EBK THERMODYNAMICS: AN ENGINEERING APPR
EBK THERMODYNAMICS: AN ENGINEERING APPR
8th Edition
ISBN: 9780100257054
Author: CENGEL
Publisher: YUZU
bartleby

Videos

Question
Book Icon
Chapter 10.9, Problem 78P

(a)

To determine

The ratio of mass flow rate of air to mass flow rate of steam in the combined power cycle

(a)

Expert Solution
Check Mark

Answer to Problem 78P

The ratio of mass flow rate of air to mass flow rate of steam in the combined power cycle is 6.426kg air/kg steam_.

Explanation of Solution

Draw the T-s diagram for the combined gas-steam power cycle.

EBK THERMODYNAMICS: AN ENGINEERING APPR, Chapter 10.9, Problem 78P

Write the expression for the relation relative pressure and ideal pressure.

Pr9=P9P8Pr8 (I).

Here, the relative pressure at state 9 is Pr9, and relative pressure at state 8 is Pr8.

Write the expression for the efficiency of compressor.

ηC=h9sh8h9h8 (II).

Refer to properties table of air, and interpret the value of h9s for a pressure of 19.40 kPa as 635.5kJ/kg .

Write the expression for the relation relative pressure and ideal pressure.

Pr11=P11P10Pr10 (III).

Here, the relative pressure at state 11 is Pr11, and relative pressure at state 10 is Pr10.

Write the expression for the efficiency of turbine.

ηT=h10h11h10h11s (IV).

Write the expression for the specific work input of pump I to the system/

wpI,in=v1(P2P1) (V).

Write the expression for the enthalpy of steam at state 2.

h2=h1+wpI,in (VI).

Write the expression for the specific work input of pump II to the system/

wpII,in=v3(P4P3) (VII).

Write the expression for the enthalpy of steam at state 4.

h4=h3+wpII,in (VIII).

Write the expression for the quality of steam at state 6s.

x6s=s6ssfsfg (IX).

Here, specific entropy of wet steam at 0.6 MPa is sf, and specific entropy of vaporization at 0.6 MPa is sfg.

Write the expression for the specific enthalpy of steam at state 6s.

h6s=hf+x6shfg (X).

Here, specific enthalpy of wet steam at 0.6MPa is hf, and specific enthalpy of vaporization at 0.6MPa is hfg.

Write the expression for the efficiency of turbine.

ηT=h5h6h5h6s (XI).

Write the expression for the quality of steam at state 7s.

x7s=s7sfsfg (XII).

Here, specific entropy of wet steam at 20 kPa is sf, and specific entropy of vaporization at 20 kPa is sfg.

Write the expression for the specific enthalpy of steam at state 7s.

h7s=hf+x7shfg (XIII).

Here, specific enthalpy of wet steam at 20kPa is hf, and specific enthalpy of vaporization at 20kPa is hfg.

Write the expression for the efficiency of turbine.

ηT=h5h7h5h7s (XIV).

Write the expression for the energy balance equation for the heat exchanger.

E˙in=E˙out (XV).

Rewrite Equation (1) and rearrange the terms with mass and enthalpy terms.

m˙sh5+m˙airh12=m˙sh4+m˙airh11

m˙s(h5h4)=m˙air(h11h12)

m˙airm˙s=(h5h4)(h11h12) (XVI).

Here, mass flow rate of steam is m˙s, and mass flow rate of air is m˙air.

Conclusion:

Refer Table A-17, “Ideal-gas properties of air”, select the relative pressure Pr8 and the enthalpy h8 for air gas at the temperature of 300 K as 1.386 kPa, and 300.19kJ/kg respectively.

Substitute 1.386 kPa for Pr8, and 14 for P9P8 in Equation (I).

Pr9=14×1.386=19.40kPa

Refer Table A-17, “Ideal-gas properties of air”, interpret the value of the enthalpy h9 for 19.40 kPa pressure as 635.5kJ/kg.

Refer Table A-17, “Ideal-gas properties of air”, select the relative pressure Pr10 and the enthalpy h10 for air gas at the temperature of 1400 K as 1.450.5, and 1515.42kJ/kg respectively.

Substitute 450.5 kPa for Pr10, and 114 for P11P10 in Equation (III).

Pr11=114×450.5=32.18kPa

Refer Table A-17 “Ideal-gas properties of air , interpret the value of h12 for a temperature of 460 K as 462.02kJ/kg.

Refer Table A-5, “saturated water-Pressure table”, select the enthalpy h1 and the specific volume v1 for the pressure of 20kPa as 251.42kJ/kg and 0.001017m3/kg respectively.

Substitute 0.001017m3/kg for v1, 20kPa for P1, and 600kPa for P2 in Equation (V).

wpI,in=0.001017m3/kg(60020)kPa(1kJ1kPam3)=0.59kJ/kg

Substitute 251.42kJ/kg for h1, and 0.59kJ/kg for wpI,in in Equation (VI).

h2=251.42kJ/kg+0.59kJ/kg=252.01kJ/kg

Refer Table A-5, “saturated water-Pressure table”, select the enthalpy h3 and the specific volume v3 for the pressure of 600kPa as 670.38kJ/kg and 0.001101m3/kg respectively.

Substitute 0.001101m3/kg for v3, 600kPa for P3, and 8,000kPa for P4 in Equation (VII).

wpII,in=0.001101m3/kg(8,000600)kPa(1kJ1kPam3)=8.15kJ/kg

Substitute 670.38kJ/kg for h3, and 8.15kJ/kg for wpII,in in Equation (VIII).

h4=670.38kJ/kg+8.15kJ/kg=678.53kJ/kg

Refer Table A-5, “Superheated water”, select the enthalpy h5 and the entropy s5 for the pressure and temperature of 8MPa and 400°C as 3,139.4kJ/kg and 6.3658kJ/kgK respectively.

Since, the entropy at state 5 is equal to state 6s, so the entropy value of s6s is 6.3658kJ/kgK.

Interpret the value of sf and sfg for pressure of 0.6 MPa as 1.9308kJ/kgK and 4.8285kJ/kgK .

Substitute 6.3658kJ/kgK for s6s, 1.9308kJ/kgK for sf, and 4.8285kJ/kgK for sfg in Equation (IX).

x6=6.36581.93084.8285=0.9185

Refer to steam tables, and interpret the value of hf and hfg for a pressure of 0.6MPa as 670.38kJ/kg and 2,085.9kJ/kg.

Substitute 670.38kJ/kg for hf, 2,085.9kJ/kg for hfg, and 0.9185 for x6s in Equation (X).

h6=670.38kJ/kg+0.9185(2,085.9kJ/kg)=2,586.28kJ/kg

Since, the entropy at state 5 is equal to the entropy at state 7, the entropy value of s7 is 6.3658kJ/kgK.

Refer Table A-5, “Saturated water-Pressure table”, obtain the value of sf and sfg for a pressure of 20kPa as 0.8320kJ/kgK and 7.0752kJ/kgK respectively.

Substitute 6.3658kJ/kgK for s7, 0.8320kJ/kgK for sf, and 7.0752kJ/kgK for sfg in Equation (XII).

x6s=6.36580.83207.0752=0.7821

Refer Table A-5, “Saturated water-Pressure table”, obtain the value of hf and hfg for a pressure of 20kPa as 251.42kJ/kg and 2357.5kJ/kg respectively.

Substitute 251.42kJ/kg for hf, 2,357.5kJ/kg for hfg, and 0.7821 for x7s in Equation (XIII).

h7=251.42kJ/kg+0.7821(2,357.5kJ/kg)=2,095.2kJ/kg

Substitute 3,139.4kJ/kg for h5, 678.52kJ/kg for h4, and 735.80kJ/kg for h11, 462.02kJ/kg for h12 in Equation (XVI).

m˙airm˙s=(3,139.4678.52)(735.80462.02)=8.99kg air/kg steam

Thus, the ratio of mass flow rate of air to mass flow rate of steam in the combined power cycle is 8.99kg air/kg steam_.

(b)

To determine

The rate of heat input in the combustion chamber.

(b)

Expert Solution
Check Mark

Answer to Problem 78P

The rate of heat input in the combustion chamber is 720.215kW_.

Explanation of Solution

Write the expression for the energy balance equation for the open feed water heater.

E˙in=E˙out (XVII)

Rewrite Equation (3) and rearrange the terms with mass and enthalpy terms.

m˙2h2+m˙6h6=m˙3h3

yh6+(1y)h2=h3

y=h3h2h6h2 (XVIIII)

Here, fraction of steam extracted is y.

Write the expression for the specific power output of the turbine.

wT=[h5h6+(1y)(h6h7)] (XIX)

Write the expression for the specific net work output from the steam.

wnet,steam=wT(1y)wpI,inwpII,in (XX)

Write the expression for the specific net work output from the gas stream.

wnet,gas=(h10h11)(h9h8) (XXI)

Write the expression for the net work output per unit mass of gas.

wnet=wnet,gas+18.99wnet,steam (XXII)

Write the expression for the mass flow rate of air.

m˙air=W˙netwnet (XXIII)

Write the expression for the rate of heat input to the cycle.

Q˙in=m˙air(h10h9) (XXIV)

Conclusion:

Substitute 670.38kJ/kg for h3, 252.01kJ/kg for h2, and 2,663.3kJ/kg for h6 in Equation (XVIIII).

y=670.38252.012586.1252.01=0.1792

Substitute 0.86 for ηT, 0.1735 for y, 3,139.4kJ/kg for h5, 2,241.3kJ/kg for h7, and 2,663.3kJ/kg for h6 in Equation (XIX).

wT=[3,139.42,586.3+(10.1792)(2586.12095.2)]=956.23kJ/kg

Substitute 956.23kJ/kg for wT, and 0.1792 for y, 0.59kJ/kg for wpI,in, and 8.15kJ/kg for wpII,in in Equation (XX).

wnet,steam=956.23(10.1792)(0.59)8.15=948.56kJ/kg

Substitute 1,515.42kJ/kg for h10, and 735.8kJ/kg for h11, 635.5kJ/kg for h9, and 300.19kJ/kg for h8 in Equation (XXI).

wnet,gas=1,515.42735.8(635.5300.19)=444.3kJ/kg

Substitute 444.3kJ/kg for wnet,gas, and 948.56kJ/kg for wnet,steam in Equation (XXII).

wnet=261.56+18.99×815.9=549.8kJ/kg

Substitute 549.7kJ/kg for wnet, and 450,000kJ/s for W˙net in Equation (XXIIII).

m˙air=450,000kJ/s549.7kJ/kg=818.7kg/s

Substitute 818.7kg/s for m˙air, 1,515.42kJ/kg for h10, and 635.5kJ/kg for h9 in Equation (XXIV).

Q˙in=1,158.2(1,515.42635.5)=720,215kW

Thus, the rate of heat input in the combustion chamber is 720,215kW_.

(c)

To determine

The thermal efficiency of the combined power cycle

(c)

Expert Solution
Check Mark

Answer to Problem 78P

The thermal efficiency of the combined power cycle is 62.5%_.

Explanation of Solution

Write the expression for the thermal efficiency of the combined power cycle.

ηth=W˙netQ˙in (XXV)

Conclusion:

Substitute 720,215kW for Q˙in, and  450,000kW for W˙net in Equation (XXV).

ηth=450,000kW720,215kW×100=62.5%

Thus, the thermal efficiency of the combined power cycle is 62.5%_.

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 10 Solutions

EBK THERMODYNAMICS: AN ENGINEERING APPR

Ch. 10.9 - Is it possible to maintain a pressure of 10 kPa in...Ch. 10.9 - 10–12 A steam power plant operates on a simple...Ch. 10.9 - 10–13 Refrigerant-134a is used as the working...Ch. 10.9 - 10–14 A simple ideal Rankine cycle which uses...Ch. 10.9 - 10–15E A simple ideal Rankine cycle with water as...Ch. 10.9 - Consider a 210-MW steam power plant that operates...Ch. 10.9 - Consider a 210-MW steam power plant that operates...Ch. 10.9 - A steam Rankine cycle operates between the...Ch. 10.9 - A steam Rankine cycle operates between the...Ch. 10.9 - Prob. 20PCh. 10.9 - Prob. 21PCh. 10.9 - A simple Rankine cycle uses water as the working...Ch. 10.9 - The net work output and the thermal efficiency for...Ch. 10.9 - A binary geothermal power plant uses geothermal...Ch. 10.9 - Consider a coal-fired steam power plant that...Ch. 10.9 - Show the ideal Rankine cycle with three stages of...Ch. 10.9 - How do the following quantities change when a...Ch. 10.9 - Consider a simple ideal Rankine cycle and an ideal...Ch. 10.9 - An ideal reheat Rankine cycle with water as the...Ch. 10.9 - 10–31 A steam power plant operates on the ideal...Ch. 10.9 - Steam enters the high-pressure turbine of a steam...Ch. 10.9 - 10–34 Consider a steam power plant that operates...Ch. 10.9 - A steam power plant operates on an ideal reheat...Ch. 10.9 - Consider a steam power plant that operates on a...Ch. 10.9 - Repeat Prob. 1041 assuming both the pump and the...Ch. 10.9 - Prob. 39PCh. 10.9 - How do open feedwater heaters differ from closed...Ch. 10.9 - How do the following quantities change when the...Ch. 10.9 - Prob. 43PCh. 10.9 - 10–44 The closed feedwater heater of a...Ch. 10.9 - A steam power plant operates on an ideal...Ch. 10.9 - A steam power plant operates on an ideal...Ch. 10.9 - 10–47 A steam power plant operates on an ideal...Ch. 10.9 - Consider a steam power plant that operates on the...Ch. 10.9 - Consider a steam power plant that operates on the...Ch. 10.9 - Consider a steam power plant that operates on the...Ch. 10.9 - Consider an ideal steam regenerative Rankine cycle...Ch. 10.9 - A steam power plant operates on an ideal...Ch. 10.9 - Repeat Prob. 1060, but replace the open feedwater...Ch. 10.9 - 10–57 An ideal Rankine steam cycle modified with...Ch. 10.9 - Prob. 58PCh. 10.9 - Prob. 59PCh. 10.9 - Prob. 60PCh. 10.9 - Consider a steam power plant that operates on a...Ch. 10.9 - Prob. 63PCh. 10.9 - Prob. 64PCh. 10.9 - The schematic of a single-flash geothermal power...Ch. 10.9 - Prob. 66PCh. 10.9 - Prob. 67PCh. 10.9 - Consider a cogeneration plant for which the...Ch. 10.9 - Prob. 69PCh. 10.9 - A large food-processing plant requires 1.5 lbm/s...Ch. 10.9 - Steam is generated in the boiler of a cogeneration...Ch. 10.9 - Consider a cogeneration power plant modified with...Ch. 10.9 - Steam is generated in the boiler of a cogeneration...Ch. 10.9 - Prob. 75PCh. 10.9 - Why is the combined gassteam cycle more efficient...Ch. 10.9 - The gas-turbine portion of a combined gassteam...Ch. 10.9 - Prob. 78PCh. 10.9 - Prob. 80PCh. 10.9 - Consider a combined gassteam power plant that has...Ch. 10.9 - Why is steam not an ideal working fluid for vapor...Ch. 10.9 - Prob. 86PCh. 10.9 - What is the difference between the binary vapor...Ch. 10.9 - Why is mercury a suitable working fluid for the...Ch. 10.9 - By writing an energy balance on the heat exchanger...Ch. 10.9 - Steam enters the turbine of a steam power plant...Ch. 10.9 - Prob. 91RPCh. 10.9 - A steam power plant operates on an ideal Rankine...Ch. 10.9 - Consider a steam power plant operating on the...Ch. 10.9 - Consider a steam power plant that operates on a...Ch. 10.9 - Repeat Prob. 1098 assuming both the pump and the...Ch. 10.9 - Consider an ideal reheatregenerative Rankine cycle...Ch. 10.9 - Prob. 97RPCh. 10.9 - Prob. 98RPCh. 10.9 - A textile plant requires 4 kg/s of saturated steam...Ch. 10.9 - Consider a cogeneration power plant that is...Ch. 10.9 - Prob. 101RPCh. 10.9 - Reconsider Prob. 10105E. It has been suggested...Ch. 10.9 - Reconsider Prob. 10106E. During winter, the system...Ch. 10.9 - Prob. 104RPCh. 10.9 - Prob. 105RPCh. 10.9 - Prob. 106RPCh. 10.9 - A steam power plant operates on an ideal...Ch. 10.9 - Show that the thermal efficiency of a combined...Ch. 10.9 - Prob. 113RPCh. 10.9 - Starting with Eq. 1020, show that the exergy...Ch. 10.9 - A solar collector system delivers heat to a power...Ch. 10.9 - Consider a simple ideal Rankine cycle. If the...Ch. 10.9 - Consider a simple ideal Rankine cycle with fixed...Ch. 10.9 - Consider a simple ideal Rankine cycle with fixed...Ch. 10.9 - Consider a simple ideal Rankine cycle with fixed...Ch. 10.9 - Prob. 120FEPCh. 10.9 - A simple ideal Rankine cycle operates between the...Ch. 10.9 - Prob. 122FEPCh. 10.9 - Prob. 123FEPCh. 10.9 - Consider a combined gas-steam power plant. Water...Ch. 10.9 - Pressurized feedwater in a steam power plant is to...Ch. 10.9 - Consider a steam power plant that operates on the...
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