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 172RQ

a)

To determine

The maximum temperature and pressure during the cycle.

a)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Draw the Pν for an ideal Otto cycle as shown in Figure 1.

Fundamentals of Thermal-Fluid Sciences, Chapter 9, Problem 172RQ

Calculate the clearance volume of one cylinder.

  r=Vc+Vd/4Vc11=Vc+1.8L4Vc11=Vc+1.8L(1m31000L)4VcVc=V2=0.000045m3

Calculate the volume at state 1.

  V1=Vc+Vd4=0.000045m3+1.8L4=0.000045m3+1.8L4(1m31000L)=0.000495m3

Calculate the mass of the air.

  P1V1=mRT1m=P1V1RT1=90kPa×0.000495m30.287kPam3/kgK×50°C=90kPa×0.000495m30.287kPam3/kgK×(50+273)K=0.0004805kg

The properties at during process 1-2 are as follows:

  T1=50°C=323Ku1=230.88kJ/kgT1=50°C=323KP1=90kPa}s1=5.8100kJ/kgK

  v1=V1m=0.000495m30.0004805kg=1.0302m3/kgV2=Vc=0.000045m3v2=V2m=0.000045m30.0004805kg=0.09364m3/kg

  s2=s1=5.8100kJ/kg.Kv2=0.09364m3/kg}T2=807.3KT2=807.3Ku2=598.33kJ/kgP2=P1V1V2T2T1P2=(90kPa)(0.000495m30.000045m3)(807.3K323K)P2=2474kPa

During process 2-3:

  Qin=m(u3u2)1.5kJ=(0.0004805kg)(u3598.33)kJ/kgu3=3719.8kJ/kg

  u2=598.33kJ/kgT3=4037KP3=P2(T3T2)=(2474kPa)(4037K807.3K)P3=12,375kPaT3=4037KP3=12,375kPa}s3=7.3218kJ/kgK

Thus, the maximum temperature and pressure during the cycle are 4037K and 12375 kPa respectively.

b)

To determine

The net work per cycle per cylinder and the thermal efficiency of the cycle.

b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

During process 3-4:

  s4=s3=7.3218kJ/kg.Kv4=v1=1.0302m3/kg}{T4=2028Ku4=1703.6kJ/kg

  P4=P3V3V4T4T3=(12,375kPa)(111)(2028K4037K)=565kPa

During process 4-1:

  Qout=m(u4u1)=(0.0004805kg)(1703.6230.88)kJ/kg=0.7077kJ

Calculate the net power output Wnet.

  Wnet=QinQoutWnet=1.5kJ0.7077kJ=0.792kJ

Thus, the net power output is 0.792kJ.

Calculate the thermal efficiency of the cycle (ηth).

  ηth=WnetQin=0.7921.5=0.528

Thus, the thermal efficiency is 0.528.

c)

To determine

The mean effective pressure of the cycle.

c)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the mean effective pressure for an ideal Otto cycle (MEP).

  MEP=Wnetv1v2=0.792kJ0.000495m30.000045m3=1761kPa

Thus, the mean effective pressure of the cycle is 1761kPa.

d)

To determine

The power output for an engine speed of 3000 rpm.

d)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the power produced by the engine (W˙net).

  W˙net=(ncyl×Wnet)n˙nrev=(4cylinder×0.792kJ/cylinder-cycle)3000rev/min2rev/cycle=(4cylinder×0.792kJ/cylinder-cycle)3000rev/min(1min60s)2rev/cycle=79.2kW

Thus, the power output for an engine speed of 3000 rpm is 79.2kW.

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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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