Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
bartleby

Videos

Question
Book Icon
Chapter 8, Problem 133P

a)

To determine

The mass flow rate of the steam.

a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The initial pressure of the steam (P1) is 7 MPa.

The initial temperature of the steam (T1) is 500°C.

The initial velocity (V1) is 45m/s.

The final pressure of the steam (P2) is 100 kPa.

The final velocity (V2) is 75m/s.

The power output of the turbine (W˙a) is 5 MW.

The isentropic efficiency (η) is 77%.

Conclusion:

Refer the Table A-6, “superheated water table”, obtain the following properties at a pressure of 7MPa and temperature of 500 C.

The initial enthalpy (h1) is 3,411.4kJ/kg.

The initial entropy (s1) is 6.800kJ/kgK.

The entropy remains constant since the process is isentropic (s2s=s1).

Refer the Table A-6, “superheated water table”, obtain the following properties at a pressure of 100kPa and entropy of 6.800kJ/kgK.

The enthalpy at final state in isentropic process (h2s) is 2466.6kJ/kg.

Calculate the power output for the isentropic process.

  W˙s=W˙aηT

  W˙s=5,000kW70%=5,000kW70(1100)=6494kW=6494kJ/s

Write the expression for the energy balance equation for closed system.

  E˙inE˙out=ΔE˙system        (I)

Here, rate of net energy transfer in to the control volume is E˙in, rate of net energy transfer exit from the control volume is E˙out and rate of change in internal energy of system is ΔE˙system.

The rate of change in internal energy of the system is zero at steady state.

Substitute ΔE˙system=0 in Equation (I).

  E˙inE˙out=0E˙in=E˙outm˙(h1+V122)=m˙(h2s+V222)+W˙s

  m˙(3411.4kJ/kg+(45m/s)22)={m˙(2466.6kJ/kg+(75m/s)22)+6494kJ/s}m˙(3411.4kJ/kg+(45m/s)22(1kJ/kg1000m2/s2))={m˙(2466.6kJ/kg+(75m/s)22(1kJ/kg1000m2/s2))+6494kJ/s}m˙=6.886kg/s

Thus, the mass flow rate of the steam is 6.886kg/s.

b)

To determine

The exit temperature of the steam.

b)

Expert Solution
Check Mark

Explanation of Solution

Write the expression to calculate the mass flow rate of the steam.

  m˙(h1+V122)=m˙(h2s+V222)+W˙a

  6.886kg/s(3411.4kJ/kg+(45m/s)22)={6.886kg/s×(h2+(75m/s)22)+5000kJ/s}6.886kg/s(3411.4kJ/kg+(45m/s)22(1kJ/kg1000m2/s2))={6.886kg/s×(h2+(75m/s)22(1kJ/kg1000m2/s2))+5000kJ/s}h2=2683.5kJ/kg

Refer the Table A-6, “superheated water table”, obtain final entropy at pressure of 100kPa and enthalpy of 2683.5kJ/kg as 7.3817kJ/kgK.

Refer the Table A-6, “Superheated water”, obtain the value of exit temperature (T2) at final enthalpy (h2) of 2683.5kJ/kg by using interpolation method.

Show exit temperature and enthalpy values from the Table A-6.

Temperature (T2),in °CEnthalpy (h2), in Btu/lbmR
2675100
2683.5?
2776.6150

Write the formula of interpolation method of two variables.

  y2=(x2x1)(y3y1)(x3x1)+y1        (V)

Here, the variables denoted by x and y are exit temperature and enthalpy.

Substitute x1=2675, x2=2683.5, x3=2776.6, y1=100, and y3=150 in Equation (V).

  y2=(2683.52675)(150100)(2776.62675)+100=104.18

The value of exit temperature (T2) at final enthalpy (h2) of 2683.5kJ/kg is 104.18°C.

Thus, the exit temperature of the steam is 104.18°C.

c)

To determine

The entropy generation in the turbine.

c)

Expert Solution
Check Mark

Explanation of Solution

Calculate the entropy generation in the turbine (Sgen).

  Sgen=m˙(s2s1)

  Sgen=6.886kg/s(7.3817kJ/kgK6.800kJ/kgK)=4.01kJ/Ks(1kW1kJ/s)=4.01kW/K

Thus, the entropy generation in the turbine is 4.01kW/K.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 8 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 8 - Prob. 11PCh. 8 - A piston–cylinder device contains superheated...Ch. 8 - The entropy of steam will (increase, decrease,...Ch. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - What three different mechanisms can cause the...Ch. 8 - A completely reversible heat engine operates with...Ch. 8 - Air is compressed by a 15-kW compressor from P1 to...Ch. 8 - Heat in the amount of 100 kJ is transferred...Ch. 8 - In Prob. 8–21, assume that the heat is transferred...Ch. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 27PCh. 8 - Is a process that is internally reversible and...Ch. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Prob. 32PCh. 8 - An insulated piston–cylinder device contains 5 L...Ch. 8 - Prob. 34PCh. 8 - Water vapor enters a turbine at 6 MPa and 400°C,...Ch. 8 - Prob. 36PCh. 8 - Prob. 37PCh. 8 - Prob. 38PCh. 8 - Prob. 40PCh. 8 - A rigid tank contains 5 kg of saturated vapor...Ch. 8 - Prob. 42PCh. 8 - Determine the heat transfer, in kJ/kg, for the...Ch. 8 - Calculate the heat transfer, in Btu/lbm, for the...Ch. 8 - Prob. 46PCh. 8 - Prob. 47PCh. 8 - Prob. 49PCh. 8 - Prob. 50PCh. 8 - Prob. 51PCh. 8 - 2-kg of saturated water vapor at 600 kPa are...Ch. 8 - Prob. 53PCh. 8 - Prob. 54PCh. 8 - Prob. 55PCh. 8 - A piston–cylinder device contains 5 kg of steam at...Ch. 8 - Prob. 57PCh. 8 - Prob. 58PCh. 8 - Prob. 59PCh. 8 - Prob. 60PCh. 8 - Prob. 61PCh. 8 - Prob. 62PCh. 8 - Prob. 63PCh. 8 - Prob. 65PCh. 8 - Prob. 66PCh. 8 - Prob. 67PCh. 8 - Prob. 68PCh. 8 - An ideal gas undergoes a process between two...Ch. 8 - Prob. 70PCh. 8 - Prob. 71PCh. 8 - Which of the two gases—helium or...Ch. 8 - Air is expanded from 2000 kPa and 500°C to 100 kPa...Ch. 8 - What is the difference between the entropies of...Ch. 8 - Prob. 75PCh. 8 - Prob. 76PCh. 8 - Prob. 77PCh. 8 - Prob. 78PCh. 8 - Air is compressed steadily by a 5-kW compressor...Ch. 8 - Prob. 81PCh. 8 - A mass of 25 lbm of helium undergoes a process...Ch. 8 - Prob. 84PCh. 8 - Prob. 85PCh. 8 - Air at 3.5 MPa and 500°C is expanded in an...Ch. 8 - Prob. 87PCh. 8 - Prob. 88PCh. 8 - Prob. 89PCh. 8 - Prob. 90PCh. 8 - Prob. 91PCh. 8 - Prob. 92PCh. 8 - Prob. 93PCh. 8 - Prob. 94PCh. 8 - Prob. 95PCh. 8 - Prob. 96PCh. 8 - Prob. 97PCh. 8 - Prob. 98PCh. 8 - Prob. 99PCh. 8 - Prob. 100PCh. 8 - Prob. 101PCh. 8 - Prob. 102PCh. 8 - Prob. 103PCh. 8 - Prob. 104PCh. 8 - Prob. 105PCh. 8 - Prob. 106PCh. 8 - Prob. 107PCh. 8 - Prob. 109PCh. 8 - Prob. 110PCh. 8 - Prob. 111PCh. 8 - Steam at 100 psia and 650°F is expanded...Ch. 8 - Prob. 113PCh. 8 - Prob. 114PCh. 8 - Prob. 115PCh. 8 - Prob. 116PCh. 8 - Carbon dioxide enters an adiabatic compressor at...Ch. 8 - Prob. 119PCh. 8 - Prob. 120PCh. 8 - Prob. 122PCh. 8 - Prob. 123PCh. 8 - Prob. 124PCh. 8 - The exhaust nozzle of a jet engine expands air at...Ch. 8 - An adiabatic diffuser at the inlet of a jet engine...Ch. 8 - Hot combustion gases enter the nozzle of a...Ch. 8 - Refrigerant-134a is expanded adiabatically from...Ch. 8 - Prob. 130PCh. 8 - Prob. 131PCh. 8 - Prob. 132PCh. 8 - Prob. 133PCh. 8 - Prob. 134PCh. 8 - Prob. 135PCh. 8 - Prob. 136PCh. 8 - Prob. 137PCh. 8 - Prob. 138PCh. 8 - Prob. 139PCh. 8 - Prob. 140PCh. 8 - Prob. 141PCh. 8 - Prob. 142PCh. 8 - Prob. 143PCh. 8 - Prob. 144PCh. 8 - Prob. 145PCh. 8 - Prob. 146PCh. 8 - Prob. 147PCh. 8 - Prob. 148PCh. 8 - Prob. 149PCh. 8 - Prob. 150PCh. 8 - Prob. 151PCh. 8 - Prob. 152PCh. 8 - Prob. 153PCh. 8 - Prob. 154PCh. 8 - Prob. 155RQCh. 8 - Prob. 156RQCh. 8 - Prob. 157RQCh. 8 - Prob. 158RQCh. 8 - Prob. 159RQCh. 8 - Prob. 160RQCh. 8 - Prob. 161RQCh. 8 - Prob. 162RQCh. 8 - Prob. 163RQCh. 8 - Prob. 164RQCh. 8 - Prob. 165RQCh. 8 - Prob. 166RQCh. 8 - Prob. 167RQCh. 8 - Prob. 168RQCh. 8 - Prob. 169RQCh. 8 - Prob. 170RQCh. 8 - Prob. 171RQCh. 8 - Prob. 172RQCh. 8 - Prob. 173RQCh. 8 - Determine the work input and entropy generation...Ch. 8 - Prob. 175RQCh. 8 - Prob. 176RQCh. 8 - Prob. 177RQCh. 8 - Prob. 178RQCh. 8 - Prob. 180RQCh. 8 - Prob. 181RQCh. 8 - Prob. 182RQCh. 8 - A 1200-W electric resistance heating element whose...Ch. 8 - Prob. 184RQCh. 8 - Prob. 185RQCh. 8 - Prob. 186RQCh. 8 - Prob. 187RQCh. 8 - Prob. 188RQCh. 8 - Prob. 189RQCh. 8 - Prob. 190RQCh. 8 - Consider a 50-L evacuated rigid bottle that is...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Power Plant Explained | Working Principles; Author: RealPars;https://www.youtube.com/watch?v=HGVDu1z5YQ8;License: Standard YouTube License, CC-BY