CONNECT FOR THERMODYNAMICS: AN ENGINEERI
CONNECT FOR THERMODYNAMICS: AN ENGINEERI
9th Edition
ISBN: 9781260048636
Author: CENGEL
Publisher: MCG
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Chapter 9.12, Problem 180RP

(a)

To determine

Draw the Pv and Ts diagrams for the given cycle.

(a)

Expert Solution
Check Mark

Answer to Problem 180RP

The Pv and Ts diagrams for the given cycle are shown as in Figure (1).

Explanation of Solution

Draw the Pv and Ts diagram for the given cycle.

CONNECT FOR THERMODYNAMICS: AN ENGINEERI, Chapter 9.12, Problem 180RP

Thus, the Pv and Ts diagrams for the given cycle are shown as in Figure (1)

(b)

To determine

The expression for the back work ratio as a function of k and r.

(b)

Expert Solution
Check Mark

Answer to Problem 180RP

The expression for the back work ratio as a function of k and r is 1k11rk1rk11r1_.

Explanation of Solution

Find the work of compression using the first law for process 1-2.

q12w12=Δu12w12=Δu12w12=cv(T2T1)wcomp=w12

wcomp=cv(T2T1) (I)

Here, heat interaction during the process 1-2 is q12, work interaction for process 1-2 is w12, change in specific internal energy for process 1-2 is Δu12, constant volume specific heat is cv, temperature at state 1 and 2 is T1,andT2 respectively.

Write the expression of expansion work.

wexp=w23=23Pdv=P(v3v2)=R(T3T2) (II)

Here, gas constant is R, specific volume at state 2 and 3 is v2andv3, and work interaction for process 2-3 is w23.

Write the expression of back work ratio using the equations (I) and (II).

wcompwexp=cv(T3T1)R(T3T2)=cvRT1T2(T3/T1)1(T3/T2)1 (III)

Here, temperature at state 1, 2, and 3 are T1,T2,andT3 respectively.

Conclusion:

Process 1-2: Isentropic

Calculate the ratio of T1/T2 and P2/P1.

T1T2=(v2v1)k1=1rk1

P2P1=(v1v2)k=rk

Here, pressure at state 1 and 2 is P1,P2, volume at states 1 and 2 is v1,v2, compression ratio is r, and specific heat ratio is k.

Process 2-3: Constant pressure

Calculate the expression for T3/T2.

P3v3T3=P2v2T2T3T2=v3v2=v1v2=rT3T2=v1v2T3T2=r

Here, volume at state 1 and 2 is v1andv2.

Process 3-1: Constant volume

Calculate the expression for T3/T1.

P3v3T3=P1v1T1T3T1=P3P1T3T1=P2P1T3T1=rk

Substitute rk for T3T1 and r for T3T2, 1rk1 for T1T2, and Rk1 for cv in Equation (III).

wcompwexp=Rk1R(1rk1)(rk)1(r)1=1k1(1rk1)(rk)1(r)1

Thus, the expression for the back work ratio as a function of k and r is 1k11rk1rk1r1_.

(c)

To determine

The expression for the cycle thermal efficiency as a function of k and r.

(c)

Expert Solution
Check Mark

Answer to Problem 180RP

The expression for the cycle thermal efficiency as a function of k and r is 11k1rk1rk1r1.

Explanation of Solution

Express out the heat addition and heat rejection in the process using first law to the closed system for processes 2-3 and 3-1.

qin=cp(T3T2)

qout=cv(T3T1)

Here, constant pressure specific heat is cp.

Express the cycle thermal efficiency.

ηth=1qoutqin (IV)

Conclusion:

Substitute cp(T3T2) for qin and cv(T3T1) for qout in Equation (IV).

ηth=1cv(T3T1)cp(T3T2)=11kT1(T3/T11)T2(T3/T21)

Substitute rk1 for T3T1, r for T3T2, and 1rk1 for T1T2.

ηth=1cv(T3T1)cp(T3T2)=11k1rk1(rk1)(r1)

Thus, the expression for the cycle thermal efficiency as a function of k and r is 11k1rk1rk1r1.

(d)

To determine

The value of the back work ratio and thermal efficiency as r goes to unity.

(d)

Expert Solution
Check Mark

Answer to Problem 180RP

The value of the back work ratio and thermal efficiency as r goes to unity is 1_ and 0_.

Explanation of Solution

Recall the expression of back work ratio and apply the limits as r goes to infinity.

wcompwexp=1k1(1rk1)(rk1)1(r)1limr1wcompwexp=1k1{limr11rk1(rk1)1(r)1}limr1wcompwexp=1k1{limr1(rk1)1(rk)rk1}limr1wcompwexp=1k1{limr1(k1)rk2krk1(k1)rk2}

limr1wcompwexp=1k1{k1kk+1}=1k1{k11}=1

Thus, the value of the back work ratio as r goes to unity is 1_.

Recall the expression of cycle thermal efficiency and apply the limits as r goes to infinity.

ηth=11k1rk1rk1r1limr1ηth=11k{limr11rk1rk1r1}limr1ηth=11k{limr1rk1rkrk1}limr1ηth=11k{limr1krk1krk1(k1)rk2}

limr1ηth=11k{kkk+1}=11k{k1}=0

Thus, the value of the thermal efficiency as r goes to unity is 0_.

From the results of cycle thermal efficiency and back work ratio values of 0 and 1, it shows that no expansion and net work can be done whether you add heat to the system when there is no compression (r=1).

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An air-standard cycle with variable specific heats isexecuted in a closed system and is composed of the followingfour processes:1-2 Isentropic compression from 100 kPa and 228C to600 kPa2-3 v = constant heat addition to 1500 K3-4 Isentropic expansion to 100 kPa4-1 P = constant heat rejection to initial state(a) Show the cycle on P-v and T-s diagrams.(b) Calculate the net work output per unit mass.(c) Determine the thermal efficiency.
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Chapter 9 Solutions

CONNECT FOR THERMODYNAMICS: AN ENGINEERI

Ch. 9.12 - Prob. 11PCh. 9.12 - Can any ideal gas power cycle have a thermal...Ch. 9.12 - Prob. 13PCh. 9.12 - Prob. 14PCh. 9.12 - Prob. 15PCh. 9.12 - Prob. 16PCh. 9.12 - Prob. 17PCh. 9.12 - Prob. 18PCh. 9.12 - Prob. 19PCh. 9.12 - Repeat Prob. 919 using helium as the working...Ch. 9.12 - The thermal energy reservoirs of an ideal gas...Ch. 9.12 - Consider a Carnot cycle executed in a closed...Ch. 9.12 - Consider a Carnot cycle executed in a closed...Ch. 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 - 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 - Determine the mean effective pressure of an ideal...Ch. 9.12 - Reconsider Prob. 932E. Determine the rate of heat...Ch. 9.12 - An ideal Otto cycle has a compression ratio of 8....Ch. 9.12 - Prob. 36PCh. 9.12 - A spark-ignition engine has a compression ratio of...Ch. 9.12 - An ideal Otto cycle has a compression ratio of 7....Ch. 9.12 - Prob. 39PCh. 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 - Someone has suggested that the air-standard Otto...Ch. 9.12 - Repeat Prob. 942 when isentropic processes are...Ch. 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 - Prob. 55PCh. 9.12 - Prob. 56PCh. 9.12 - Prob. 57PCh. 9.12 - Repeat Prob. 957, but replace the isentropic...Ch. 9.12 - Prob. 60PCh. 9.12 - Prob. 61PCh. 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. 65PCh. 9.12 - Prob. 66PCh. 9.12 - Prob. 67PCh. 9.12 - An air-standard cycle, called the dual cycle, with...Ch. 9.12 - Prob. 69PCh. 9.12 - Prob. 70PCh. 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. 75PCh. 9.12 - Prob. 76PCh. 9.12 - Prob. 77PCh. 9.12 - Prob. 78PCh. 9.12 - Prob. 79PCh. 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 stationary gas-turbine power plant operates on a...Ch. 9.12 - A gas-turbine power plant operates on the simple...Ch. 9.12 - Prob. 87PCh. 9.12 - Prob. 88PCh. 9.12 - Repeat Prob. 988 when the isentropic efficiency of...Ch. 9.12 - Repeat Prob. 988 when the isentropic efficiency of...Ch. 9.12 - Repeat Prob. 988 when the isentropic efficiencies...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 - Repeat Prob. 993 for a pressure ratio of 15.Ch. 9.12 - A gas-turbine power plant operates on the simple...Ch. 9.12 - A simple ideal Brayton cycle uses argon as the...Ch. 9.12 - A gas-turbine power plant operates on a modified...Ch. 9.12 - A gas-turbine power plant operating on the simple...Ch. 9.12 - Prob. 99PCh. 9.12 - Prob. 100PCh. 9.12 - Prob. 101PCh. 9.12 - Prob. 102PCh. 9.12 - Prob. 103PCh. 9.12 - Prob. 104PCh. 9.12 - A gas turbine for an automobile is designed with a...Ch. 9.12 - Rework Prob. 9105 when the compressor isentropic...Ch. 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. 109PCh. 9.12 - Prob. 111PCh. 9.12 - A Brayton cycle with regeneration using air as the...Ch. 9.12 - Prob. 113PCh. 9.12 - Prob. 114PCh. 9.12 - Prob. 115PCh. 9.12 - Prob. 116PCh. 9.12 - Prob. 117PCh. 9.12 - Prob. 118PCh. 9.12 - Prob. 119PCh. 9.12 - Prob. 120PCh. 9.12 - A simple ideal Brayton cycle without regeneration...Ch. 9.12 - A simple ideal Brayton cycle is modified to...Ch. 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 - A gas turbine operates with a regenerator and two...Ch. 9.12 - Prob. 128PCh. 9.12 - Prob. 129PCh. 9.12 - Prob. 130PCh. 9.12 - Prob. 131PCh. 9.12 - Air at 7C enters a turbojet engine at a rate of 16...Ch. 9.12 - Prob. 133PCh. 9.12 - A turbojet is flying with a velocity of 900 ft/s...Ch. 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. 137PCh. 9.12 - Prob. 138PCh. 9.12 - Reconsider Prob. 9138E. How much change would...Ch. 9.12 - Consider an aircraft powered by a turbojet engine...Ch. 9.12 - An ideal Otto cycle has a compression ratio of 8....Ch. 9.12 - An air-standard Diesel cycle has a compression...Ch. 9.12 - Prob. 144PCh. 9.12 - Prob. 145PCh. 9.12 - Prob. 146PCh. 9.12 - Prob. 147PCh. 9.12 - A Brayton cycle with regeneration using air as the...Ch. 9.12 - Prob. 150PCh. 9.12 - A gas turbine operates with a regenerator and two...Ch. 9.12 - A gas-turbine power plant operates on the...Ch. 9.12 - Prob. 153PCh. 9.12 - An air-standard cycle with variable specific heats...Ch. 9.12 - Prob. 155RPCh. 9.12 - Prob. 156RPCh. 9.12 - Prob. 157RPCh. 9.12 - Prob. 158RPCh. 9.12 - Prob. 159RPCh. 9.12 - Prob. 160RPCh. 9.12 - Prob. 161RPCh. 9.12 - Consider an engine operating on the ideal Diesel...Ch. 9.12 - Repeat Prob. 9162 using argon as the working...Ch. 9.12 - Prob. 164RPCh. 9.12 - Prob. 165RPCh. 9.12 - Prob. 166RPCh. 9.12 - Prob. 167RPCh. 9.12 - Consider an ideal Stirling cycle using air as the...Ch. 9.12 - Prob. 169RPCh. 9.12 - Consider a simple ideal Brayton cycle with air as...Ch. 9.12 - Prob. 171RPCh. 9.12 - A Brayton cycle with a pressure ratio of 15...Ch. 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. 176RPCh. 9.12 - Prob. 177RPCh. 9.12 - Prob. 180RPCh. 9.12 - Prob. 181RPCh. 9.12 - Prob. 182RPCh. 9.12 - For specified limits for the maximum and minimum...Ch. 9.12 - A Carnot cycle operates between the temperature...Ch. 9.12 - Prob. 194FEPCh. 9.12 - Prob. 195FEPCh. 9.12 - Helium gas in an ideal Otto cycle is compressed...Ch. 9.12 - Prob. 197FEPCh. 9.12 - Prob. 198FEPCh. 9.12 - In an ideal Brayton cycle, air is compressed from...Ch. 9.12 - In an ideal Brayton cycle, air is compressed from...Ch. 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 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...
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