MECH 230 – Thermodynamics 1 Final Workbook Solutions CREATED BY JUSTIN BONAL MECH 230 Final Exam Workbook Contents 1.0 General Knowledge ........................................................................................................................... 1 1.1 Unit Analysis .................................................................................................................................. 1 1.2 Pressure ......................................................................................................................................... 1 2.0 Energies ............................................................................................................................................ 2 2.1 Work .............................................................................................................................................. 2 2.2 Internal Energy .............................................................................................................................. 3 2.3 Heat ............................................................................................................................................... 3 2.4 First Law of Thermodynamics ....................................................................................................... 3 3.0 Ideal gas ............................................................................................................................................ 4 3.1 Universal Gas Constant .................................................................................................................. 4 3.2 Polytropic Work Using Ideal Gas .................................................................................................... 4 4.0 Specific Heat ..................................................................................................................................... 5 4.1 Constant Volume Heat Addition .................................................................................................... 5 4.2 Constant Pressure Heat Addition .................................................................................................. 6 4.3 Relating cv and cp for an Ideal Gas................................................................................................... 6 5.0 Control Volume (CV) Analysis ............................................................................................................ 8 5.1 Mass Flow Rate .............................................................................................................................. 8 5.2 Conservation of Energy with CV .............................................................................................. 8 6.0 Applications of CV ....................................................................................................................... 9 6.1 Nozzles and Diffusers .............................................................................................................. 9 6.2 Turbine .................................................................................................................................... 9 6.3 Compressor/Pump ................................................................................................................. 10 6.4 Throttling Device ................................................................................................................... 11 6.5 Heat Exchangers .................................................................................................................... 11 7.0 Second Law of Thermodynamics ..................................................................................................... 12 7.1 Efficiencies ................................................................................................................................... 12 7.2 Reversible and Irreversible Processes........................................................................................... 12 7.3 Entropy ........................................................................................................................................ 13 7.3.1 Entropy Change for Ideal Gas ................................................................................................ 13 7.3.2 Isentropic Processes for Ideal Gas ......................................................................................... 14 8.5 Control Volume Entropy Balance ................................................................................................. 15 8.5.1 Isentropic Efficiencies of Turbines and Compressors ............................................................. 15 i MECH 230 Final Exam Workbook 8.5.2 Internally Reversible Steady-State Flow Work .......................................................................... 16 9.0 The Rankine Cycle ........................................................................................................................... 18 9.1 Steps ........................................................................................................................................... 18 9.1 Thermal Efficiency ................................................................................................................. 19 9.2 Back Work Ratio .................................................................................................................... 20 9.3 Ideal Rankine Cycle ................................................................................................................ 20 9.4 Increasing Thermal Efficiency ................................................................................................ 21 10.0 Gas Powered Cycles .................................................................................................................. 22 10.1 General Engine Knowledge ........................................................................................................ 23 10.2 Air Standard Otto Cycle ......................................................................................................... 23 10.2.1 Otto Cycle Thermal Efficiency ............................................................................................. 24 10.2.2 Cold Air Standard Analysis Efficiency for Otto Cycle ........................................................... 25 10.2 Air Standard Diesel Cycle ....................................................................................................... 27 10.2.1 Diesel Cycle Thermal Efficiency ..................................................................................... 28 10.2.2 Cold Air-Standard Analysis for Diesel Cycle ................................................................... 29 11.0 Gas Turbine Power Plants .............................................................................................................. 31 11.1 Air Standard Brayton Cycle ........................................................................................................ 31 11.1.1 Ideal Air Standard Brayton Cycle ......................................................................................... 32 11.1.2 Ideal Cold Air-Standard Brayton Cycle................................................................................. 32 11.1.3 Increasing Cycle Efficiency ................................................................................................... 33 11.2 Aircraft Gas Turbines ................................................................................................................. 35 References ............................................................................................................................................ 39 List of Figures Figure 1: A useful way to conceptualize measuring pressures[1] ............................................................. 1 Figure 2: Example of a manometer [https://www.researchgate.net/figure/Fig3-9-Simple-U-tube- manometer_fig2_318378486] ................................................................................................................. 2 Figure 3: A schematic of a nozzle and diffuser ......................................................................................... 9 Figure 4: A schematic of a turbine ......................................................................................................... 10 Figure 5: A schematic of a pump ........................................................................................................... 10 Figure 6: A schematic of a throttling device .......................................................................................... 11 Figure 7: A schematic of a tube-in-tube heat exchanger ........................................................................ 11 Figure 8: Ts and hs diagrams of an isentropic expansion versus real expansion ..................................... 15 Figure 9: Ts and hs diagrams of an isentropic compression versus real compression ............................. 16 Figure 10: Schematic of the Basic Rankine Cycle ................................................................................... 19 ii MECH 230 Final Exam Workbook Figure 11: Schematic for the ideal Rankine Cycle. Since the cycle is ideal, processes 1->2 and 3->4 are vertical (no change in entropy) .............................................................................................................. 20 Figure 12: Schematic of the Rankine Cycle with reheat, along with the Ts diagram of the ideal cycle ... 21