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  Unit Five Homework Solutions

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  1. Steam flows steadily through an adiabatic turbine. The inlet conditions of the steam are 10 MPa, 450^oC, and 80 m/s. The exit conditions are 10 kPa, 92% quality, and 50 m/s. The mass flow rate of the steam is 12 kg/s. Determine (a) the change in kinetic energy, (b) the power output, and (c) the turbine inlet area.
  2. Argon gas enters an adiabatic turbine steadily at 900 kPa and 450^oC with a velocity of 80 m/s and leaves at 150 kPa with a velocity of 150 m/s. The inlet area of the turbine is is 60 cm². If the power output of the turbine is 250 kW, determine the exit temperature of the argon.
  3. Refrigerant-134a enters an adiabatic compressor as saturated vapor at -24^oC and leaves at 0.8 MPa and 60^oC. The mass flow rate of the refrigerant is 1.2 kg/s. Determine (a) the power input to the compressor and (b) the volume flow rate of the refrigerant at the compressor inlet.
  4. Refrigerant-134a is throttled from the saturated liquid state at 700 kPa to a pressure of 160 kPa. Determine the temperature drop during this process and the final specific volume of the refrigerant.
  5. Refrigerant-134a at 1 MPa and 90^oC is to be cooled to 1 MPa and 30^oC in a condenser by air. The air enters at 100 kPa and 27^oC with a volume flow rate of 600 m³/min and leaves at 95 kPa and 60^oC. Determine the mass flow rate of the refrigerant.
  6. Air enters the evaporator section of a window air conditioner at 14.7 psia and 90 ^oF with a volume flow rate of 200 ft³/min. Refrigerant-134a at 20 psia with a quality of 30% enters the evaporator at a rate of 4 lb_m/min and leaves as a saturated vapor at the same pressure. Determine (a) the exit temperature of the air and (b) the rate of heat transfer from the air.
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  Determine the power developed by the turbine for an expansion between these states

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  Text: Air enters a turbine operating at steady state at 500 kPa, 860 K and exits at 100 kPa. A temperature sensor indicates that the exit air temperature is 460 K. Stray heat transfer and kinetic and potential energy effects are negligible, and the air can be modeled as an ideal gas. Determine if the exit temperature reading can be correct. It yes, determine the power developed by the turbine for an expansion between these states, in kJ per kg of air flowing. If no, provide an explanation with supporting calculations.
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  Determine the power

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  Text: As shown in Fig. P4.105, hot industrial waste water at 15 bar, 180degreeC with a mass flow rate of 5 kg/s enters a flash chamber via a valve. Saturated vapor and saturated liquid streams, each at 4 bar, exit the flash chamber. The saturated vapor enters the turbine and expands to 0.08 bar, x = 90%. Stray heal transfer and kinetic and potential energy effects are negligible. For operation at steady state, determine the power, in hp, developed by the turbine.
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  Steady-State Operating data

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  Steady-State Operating data are provided for a compressor and heat exchanger. The Power input to the compressor is 50 kW. Nitrogen flows through the compressor and heat exchanger with a mass flow rate of .25 kg/s . The nitrogen is modeled as an ideal gas. A separate cooling stream of helium, modeled as an ideal gas with k=1.67, also flows through the heat exchanger. Stray heat transfer and kinetic and potential energy effects are negligible. Determine the mass flow rate of the helium, in kg/s.
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  Antireflection coatings can be used on the inner surfaces of eyeglasses

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  Antireflection coatings can be used on the inner surfaces of eyeglasses to reduce the reflection of stray light into the eye, thus reducing eyestrain.

  a.)A 89 nm thick coating is applied to the lens. What must be the coating’s index of refraction to be most effective at 461 nm? Assume that the coating’s index of refraction is less than that of the lens.

  b.)If the index of refraction of the coating is 1.39, what thickness should the coating be so as to be most effective at 461 nm? The thinnest possible coating is best.
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  Differences between the UCC and the CISG

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  The paper provides the major differences between the Uniform Commercial Code (UCC) and the United Nations Convention on Contracts of International Sales of Goods (CISG)
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  EGR 334 Homework Solutions HW Set32

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  EGR 334         HW Set32_

  Problem 8: 21

  The figure provides steady state operating data for a vapor power plant using water as the working fluid. The mass flow rate of water is 12 kg/s. The turbine and pump operate adiabatically but not reversibly. Determine

  1. a) the thermal efficiency
  2. b) the rates of heat transfer Q_in dot and Q_outdot each in kW.

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  EGR 334         HW Set32

  Problem 8: 29

  Water is the working fluid in an ideal Rankine cycle with reheat. Superheated vapor enters the turbine at 10 MPa, 480 C and the condenser pressure is 6 kPa. Steam expands through the first stage turbine to 0.7 MPa and then is reheated to 480 C. Determine for the cycle

  1. a) the rate of heat addition in kJ per kg of steam entering the first stage turbine.
  2. b) the thermal efficiency.
  3. c) the rate of heat transfer from the working fluid passing through the condenser to the cooling water in kJ per kg of steam entering the first stage turbine.

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  EGR 334         HW Set32_

  Problem 8: 49

  Water is the working fluid in an ideal regenerative Rankine cycle with one closed feedwater heater. Superheated vapor enters the turbine at 10 MPa, 480 C and the condenser pressure is 6 kPa. Steam expands through the first stage turbine where some is extracted and diverted to a closed feedwater heater at 0.7 MPa. Condensate drains from the feedwater heater as saturated liquid at 0.7 MPa and is trapped into the condenser. The feedwater leaves the heater at 10 MPa and a temperature equal to the saturation temperature at 0.7 MPa. Determine for the cycle.

  1. a) the rate of heat transfer to the working fluid passing through the steam generator in kJ per kg of steam entering the first stage turbine.
  2. b) the thermal efficiency
  3. c) the rate of heat transfer from the working fluid passing through the condenser to the cooling water in kJ per kg of steam entering the first stage turbine.

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  EGR 334         HW Set32_

  Problem 8: 60

  Consider a regenerative vapor power cycle with two feedwater heaters, a closed one and an open one as shown in the figure. Steam enters the first turbine stage at 12 MPa, 480 C and expands to 2 MPa. Some steam is extracted at 2 MPa and fed to the closed feedwater heater. The remainder expands through the second stage turbine to 0.3 MPa where an additional amount is extracted and fed into the open feedwater heater operating at 0.3 MPa. The steam expanding through the third stage turbine exits at the condenser pressure of 6 kPa.

  Feedwater leaves the closed heater at 210 C, 12 MPa, and condensate exiting as saturated liquid at 2 MPa is trapped into the open feedwater heater. Saturated liquid at 0.3 MPa leaves the open feedwater heater. Assume all pumps and turbine stages operate isentropically. Determine for the cycle

  1. a) the rate of heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam entering the first stage turbine.
  2. b) the thermal efficiency.
  3. c) the rate of heat transfer from the working fluid passing through the condenser to the cooling water in kJ per kg of steam entering the first stage turbine.
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  Solve the following question

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  Text: a simple vapor power plant operating at steady state with water as the working fluid. Data at key locations are given on the figure. The mass flow rate of the water circulating through the components is 109 kg/s. Stray heat transfer and kinetic and potential energy effects can be ignored. Determine the net power developed, in MW. the thermal efficiency. the isentropic turbine efficiency. the isentropic pump efficiency. the mass flow rate of the cooling water, in kg.’s. the rates of entropy production, each in kW/K, for the turbine, condenser, and pump
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  Steve and Ed are cousins who were both born on the same day

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  Steve and Ed are cousins who were both born on the same day, and both turned 25 today. Their grandfather began putting $2,500 per year into a trust fund for Steve on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate’s©2011 Strayer University. All Rights Reserved. This document contains Strayer University Confidential and Proprietary information
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  FIN 534 Homework Chapter 4 Page 2 of 2
  trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Steve’s 65th birthday. The grandfather set things up this way because he wants Steve to work, not be a “trust fund baby,” but he also wants to ensure that Steve is provided for in his old age.
  Until now, the grandfather has been disappointed with Ed, hence has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Ed. He will make the first payment to a trust for Ed today, and he has instructed his trustee to make 40 additional equal annual payments until Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Ed’s trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday?
  a. $3,726
  b. $3,912
  c. $4,107
  d. $4,313
  e. $4,528