THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I
THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I
8th Edition
ISBN: 9781307434316
Author: CENGEL
Publisher: INTER MCG
Question
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Chapter 9.12, Problem 143P
To determine

The minimum work that must be supplied to the compressor and turbine due to irreversibilities.

Expert Solution & Answer
Check Mark

Answer to Problem 143P

The minimum work that must be supplied to the compressor due to irreversibilities is 40.1kJ/kg.

The minimum work that is developed by the turbine due to irreversibilities is 34.8kJ/kg.

It can be noted that the compressor is more sensitive to irreversibilities than the turbine.

Explanation of Solution

Show the simple Brayton cycle, with air as the working fluid on Ts diagram.

THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I, Chapter 9.12, Problem 143P

For the given Brayton cycle with air as the working fluid Ti, hi, and Pi are the temperature at ith state, specific enthalpy at ith state and pressure at ith state respectively.

Write the expression of temperature and pressure relation ratio for the compression process 1-2.

T2s=T1(P2P1)(k1)/k (I)

Here, specific heat ratio is k.

Write the expression of efficiency of the compressor (ηC).

ηC=h2sh1h2h1

ηC=cp(T2sT1)cp(T2T1) (II)

Here, specific heat at constant pressure is cp.

Write the expression of temperature and pressure relation ratio for the expansion process 3-4.

T4s=T3(P4P3)(k1)/k (III)

Write the expression of efficiency of the turbine (ηT).

ηT=h3h4h3h4s

ηT=cp(T3T4)cp(T3T4s) (IV)

For compression processes

Write the expression for the entropy change for the isentropic process 1-2s (s2ss1).

s2ss1=cplnT2sT1RlnP2P1 (V)

Here, gas constant of air is R.

Write the expression for reversible work for the isentropic process 1-2s (wrev,1-2s).

wrev,1-2s=cp(T2sT1)T0(s2ss1) (VI)

Here, temperature of the surroundings is T0.

Write the expression for the entropy change for the process 1-2 (s2s1).

s2s1=cplnT2T1RlnP2P1 (VII)

Write the expression for the reversible work for the process 1-2 (wrev,1-2).

wrev,1-2=cp(T2T1)T0(s2s1) (VIII)

Write the expression for the minimum work that must be supplied to the compressor due to irreversibilities (Δwrev,C).

Δwrev,C=wrev,1-2wrev,1-2s (IX)

For expansion processes

Write the expression for the entropy change for the isentropic process 3-4s (s3s4s).

s3s4s=cplnT3T4sRlnP3P4 (X)

Write the expression for the reversible work for the isentropic process 3-4s (wrev,3-4s).

wrev,3-4s=cp(T3T4s)T0(s3s4s) (XI)

Write the expression for the entropy change for the process 3-4 (s3s4).

s3s4=cplnT3T4RlnP3P4 (XII)

Write the expression for the reversible work for the process 3-4 (wrev,3-4).

wrev,3-4=cp(T3T4)T0(s3s4) (XIII)

Write the expression for the minimum work that is developed by the turbine due to irreversibilities (Δwrev,T).

Δwrev,T=wrev,3-4swrev,3-4 (XIV)

Conclusion:

Substitute 288 K for T1, 12 for P2P1, and 1.4 for k in Equation (I).

T2s=(288K)(12)1.41/1.4=585.8K

Rearrange Equation (II), and solve for T2. Substitute 288 K for T1, 585.8 K for T2s, and 0.80 for ηC in Equation (II).

T2=T1+T2sT1ηC=288 K+(585.8288)K0.80=660.2K

Substitute 873 K for T3, 112 for P4P3, and 1.4 for k in Equation (III).

T4s=(873K)(112)1.41/1.4=429.2K

Rearrange Equation (IV), and substitute 873 K for T3, 429.2 K for T4s, and 0.80 for ηT.

T4=T3ηT(T3T4s)=873 K(0.80)(873 K429.2 K)=518K

Substitute 1.005kJ/kgK for cp, 585.8 K for T2s, 288 K for T1, 0.287kJ/kgK for R, and 12 for P2P1 in Equation (V).

s2ss1=(1.005kJ/kgK)ln585.8K288K(0.287kJ/kgK)ln(12)=0.0003998kJ/kgK

Substitute 1.005kJ/kgK for cp, 585.8 K for T2s, 288 K for T1, 288 K for T0, and 0.0003998kJ/kgK for (s2ss1) in Equation (VI).

wrev,1-2s=(1.005kJ/kgK)(585.8288)K(288K)(0.0003998kJ/kgK)=299.2kJ/kg

Substitute 1.005kJ/kgK for cp, 660.2 K for T2, 288 K for T1, 0.287kJ/kgK for R, and 12 for P2P1 in Equation (VII).

s2s1=(1.005kJ/kgK)ln660.2K288K(0.287kJ/kgK)ln(12)=0.1206kJ/kgK

Substitute 1.005kJ/kgK for cp, 660.2 K for T2, 288 K for T1, 288 K for T0, and 0.1206kJ/kgK for (s2s1) in Equation (VIII).

wrev,1-2=(1.005kJ/kgK)(660.2288)K(288K)(0.1206kJ/kgK)=339.3kJ/kg

Substitute 339.3kJ/kg for wrev,1-2, and 299.2kJ/kg for wrev,1-2s in Equation (IX).

Δwrev,C=(339.3299.2)kJ/kg=40.1kJ/kg

Thus, the minimum work that must be supplied to the compressor due to irreversibilities is 40.1kJ/kg.

Substitute 1.005kJ/kgK for cp, 873 K for T3, 429.2 K for T4s, 0.287kJ/kgK for R, and 12 for P3P4 in Equation (X).

s3s4s=(1.005kJ/kgK)ln873K429.2K(0.287kJ/kgK)ln(12)=0.0003944kJ/kgK

Substitute 1.005kJ/kgK for cp, 873 K for T3, 429.2 K for T4s, 288 K for T0, and 0.0003944kJ/kgK for (s3s4s) in Equation (XI).

wrev,3-4s=(1.005kJ/kgK)(873429.2)K(288K)(0.0003944kJ/kgK)=445.9kJ/kg

Substitute 1.005kJ/kgK for cp, 873 K for T3, 518.0 K for T4, 0.287kJ/kgK for R, and 12 for P3P4 in Equation (XII).

s3s4=(1.005kJ/kgK)ln873K518.0K(0.287kJ/kgK)ln(12)=0.1885kJ/kgK

Substitute 1.005kJ/kgK for cp, 873 K for T3, 518.0 K for T4, 288 K for T0, and 0.1885kJ/kgK for (s3s4) in Equation (XIII).

wrev,3-4=(1.005kJ/kgK)(873518.0)K(288K)(0.1885kJ/kgK)=411.1kJ/kg

Substitute 445.9kJ/kg for wrev,3-4s, and 411.1kJ/kg for wrev,3-4 in Equation (XIV).

Δwrev,T=(445.9411.1)kJ/kg=34.8kJ/kg

Thus, the minimum work that is developed by the turbine due to irreversibilities is 34.8kJ/kg.

It can be noted that the compressor is more sensitive to irreversibilities than the turbine.

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Chapter 9 Solutions

THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I

Ch. 9.12 - Prob. 11PCh. 9.12 - Prob. 12PCh. 9.12 - Prob. 13PCh. 9.12 - Prob. 15PCh. 9.12 - Prob. 16PCh. 9.12 - Prob. 17PCh. 9.12 - Prob. 18PCh. 9.12 - Repeat Prob. 919 using helium as the working...Ch. 9.12 - Consider a Carnot cycle executed in a closed...Ch. 9.12 - Prob. 21PCh. 9.12 - Prob. 22PCh. 9.12 - What four processes make up the ideal Otto cycle?Ch. 9.12 - Are the processes that make up the Otto cycle...Ch. 9.12 - How do the efficiencies of the ideal Otto cycle...Ch. 9.12 - How does the thermal efficiency of an ideal Otto...Ch. 9.12 - Prob. 27PCh. 9.12 - Why are high compression ratios not used in...Ch. 9.12 - An ideal Otto cycle with a specified compression...Ch. 9.12 - Prob. 30PCh. 9.12 - Prob. 31PCh. 9.12 - Prob. 32PCh. 9.12 - An ideal Otto cycle has a compression ratio of 8....Ch. 9.12 - Prob. 35PCh. 9.12 - Prob. 36PCh. 9.12 - Prob. 37PCh. 9.12 - An ideal Otto cycle with air as the working fluid...Ch. 9.12 - Repeat Prob. 940E using argon as the working...Ch. 9.12 - Prob. 40PCh. 9.12 - Prob. 41PCh. 9.12 - Prob. 42PCh. 9.12 - Prob. 43PCh. 9.12 - Prob. 44PCh. 9.12 - Prob. 45PCh. 9.12 - Prob. 46PCh. 9.12 - Prob. 47PCh. 9.12 - Prob. 48PCh. 9.12 - Prob. 49PCh. 9.12 - Prob. 50PCh. 9.12 - Prob. 51PCh. 9.12 - Prob. 52PCh. 9.12 - Prob. 53PCh. 9.12 - Prob. 54PCh. 9.12 - Repeat Prob. 957, but replace the isentropic...Ch. 9.12 - Prob. 57PCh. 9.12 - Prob. 58PCh. 9.12 - Prob. 59PCh. 9.12 - The compression ratio of an ideal dual cycle is...Ch. 9.12 - Repeat Prob. 962 using constant specific heats at...Ch. 9.12 - Prob. 63PCh. 9.12 - An air-standard cycle, called the dual cycle, with...Ch. 9.12 - Prob. 65PCh. 9.12 - Prob. 66PCh. 9.12 - Consider the ideal Otto, Stirling, and Carnot...Ch. 9.12 - Consider the ideal Diesel, Ericsson, and Carnot...Ch. 9.12 - An ideal Ericsson engine using helium as the...Ch. 9.12 - An ideal Stirling engine using helium as the...Ch. 9.12 - Prob. 71PCh. 9.12 - Prob. 72PCh. 9.12 - Prob. 73PCh. 9.12 - Prob. 74PCh. 9.12 - Prob. 75PCh. 9.12 - For fixed maximum and minimum temperatures, what...Ch. 9.12 - What is the back work ratio? What are typical back...Ch. 9.12 - Why are the back work ratios relatively high in...Ch. 9.12 - How do the inefficiencies of the turbine and the...Ch. 9.12 - A simple ideal Brayton cycle with air as the...Ch. 9.12 - A gas-turbine power plant operates on the simple...Ch. 9.12 - Prob. 82PCh. 9.12 - Prob. 83PCh. 9.12 - Prob. 85PCh. 9.12 - 9–86 Consider a simple Brayton cycle using air as...Ch. 9.12 - 9–87 Air is used as the working fluid in a simple...Ch. 9.12 - Air is used as the working fluid in a simple ideal...Ch. 9.12 - An aircraft engine operates on a simple ideal...Ch. 9.12 - 9–91E A gas-turbine power plant operates on a...Ch. 9.12 - Prob. 92PCh. 9.12 - 9–93 A gas-turbine power plant operates on the...Ch. 9.12 - A gas-turbine power plant operates on a modified...Ch. 9.12 - Prob. 95PCh. 9.12 - Prob. 96PCh. 9.12 - Prob. 97PCh. 9.12 - Prob. 98PCh. 9.12 - 9–99 A gas turbine for an automobile is designed...Ch. 9.12 - Prob. 100PCh. 9.12 - A gas-turbine engine operates on the ideal Brayton...Ch. 9.12 - An ideal regenerator (T3 = T5) is added to a...Ch. 9.12 - Prob. 103PCh. 9.12 - Prob. 104PCh. 9.12 - Prob. 106PCh. 9.12 - A Brayton cycle with regeneration using air as the...Ch. 9.12 - Prob. 108PCh. 9.12 - Prob. 109PCh. 9.12 - Prob. 110PCh. 9.12 - Prob. 111PCh. 9.12 - Prob. 112PCh. 9.12 - Prob. 113PCh. 9.12 - Prob. 114PCh. 9.12 - Prob. 115PCh. 9.12 - A simple ideal Brayton cycle without regeneration...Ch. 9.12 - A simple ideal Brayton cycle is modified to...Ch. 9.12 - Prob. 118PCh. 9.12 - Consider a regenerative gas-turbine power plant...Ch. 9.12 - Repeat Prob. 9123 using argon as the working...Ch. 9.12 - Consider an ideal gas-turbine cycle with two...Ch. 9.12 - Repeat Prob. 9125, assuming an efficiency of 86...Ch. 9.12 - Prob. 123PCh. 9.12 - Prob. 124PCh. 9.12 - Prob. 126PCh. 9.12 - Prob. 127PCh. 9.12 - Prob. 128PCh. 9.12 - Prob. 129PCh. 9.12 - A turbojet is flying with a velocity of 900 ft/s...Ch. 9.12 - Prob. 131PCh. 9.12 - A pure jet engine propels an aircraft at 240 m/s...Ch. 9.12 - A turbojet aircraft is flying with a velocity of...Ch. 9.12 - Prob. 134PCh. 9.12 - Consider an aircraft powered by a turbojet engine...Ch. 9.12 - 9–137 Air at 7°C enters a turbojet engine at a...Ch. 9.12 - Prob. 138PCh. 9.12 - Prob. 139PCh. 9.12 - 9–140E Determine the exergy destruction associated...Ch. 9.12 - Prob. 141PCh. 9.12 - Prob. 142PCh. 9.12 - Prob. 143PCh. 9.12 - Prob. 144PCh. 9.12 - Prob. 146PCh. 9.12 - A gas-turbine power plant operates on the...Ch. 9.12 - Prob. 149PCh. 9.12 - Prob. 150RPCh. 9.12 - Prob. 151RPCh. 9.12 - Prob. 152RPCh. 9.12 - Prob. 153RPCh. 9.12 - Prob. 154RPCh. 9.12 - Prob. 155RPCh. 9.12 - Prob. 156RPCh. 9.12 - Prob. 157RPCh. 9.12 - Prob. 159RPCh. 9.12 - Prob. 161RPCh. 9.12 - Prob. 162RPCh. 9.12 - Prob. 163RPCh. 9.12 - Consider a simple ideal Brayton cycle with air as...Ch. 9.12 - Prob. 165RPCh. 9.12 - Helium is used as the working fluid in a Brayton...Ch. 9.12 - Consider an ideal gas-turbine cycle with one stage...Ch. 9.12 - Prob. 169RPCh. 9.12 - Prob. 170RPCh. 9.12 - Prob. 173RPCh. 9.12 - Prob. 174RPCh. 9.12 - Prob. 184FEPCh. 9.12 - For specified limits for the maximum and minimum...Ch. 9.12 - Prob. 186FEPCh. 9.12 - Prob. 187FEPCh. 9.12 - Helium gas in an ideal Otto cycle is compressed...Ch. 9.12 - Prob. 189FEPCh. 9.12 - Prob. 190FEPCh. 9.12 - Consider an ideal Brayton cycle executed between...Ch. 9.12 - An ideal Brayton cycle has a net work output of...Ch. 9.12 - In an ideal Brayton cycle, air is compressed from...Ch. 9.12 - In an ideal Brayton cycle with regeneration, argon...Ch. 9.12 - In an ideal Brayton cycle with regeneration, air...Ch. 9.12 - Consider a gas turbine that has a pressure ratio...Ch. 9.12 - An ideal gas turbine cycle with many stages of...Ch. 9.12 - Prob. 198FEP
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