

39 HW-38: Due by 4:30 pm EDT on Friday 8 December 2017 to GradeScope. Air at an absolute pressure of 100 kpa and a temperature of 300 K (State 1) steadily enters an adiabatic compressor of a gas turbine power plant with a mass flow rate of 6 kg/s. Air exits the compressor at an absolute pressure of 1000 kpa (State 2). Air exiting the compressor then enters a heat exchanger and is heated to a temperature of 1400 K (State 3). Air leaving from heat exchanger expands through an adiabatic turbine to an absolute pressure of 100 kpa (State 4). Consider that the compressor and turbine are internally reversible. (a) Calculate the net power (kw) produced by the power plant. (b) Determine the thermal efficiency (%) of the power plant cycle. (c) Find the back work ratio of the power plant. Suppose that the compressor and turbine each have an isentropic efficiency of 80% (not internally reversible) and that all other conditions remain unchanged. (d) Calculate the net power (kw), thermal efficiency (%), and back work ratio of the power plant for non-isentropic compression and expansion.

40 HW-39: Due by 4:30 pm EDT on Friday 8 December 2017 to GradeScope. Air at an absolute pressure of 1000 kpa and a temperaturee of 300 K (State 1) steadily enters a lowkg/s. pressure compressor (Compressor 1) of a gas turbine power plant with a mass flow rate of 6 Air exits this compressor at an absolute pressure of 316 kpa (State 2). Air then enters a heat exchanger (intercooler) and is cooled to a temperature of 300 K (State 3) beforee entering a high- 4) pressure compressorr (Compressor 2). Air exits at an absolute pressure of 1000 kpa (State from the high-pressure compressor. Air then enters another heat exchanger (Regenerator) and is heated to a temperature of 1000 K (State 5). Air is thenn further heated to K (State 6) in a heat exchanger (Combustor 1). Air then enters a high-pressure turbine (Turbine 1) and expands to an absolute pressure of 316 kpa (State 7). Air is then heated to 1400 K (State 8) in a heat exchanger (Combustor 2). Air then enters a low-pressure turbine (Turbine 2) and expands to an absolute pressure of 100 kpa (State 9). Air leaving the low-pressure turbine is used to heat the air exiting the high-pressure compressor. Suppose that both the compressors and turbines have an isentropic efficiency of 80%. (a) Complete the table below. State Absolute Pressure (kpa) Temperaturee (K) Specific Enthalpy (kj/kg) (b) Calculate the net power (kw), thermal efficiency (%), and back work ratio of the power plant. Compare these values with those calculated inn HW-38 (a), (b), and (c), respectively, and comment. (c) Show the cycle on T-s diagram. Label states, show temperature values, and draw lines constantt pressure.

41 HW-40: Due by 4:30 pm EDT on Friday 8 December 2017 to GradeScope. There is no HW-40. Happy holidays