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 168RQ

a)

To determine

The thermal efficiency of the cycle using the constant specific heats at room temperature.

a)

Expert Solution
Check Mark

Explanation of Solution

Given:

Compression ratio (r) is 20.

Temperature of air at state 1(T1) is 45°F.

Temperature of air at state 3(T3) is 1800°F.

Pressure of air at state 1(P1) is 13 psia.

Calculation:

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

Fundamentals of Thermal-Fluid Sciences, Chapter 9, Problem 168RQ

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

cp=0.240Btu/lbmRcv=0.171Btu/lbmRk=1.4

Calculate the temperature at state 2(T2).

T2=T1(r)k1=(45°F)(20)1.41=(45+460R)(20)1.41=1673.8R

Calculate the ratio between the volumes at state 3 and state 2(V3V2).

V3V2=T3T2=2260R1673.8R=1.350

Calculate the temperature at state 4(T4).

T4=T3(V3V4)k1=T3(1.350V2V4)k1

=T3(1.350r)k1=(2260R)(1.35020)1.41=768.8R

Calculate the net specific work produced by the cycle (wnet).

wnet=qinqout=cp(T3T2)cv(T4T1)={(0.240Btu/lbmR)(2260R1673.8R)(0.171Btu/lbmR)(768.8R505R)}=95.59Btu/lbm

=(0.240Btu/lbmR)(1460R717.8R+480R976.3R)=59Btu/lbm

Calculate the thermal efficiency of the cycle (ηth).

ηth=wnetqin=wnetcp(T3T2)=95.59Btu/lbm(0.240Btu/lbmR)(2260R1673.8R)

=95.59Btu/lbm140.7Btu/lbm=0.6794=67.9%

Thus, the thermal efficiency of the cycle using the constant specific heats at room temperature is 67.9%.

b)

To determine

The thermal efficiency of the cycle using the variable specific heats.

b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Refer table A-21E, “Ideal gas properties of the air”, obtain the specific internal energy and relative specific volume of air at the temperature of 505R.

u1=86.06Btu/lbmvr1=170.52

Calculate the relative specific volume at state 2(vr2).

vr2=v2v1vr1=(1r)vr1=(120)(170.82)=8.541

Refer table A-21E, “Ideal gas properties of the air”, obtain the specific enthalpy and temperature of air at the relative pressure of 8.541.

h2=391.01Btu/lbmT2=1582.3R

Refer table A-21E, “Ideal gas properties of the air”, obtain the specific enthalpy and relative specific volume of air at the temperature of 2260R.

h3=577.52Btu/lbmvr3=2.922

Calculate the ratio between the specific volumes at state 3 and state 2(v3v2).

v3v2=T3T2=2260R1582.3R=1.428

Calculate the relative specific volume at state 4(vr4).

vr4=v4v3vr3=(v41.428v2)vr3=(r1.428)vr3

=(201.428)(2.922)=40.92

Refer table A-21E, “Ideal gas properties of the air”, obtain the specific internal energy of air at the relative specific volume of 40.92.

u4=152.62Btu/lbm

Calculate the thermal efficiency of the cycle (ηth).

ηth=1qoutqin=1u4u1h3h2

=1(152.65Btu/lbm86.06Btu/lbm)(577.52Btu/lbm391.01Btu/lbm)=0.643=64.3%

Thus, the thermal efficiency of the cycle using the variable specific heats is 64.3%.

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Chapter 9 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Prob. 15PCh. 9 - Prob. 16PCh. 9 - Prob. 17PCh. 9 - Prob. 18PCh. 9 - Prob. 19PCh. 9 - Prob. 20PCh. 9 - Prob. 21PCh. 9 - Prob. 22PCh. 9 - Prob. 23PCh. 9 - Prob. 24PCh. 9 - Prob. 25PCh. 9 - Prob. 26PCh. 9 - Prob. 27PCh. 9 - Prob. 28PCh. 9 - Prob. 29PCh. 9 - Prob. 30PCh. 9 - Prob. 31PCh. 9 - Prob. 33PCh. 9 - Prob. 34PCh. 9 - Prob. 35PCh. 9 - Prob. 36PCh. 9 - Prob. 37PCh. 9 - Prob. 38PCh. 9 - Prob. 39PCh. 9 - Prob. 40PCh. 9 - Prob. 41PCh. 9 - Prob. 42PCh. 9 - Prob. 43PCh. 9 - Prob. 44PCh. 9 - Prob. 45PCh. 9 - Prob. 46PCh. 9 - Prob. 47PCh. 9 - Prob. 48PCh. 9 - Prob. 49PCh. 9 - Prob. 50PCh. 9 - Prob. 51PCh. 9 - Prob. 52PCh. 9 - Prob. 53PCh. 9 - Prob. 55PCh. 9 - Prob. 56PCh. 9 - Prob. 57PCh. 9 - Prob. 58PCh. 9 - Prob. 60PCh. 9 - Prob. 61PCh. 9 - Prob. 62PCh. 9 - Prob. 63PCh. 9 - Prob. 64PCh. 9 - Prob. 65PCh. 9 - Prob. 66PCh. 9 - Prob. 67PCh. 9 - A simple Brayton cycle using air as the working...Ch. 9 - Prob. 70PCh. 9 - Consider a simple Brayton cycle using air as the...Ch. 9 - Prob. 72PCh. 9 - Prob. 73PCh. 9 - Prob. 74PCh. 9 - A gas-turbine power plant operates on a simple...Ch. 9 - Prob. 77PCh. 9 - Prob. 78PCh. 9 - Prob. 79PCh. 9 - Prob. 80PCh. 9 - Prob. 81PCh. 9 - Prob. 82PCh. 9 - Prob. 83PCh. 9 - Prob. 84PCh. 9 - Prob. 85PCh. 9 - Prob. 86PCh. 9 - Prob. 87PCh. 9 - Prob. 89PCh. 9 - Prob. 90PCh. 9 - Prob. 91PCh. 9 - Prob. 92PCh. 9 - Prob. 93PCh. 9 - Prob. 94PCh. 9 - Prob. 95PCh. 9 - Prob. 96PCh. 9 - Prob. 97PCh. 9 - Prob. 98PCh. 9 - Prob. 99PCh. 9 - Prob. 100PCh. 9 - Prob. 101PCh. 9 - Prob. 102PCh. 9 - Prob. 103PCh. 9 - Prob. 104PCh. 9 - Prob. 105PCh. 9 - Prob. 106PCh. 9 - Prob. 107PCh. 9 - Refrigerant-134a is used as the working fluid in a...Ch. 9 - Prob. 109PCh. 9 - A simple ideal Rankine cycle with water as the...Ch. 9 - Prob. 111PCh. 9 - Prob. 112PCh. 9 - Prob. 113PCh. 9 - Prob. 114PCh. 9 - Prob. 115PCh. 9 - Prob. 116PCh. 9 - Prob. 117PCh. 9 - Prob. 119PCh. 9 - Prob. 120PCh. 9 - Prob. 121PCh. 9 - Prob. 122PCh. 9 - Prob. 123PCh. 9 - Prob. 124PCh. 9 - Prob. 125PCh. 9 - Prob. 127PCh. 9 - Prob. 128PCh. 9 - Prob. 129PCh. 9 - Prob. 130PCh. 9 - Prob. 131PCh. 9 - Prob. 132PCh. 9 - Why is the reversed Carnot cycle executed within...Ch. 9 - Prob. 134PCh. 9 - Prob. 135PCh. 9 - Refrigerant-134a enters the condenser of a...Ch. 9 - Prob. 137PCh. 9 - Prob. 138PCh. 9 - Prob. 139PCh. 9 - Prob. 140PCh. 9 - Prob. 141PCh. 9 - Prob. 142PCh. 9 - Prob. 143PCh. 9 - Prob. 144PCh. 9 - Prob. 145PCh. 9 - Prob. 146PCh. 9 - Prob. 148PCh. 9 - Prob. 149PCh. 9 - A commercial refrigerator with refrigerant-134a as...Ch. 9 - Prob. 151PCh. 9 - Prob. 153PCh. 9 - Prob. 154PCh. 9 - Prob. 155PCh. 9 - Prob. 156PCh. 9 - Prob. 157PCh. 9 - Prob. 158PCh. 9 - Prob. 159PCh. 9 - Refrigerant-134a enters the condenser of a...Ch. 9 - Prob. 161PCh. 9 - Prob. 162PCh. 9 - Prob. 164RQCh. 9 - Prob. 165RQCh. 9 - Prob. 166RQCh. 9 - Prob. 167RQCh. 9 - Prob. 168RQCh. 9 - A Brayton cycle with a pressure ratio of 12...Ch. 9 - Prob. 170RQCh. 9 - Prob. 171RQCh. 9 - Prob. 172RQCh. 9 - Prob. 173RQCh. 9 - Prob. 175RQCh. 9 - Prob. 176RQCh. 9 - Prob. 177RQCh. 9 - Prob. 178RQCh. 9 - Prob. 179RQCh. 9 - Prob. 180RQCh. 9 - Prob. 181RQCh. 9 - Prob. 182RQCh. 9 - Prob. 183RQCh. 9 - Prob. 184RQCh. 9 - Prob. 185RQCh. 9 - Prob. 186RQCh. 9 - A large refrigeration plant is to be maintained at...Ch. 9 - An air conditioner with refrigerant-134a as the...
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