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
Question
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Chapter 9, Problem 57P
To determine

The cycle’s net specific work, the specific heat addition and the thermal efficiency.

Expert Solution & Answer
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Explanation of Solution

Given:

Compression ratio (r) is 15.

Cut off ratio (rc) is 1.4.

Pressure ratio (rp) is 1.1.

Temperature of air at state 1(T1) is 75°F.

Pressure of air at state 1(P1) is 14.2psia.

Calculation:

Draw the Pv diagram of the cycle as in Figure (1).

Fundamentals of Thermal-Fluid Sciences, Chapter 9, Problem 57P

Refer Table A-2E, “Ideal-gas specific heats of various common gases”, obtain the following properties of the air.

  R=0.37047psiaft3/lbmRcv=0.240Btu/lbmRcp=0.171Btu/lbmRk=1.4

Calculate the temperature at state 2(T2).

  T2=T1(v1v2)k1=T1(r)k1=(535R)(15)1.41=1580R

Calculate the pressure at state 2(P2).

  P2=P1(v1v2)k=P1(r)k=(14.2psia)(15)1.4=629.2psia

Calculate the pressure at state x(Px).

  Px=P3=rpP2=(1.1)(629.2psia)=692.1psia

Calculate the temperature at state x(Tx).

  Tx=T2(PxP2)=(1580R)(692.1psia629.2psia)=1738R

Calculate the temperature at state 3(T3).

  T3=Tx(v3vx)=Tx(rc)=(1738R)(1.4)=2433R

Calculate the temperature at state 4(T4).

  T4=T3(v3v4)k1=T3(rcr)k1=(2433R)(1.415)1.41=942.2R

Calculate the amount of work during the process 1-2(w12).

  w12=cv(T2T1)=(0.171Btu/lbmR)(1580R535R)=178.7Btu/lbm

Calculate the amount of heat during the process 2-x(q2x).

  q2x=cv(TxT2)=(0.171Btu/lbmR)(1738R1580R)=27.02Btu/lbm

Calculate the amount of heat during the process x-3(qx3).

  qx3=cp(T3Tx)=(0.240Btu/lbmR)(2433R1738R)=166.8Btu/lbm

Calculate the amount of work during the process x-3(wx3).

  wx3=qx3cv(T3Tx)=166.8Btu/lbm(0.171Btu/lbmR)(2433R1738R)=47.96Btu/lbm

Calculate the amount of work during the process 3-4(w34).

  w34=cv(T3T4)=(0.171Btu/lbmR)(2433R942.2R)=254.9Btu/lbm

Calculate the cycle’s net specific work (wnet).

  wnet=w34+wx3w12=254.9Btu/lbm+47.96Btu/lbm178.7Btu/lbm=124.2Btu/lbm

Thus, the cycle’s net specific work is 124.2Btu/lbm.

Calculate the specific heat addition (qin).

  qin=q2x+qx3=27.02Btu/lbm+166.8Btu/lbm=193.8Btu/lbm

Thus, the specific heat addition is 193.8Btu/lbm.

Calculate the thermal efficiency of the cycle (ηth).

  ηth=wnetqin=124.2Btu/lbm193.8Btu/lbm=0.641=64.1%

Thus, the thermal efficiency of the cycle is 64.1%.

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Chapter 9 Solutions

Fundamentals of Thermal-Fluid Sciences

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