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 53P

a)

To determine

The thermal efficiency of the diesel engine.

a)

Expert Solution
Check Mark

Explanation of Solution

Given:

Compression ratio (r) is 20.

Initial temperature of the cycle (T1) is 20°C.

Initial pressure of the cycle (P1) is 95kPa.

Maximum temperature of the cycle (T3) is 2200K.

Calculation:

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

Fundamentals of Thermal-Fluid Sciences, Chapter 9, Problem 53P

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

  R=0.287kJ/kgK

Refer table A-21, “Ideal gas properties of the air”, obtain the enthalpy and relative specific volume of air at the temperature of 293K .

  u1=209.06kJ/kgvr1=659.2

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

  vr2=V2V1vr1

  vr2=1rvr1=120(659.2)=32.96

Refer table A-21, “Ideal gas properties of the air”, obtain the temperature and enthalpy of air at the relative specific volume of 32.96.

  T2=912.7Kh2=947.17kJ/kg

Calculate the cut-off ratio (rc).

  P3v3T3=P2v2T2

  T3=v3v2T2=(rc)T2

  rc=T3T2=2200K912.7K=1.854

Refer table A-21, “Ideal gas properties of the air”, obtain the internal energy and enthalpy of air at the temperature of 2200K.

  u3=1872.4kJ/kgh3=2503.2kJ/kg

Calculate the heat addition in the constant pressure heat addition process 2-3(qin).

  qin=h3h2=2503.2kJ/kg941.17kJ/kg=1556kJ/kgK

Calculate the temperature at state 4(T4).

  T4=T3(V3V4)n1=T3(2.410V2V4)n1=T3(2.410r)n1

  =(2200K)(2.41020)1.351=1049K

Calculate the work output for the polytrophic process 3-4(w34,out).

  w34,out=R(T4T3)1n=(0.287kJ/kgK)(1049K2200K)11.35=943.8kJ/kg

Calculate the heat rejected for the polytrophic process 3-4(q34,out).

  q34,out=w34,out(u4u3)=(943.8kJ/kg)(801.13kJ/kg1872.4kJ/kg)=127.5kJ/kg

Calculate the heat rejected by the constant volume heat rejection process 4-1(q41,out).

  q41,out=u4u1=801.13kJ/kg209.06kJ/kg=592.1kJ/kg

Calculate the total heat rejected by the cycle (qout).

  qout=q34,out+q41,out=127.5kJ/kg+592.1kJ/kg=719.6kJ/kg

Calculate the thermal efficiency of the diesel engine (ηth).

  ηth=1qoutqin=1719.6kJ/kg1556kJ/kgK=0.5375=53.75%

Thus, the thermal efficiency of the diesel engine is 63.5%.

b)

To determine

The mean effective pressure.

b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the specific volume at state 1(v1).

  v1=RT1P1=(0.287kPam3/kgK)(293K)95kPa=0.885m3/kg

Calculate the mean effective pressure (MEP).

  MEP=wnet,outv1v2=qinqoutv1(11/r)=1556kJ/kgK719.6kJ/kgK(0.885m3/kg)(11/20)

  =836.4kJ/kgK(0.885m3/kg)(11/20)(kPam3kJ)=995kPa

Thus, the mean effective pressure is 933kPa.

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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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