AREN 2110: Thermodynamics Spring 2010 Homework 7: Due Friday, March 12, 6 PM

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James Walter Bennett
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1 AREN 2110: Thermodynamics Spring 2010 Homework 7: Due Friday, March 12, 6 PM 1. Answer the following by circling the BEST answer. 1) The boundary work associated with a constant volume process is always (a) negative (b) zero (d) positive (d) equal to the heat transfer (e) equal to the change in internal energy (f) equal to the change in enthalpy 2) For an open system, steady-state is associated with which unique condition? (a) Mass is conserved (b) Energy is conserved (c) Energy of the control volume does not change with time (d) The process is adiabatic (e) Inlet velocity = outlet velocity (f) Inlet temp = outlet temp 3) Boundary work can be done by an ideal gas in a closed system in an isothermal process if, and only if (a) the process is not adiabatic (b) the process is isobaric (c) the process is polytropic (d) the process is adiabatic (e) the process is isochoric (f) isothermal process cannot have boundary work 4) The purpose of an adiabatic turbine is to (a) produce work from heat transfer to fluid (b) produce work from evaporation of fluid (d) increase pressure from enthalpy decrease of fluid (e) produce work from enthalpy decrease of fluid (c) reduce the pressure and temperature of fluid (f) produce work from enthalpy increase of fluid 5) An ideal gas flows through a steady-state adiabatic diffuser. The temperature of the gas MUST (a) remain constant (b) decrease (c) depend on work done by the system (d) increase (e) depend on heat loss from the system (f) cannot tell from information given

2 Pressure (kpa) 2. Refrigerant (R-134a) is the working fluid in a heat pump cycle consisting of four processes in sequence transferring heat from outside air at 0 o C to a house at 22 o C: 1 2 Adiabatic throttling of R-134a from a saturated liquid at 1 MPa to 200 kpa. 2 3 Heat exchange (evaporator) to produce saturated vapor at 200 kpa. 3 4 Adiabatic compressor raises pressure of the R-134a to 1 MPa and 50 o C. 4 1 Heat exchange (condenser) to convert refrigerant to saturated liquid at 1 MPa at the outlet, with the rejected heat transferred into a house to maintain temperature at 22 o C. Cycle summary: State Pressure (kpa) Temperature ( o C) Quality 1 1, , na Neglect kinetic energy changes. Solve heat transfer and power terms in kw. a. The volumetric flow rate of the R-134a at the evaporator outlet (State 3) = 0.6 m 3 /min. What is the rate of heat transfer to the refrigerant from the outside air that takes place in the evaporator (2 3), assuming no heat losses to the surroundings? b. What is the rate that heat is supplied to the house (kw) from the condenser (4 1)? c. What is the power requirement for the adiabatic compressor (3 4)? 3. Heat is removed from 0.5 m 3 of saturated refrigerant vapor at 1.4 MPA in a constant pressure process until half the R-134a vapor has condensed. a. Draw the process on the P-v diagram below Saturated Liquid-Vapor Phase Diagram R- 134a Specific volume (m 3 /kg)

3 Pressure (kpa) b) What is the boundary work of the process in kj? c) How much heat must be removed in kj? d) What is the mass of liquid at the end of the process in kg? e) If this process were carried out at constant volume, how much heat (kj) would have to be removed to condense half the R-134a? 4. The pressure of air is increased from 150 kpa to 600 kpa in an adiabatic compressor operating at steady state with 25 kw power from the motor. The inlet air flow rate is 6 m 3 /min and inlet air temperature is 40 o C. a) What is the temperature of the air at the compressor outlet? Neglect kinetic energy change. b) What is the volumetric flowrate at the compressor outlet? The compressed air now flows into an adiabatic nozzle where the velocity is increased from 4 m/s at the inlet to 100 m/s at the outlet and the pressure decreases from 600 kpa to 250 kpa. c) What is the temperature of the air as it exits the nozzle? d) What is the ratio of the inlet area to the outlet area for the nozzle (A 1 /A 2 )? 5. Refer to P-V diagram for a cycle with an ideal gas in a closed system to answer a) e) 150 Cycle P-V Diagram Volume (m 3 ) Process 1 2: linear expansion Process 2 3: isobaric expansion Process 3 4: linear expansion Process 4 1: isobaric compression

4 Be sure to use the correct sign convention. a) The work for 1 2 is kj. b) The work for 4 1 is kj c) The work for 2 3 is kj. d) The net work for the cycle is kj e) The net heat transfer for the cycle is kj 6. A house kept at 20 o C loses 600 kj/min heat during January when the average outside temperature is 5 o C. In addition, cold air infiltrates the house at a rate of m 3 /s. Since the mass of air in the house does not change, the house loses warm air to the outdoors at the same mass flow rate. Finally, appliances use 2 kw electricity which adds energy to the house air. a) What is the mass flow rate of infiltrating air? 5 o C 100 kpa m 3 /s m 2 kw electric power for appliances 20 o C 600 kj/min m m b) At what rate must heat be added to keep the house at 20 o C? c) Heat for the house is provided from the condenser (heat exchanger) of a heat pump containing R-134a. The pressure of the condenser is constant at 1 MPa, and the temperature at the inlet is 50 o C. The refrigerant is saturated liquid at the outlet. What is the temperature of the R-134a at the outlet? d) Calculate the mass flow rate of R-134a required to keep the house at 20 o C. e) The refrigerant leaves the condenser and enters a throttling valve where the pressure is reduced from 1 MPa to 200 kpa. What is the temperature of the R-134a at the throttling valve outlet? Justify your answer. f) What is the vapor content of the refrigerant at the throttling valve outlet?

5 7. A piston-cylinder device containing nitrogen gas (N 2 ) is used to recover work done against a resistance (that is, not isobaric). The nitrogen expands in a polytropic process: PV 0.82 = constant The initial volume of the cylinder = 0.5 m 3, initial pressure = 400 kpa, and initial temperature = 27 o C. An electric heater is turned on for 10 minutes to expand the nitrogen. During the process, 12.8 kj of heat is also lost. After expansion, the cylinder volume is twice as large as the initial volume. N 2 Q = kj a) Find P 2 after expansion b) Find T 2 after expansion c) Find the boundary work for the process in kj d) Find the power required to expand the nitrogen in 10 minutes Electric heater

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