HW 7 - Due Wednesday, March 11
Transcription
HW 7 - Due Wednesday, March 11
ME 200 Homework #07 - Spring 2015 Homework Due: Wednesday, March 11, 2015 HW07(1) In a dairy plant, milk at 40 oF is pasteurized continuously at 160 oF at a rate of 0.4 ft3/s for 24 hours a day and 365 days a year. The milk is heated to the pasteurizing temperature by hot water heated in a natural gas fired boiler that has an efficiency of 82%. The pasteurized milk is then cooled by cold water at 65 oF before it is finally refrigerated back to 40 oF. To save energy and money, the plant installs a regenerator that has an effectiveness of 82%. If the cost of natural gas is $0.52/therm (1 therm = 100000 Btu), determine how much energy and money the regenerator will save this company per year. In your analysis, you can approximate the properties of milk as water. (Answer: $488845) HW07(2) For the desuperheater shown in the figure, liquid water at state 1 is injected into a stream of superheated vapor entering at state 2. As a result, a saturated vapor exits at state 3. Data for steady state operation are shown in the figure. Ignoring stray heat transfer and kinetic energy and potential energy effects, determine the mass flow rate of the incoming superheated vapor, in lbm/min. (Answer: 238.7 lbm/min) HW07(3) Ammonia enters the expansion valve of a refrigeration system at a pressure of 150 psia and a temperature of 100 oF and exits at 16 psia. If the ammonia undergoes a throttling process, what is the quality of the ammonia exiting the expansion valve? (Answer: 0.188) 1 HW07(4) Air flows through a system shown below. The pressure and temperatures for air at specific locations within the system have been measured and indicated. The compressor requires 10,000 kW for its operation at steady state. Between the compressor exit and turbine inlet, air is cooled using water flowing at 3000 kg/min. The water enters at 25C and leaves at 40C at 1 atm. Specific heats of air are not constant. Compressor Win = 10,000 kW Turbine P4 = 1 bar T4 = 800 K P2 = 20 bars T2 = 1400 K P1 = 5 bars T1 = 1100 K P3 = 18 bars T3 Heat Exchanger Water Out P6 = 1 bar T6 = 40C Water In P5 = 1 bar T5 = 25C (a) Complete the table below. State P (kPa) T (°C) v 3 (m /kg) h (kJ/kg) 1 2 3 4 (b) Determine the mass flow rate (kg/s) of air through the system. (Answer: 28.2 kg/s) (c) Compute the power developed by the turbine (MW). (Answer: 16.4 MW) HW07(5) Saturated liquid refrigerant 134a enters a throttling valve at 8 bar. The pressure of refrigerant at the exit of the throttling device is 1.8 bar. The refrigerant then enters a heat exchanger in which it is heated to saturated vapor at 1.8 bar. The volumetric flow rate at the exit of the heat exchanger is 500 L/min. The refrigerant leaving the heat exchanger is adiabatically compressed to 7 bar and 50C. (a) What is the temperature (C) at the exit of the throttling valve? (b) Calculate the rate of heat transfer (kJ/min) in the heat exchanger. (c) How much power (kW) is required to run the compressor? (Answer: -3.54kW) 2 HW07(6) As shown in the figure, hot industrial waste water at 200 psia, 400 oF with a mass flow rate of 10 lbm/s enters a flash chamber via a valve. Saturated vapor and saturated liquid streams, each at 60 psia, exit the flash chamber. The saturated vapor enters the turbine and expands to 1 psi, x = 90%. Stray heat transfer and kinetic and potential energy effects are negligible. For operation at steady state, determine the power, in hp, developed by the turbine. (Answer: 30.53 hp) HW07(7) (a) Is it possible for a heat engine to operate without rejecting any waste heat to a lowtemperature reservoir? Explain. (b) In the absence of any friction and other irreversibilities, can a heat engine have an efficiency of 100%? (c) Are the efficiencies of all the work-producing devices, including the hydroelectric power plants, limited by the Kelvin-Planck statement of the second law? Explain. HW07(8) Shown in the figure is a proposed system that undergoes a cycle while operating between cold and hot reservoirs. The system receives 500 kJ from the cold reservoir and discharges 400kJ to the hot reservoir while delivering net work to its surrounding in the amount of 100kJ. There are no other energy transfers between the system and its surroundings. Evaluating the performance of the system using: (a) Clausius statement of second law; (b) The Kelvin-Planck statement of second law. 3