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  Steam enters a turbine operating at steady state at a pressure of 1000

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  Steam enters a turbine operating at steady state at a pressure of 1000 lbf/in2 and a temperature of 1100°F, and exits at a pressure of 4.0 lbf/in2 as a saturated liquid-vapor mixture with a quality of 0.96. Stray heat transfer from the turbine to the surroundings occurs. The ambient temperature is 90°F. Measurements indicate that the magnitude of the rate of the stray heat transfer is 3% of the turbine power. The mass flow rate of water through the turbine is 10 lbm/s.
  (a) Calculate the turbine power (Btu/s).
  (b) For an enlarged control volume that includes the turbine and enough of the surroundings so that the boundary temperature is 90°F, calculate the rate of entropy production (Btu/s-°R).

  Please show work. Final answer for A) 4620 Btu/s; (B) 1.31 Btu/s·R
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  EGR 334 Homework solutions HW Set 26

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  EGR 334         HW Set 26

  Problem 6: 80

  A gas flows through a 1-inlet, 1-outlet control volume operating at steady state. Heat transfer at the rate Qdot_cv takes place only at a location on the boundary where the temperature is T_b. For each of the following cases, determine whether the specific entropy of the gas at the exit is greater than, equal to, or less than the specific entropy of the gas at the inlet.

  1. a) no internal irreversibilities, Qdot_cv = 0
  2. b) no internal irreversibilities, Qdot_cv < 0
  3. c) no internal irreversibilities, Qdot_cv > 0
  4. d) no internal irreversibilities, Qdot_cv >= 0

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  EGR 334         HW Set 26

  Problem 6:86

  By injecting liquid water into superheated steam, the desuperheater shown has a saturated vapor stream at its exit. Steady state operating data are provided in the accompanying table. Stray heat transfer and all kinetic and potential energy effect are negligible. a) Locate states 1, 2, nd 3 on a sketch on the T-s diagram. b) Determine the rate of entropy production within the desuperheater in kW/K.

  State	p(MPa)	T(deg C)	v(m3/kg)	u(kJ/kg)	h(kJ/kg)	s(kJ/kg-K)
  1	2.7	40	0.0010066	167.2	169.9	0.5714
  2	2.7	300	0.09101	2757.0	3002.8	6.6001
  3	2.5	sat. vapor	0.07998	2603.1	2803.1	6.2575

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  EGR 334         HW Set 26

  Problem 6:91

  Steam at 240 deg C and 700 kPa enters an open feedwater heater operating at steady state with a mass flow rate of 0.5 kg/s. A separate stream of liquid water enters at 45 deg C, 700 kPa with a mass flow rate of 4 kg/s. A single mixed stream exits at 700 kPa and temperature T. Stray heat transfer and KE and PE can be ignored. Determine

  1. a) T, in deg C and
  2. b) the rate of entropy production within the feedwater heater in kW/K.
  3. c) Locate the three principal states on a sketch of the T-s diagram.

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  EGR 334         HW Set 26

  Problem 6: 111

  The figure show data for a portion of the ducting in a ventilation system operating at steady state. The ducts are well insulated and the pressure is very nearly 1 atm throughout. Assuming the ideal gas law for air with c_p = 0.24 Btu/lb-R and ignoring KE and PE, determine

  1. a) the temperature of the air at the exit in deg F.
  2. b) the exit diameter in ft
  3. c) the rate of entropy production within the duct in Btu/min-R.

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  Determine the mass flow rate of the incoming superheated , in kg/min

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  For the desuperheater shown in Figure, liquid water at state 1 is injected into a stream of superheated vapor entering at state 2. As a result, saturated vapor exits at state 3. Data for steady state operation are shown on the figure. Ignoring stray heat transfer and kinetic and potential energy effects, determine the mass flow rate of the incoming superheated vapor, in kg/min.
  
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  Find the magnitude of that force

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  A nucleus that captures a stray neutron [in a nuclear reactor, for example] must bring the neutron to a stop within the diameter of the nucleus by means of the strong force.That force, which “glues” the nucleus together, is approximately zero outside the nucleus. Suppose that a stray neutron with an initial speed of 1.9 x 107 m/s is just barely captured by a nucleus with a diameter of 1.3 x 10-14 m. Assuming the strong force on the neutron is constant, find the magnitude of that force. (The neutron’s mass is 1.67×10-27 kg.)

  F = ? N

  [Hint: When the acceleration is constant, the velocity changes from vi to vf during the same interval. The average velocity over that interval is (vi + Vf)/2.]
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  A CI is desired for the true average stray-load loss

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  A CI is desired for the true average stray-load loss ? (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with

  ? = 3.3. (Round your answers to two decimal places.)

  (a) Compute a 95% CI for ? when n = 25 and x = 57.8.

  (b) Compute a 95% CI for ? when n = 100 and x = 57.8.

  (c) Compute a 99% CI for ? when n = 100 and x = 57.8.

  (d) Compute an 82% CI for ? when n = 100 and x = 57.8.

  (e) How large must n be if the width of the 99% interval for ? is to be 1.0? (Round your answer up to the nearest whole number.)
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  Unit Eleven Homework Solutions

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  1. Consider a 210 MW steam power plant that operates on a simple ideal Rankine cycle. Steam enters the turbine at 10 MPa and 500^oC and is cooled in the condenser to a pressure of 10 kPa. Show the cycle on a T-s diagram with respect to the saturation lines and determine (a) the quality of steam at the turbine exit, (b) the thermal efficiency of the cycle, and (c) the mass flow rate of the steam.
  2. Consider a solar-pond power plant that operates on a simple ideal Rankine cycle with refrigerant-134a as the working fluid. The refrigerant enters the turbine as a saturated vapor at 1.6 MPa and leaves at 0.7 MPa. The mass flow rate of the refrigerant is 6 kg/s. Show the cycle on a T-s diagram with respect to the saturation lines and determine (a) the thermal efficiency and (b) the power output of the plant.
  3. Consider a steam power plant that operates on a simple ideal Rankine cycle and has a net power output of 45 MW. Steam enters the turbine at 7 MPa and 500^oC and is cooled in the condenser to a pressure of 10 kPa by running cooling water from a lake through the condenser at a rate of 2000 kg/s. Show the cycle on a T-s diagram with respect to the saturation lines, and determine (a) the thermal efficiency of the cycle, (b) the mass flow rate of the steam, and (c) the temperature rise of the cooling water.
  4. A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine at 6 MPa and 450^oC and is condensed in the condenser at 20 kPa. Steam is extracted from the turbine at 0.4 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a T-s diagram and determine (a) the net work per kilogram of steam flowing through the boiler and (b) the thermal efficiency of the cycle.
  5. Repeat problem 4 with the open feedwater heater replaced by a closed feedwater heater. Assume that the feedwater leaves the heater at the condensation temperature of the extracted steam and that the extracted steam leaves the heater as a saturated liquid and is pumped to the line carrying the feedwater.
  6. A steam power plant operates on an ideal reheat-regenerative Rankine cycle and has a net power output of 80 MW. Steam enters the high-pressure turbine at 10 MPa and 550^oC and leaves at 0.8 MPa. Some of the steam is extracted at this pressure to heat the feedwater in an open feedwater heater. The rest of the steam is reheated to 500^oC and is expanded in the low pressure turbine to the condenser pressure of 10 kPa. Show the cycle on a T-s diagram and determine (a) the mass flow rate of steam flowing through the boiler and (b) the thermal efficiency of the cycle.
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  EGR 334: Thermodynamics Review Problems Solutions

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  Problem 1) A reversible power cycle operates between a thermal reservoir at 1540°F and 40°F.
  a) What is the maximum thermodynamic efficiency of the cycle?

  1. b) This cycle is found to have W_cycle = 50 Btu, what is Q_out?

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  Problem 2) An inventor claims to have devised a refrigeration cycle that at steady state requires a net power input of 0.8 hp to remove 13,000 Btu/hr of energy by heat transfer from the freezer compartment at -10°F and discharge energy by heat transfer to a kitchen at 65°F.
  a) What is the maximum thermodynamic coefficient of performance for the cycle?

  1. b) Is this process thermodynamically possible? Why or why not?

  Problem 3) One kilogram of water executes a Carnot power cycle. The following table describes the thermodynamic cycle.

  1. a) Complete the following tables

  State	1	2	3	4		Process	Q (kJ)	W (kJ)
  p (bar)	40	40	1.5	1.5		1 – 2
  T (°C)						2 – 3
  x	0.15	1	0.801	0.32		3 – 4
  v (m3/kg)						4 – 1
  u (kJ/kg)
  s (kJ/kg-K)

  1. b) Draw the cycle on the p-v and T-s diagrams.

  Problem 4) A 2 m³ ridged, insulated container is filled with 4.76 kg of air and fitted with a paddle wheel. The container and its contents are initially at 293 K. The paddle wheel does 710 kJ of work on the air. Treat the air as an ideal gas with c_v = 0.72 kJ/kg·K.

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  1. a) What is the initial pressure?

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  1. b) What is the final temperature?

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  1. b) How much entropy is produced?

  Problem 5) Steam enters a turbine operating at steady state at 6 MPa, 600°C with a mass flow rate 125 kg/min and exits as a saturated vapor at 20 kPa. The turbine produces energy at a rate of 2 MW. Kinetic and potential energy effects are negligible. The rate of heat loss from the turbine occurs to the air around the turbine at 27°C.

  1. a)   What the rate of entropy production for within the turbine?
  2. b)   What is the isentropic efficiency of the turbine?
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  EGR 334 Thermodynamics: Homework 18

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  EGR 334 Thermodynamics:   Homework 18

  Problem 4: 95

  A turbine operating at a steady state that provides power to an air compressor and an electric generator. Air enters the turbine with a mass flow rate of 5.4 kg/s at 527 deg C and exits the turbine at 107 deg C, 1 bar. The turbine provides power at a rate of 900 kW to the compressor and at a rate of 1400 kW to the generator.   Air can be modeled as an ideal gas, and kinetic and potential energy changes are negligible. Determine

  1. a) the volumetric flow rate of the air at the turbine exit, in m³/s and
  2. b) the rate of heat transfer between the turbine and its surroundings in kW.

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  EGR 334 Thermodynamics:   Homework 18

  Problem 4: 98

  A refrigeration system consists of a heat exchanger, an evaporator, a throttling valve, and associated piping. Data for steady state operation with R134a are given in the figure. There is no significant heat transfer to or from the heat exchanger, valve, and piping. Ignore KE and PE. Determine the rate of heat transfer between the evaporator and its surroundings in Btu/h.

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  EGR 334 Thermodynamics:   Homework 18

  Problem 4: 102

  Steady state operating data for a simple steam power plant are provided in the figure. Stray heat transfer, KE and PE effects are small. Determine

  1. a) thermal efficiency
  2. b) mass flow rate of cooling water in kg/kg of stream flowing.

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  Determine the thermal efficiency and the mass flow rate of the cooling water

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  Steady-state operating data for a simple steam power plant are provided in figure. Stray heat transfer and kinetic and potential energy effects can be ignored. Determine the (a) thermal efficiency and (b) the mass flow rate of the cooling water, in kg per kg of steam flowing.