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# Engineering Thermodynamics I MAE 301

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This 23 page Class Notes was uploaded by Rowan Spinka DVM on Thursday October 15, 2015. The Class Notes belongs to MAE 301 at North Carolina State University taught by Michael Boles in Fall. Since its upload, it has received 15 views. For similar materials see /class/224023/mae-301-north-carolina-state-university in Aerospace Engineering (AE) at North Carolina State University.

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Date Created: 10/15/15

Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 81 Chapter 8 Exergy A Measure of Work Potential The energy content of the universe is constant just as its mass content is Yet at times of crisis we are bombarded with speeches and articles on how to conserve energy As engineers we know that energy is already conserved What is not conserved is exergy which is the useful work potential of the energy Once the exergy is wasted it can never be recovered When we use energy to heat our homes for example we are not destroying any energy we are merely converting it to a less useful form a form of less exergy Exergy and the Dead State The useful work potential of a system is the amount of energy we extract as useful work The useful work potential of a system at the specified state is called exergy Exergy is a property and is associated with the state of the system and the environment A system that is in equilibrium with its surroundings has zero exergy and is said to be at the dead state The exergy of the thermal energy of thermal reservoirs is equivalent to the work output of a Carnot heat engine operating between the reservoir and the environment Exergy Forms Now let s determine the exergy of various forms of energy Exergy of kinetic energy Kinetic energy is a form of mechanical energy and can be converted directly into work Kinetic energy itself is the work potential or exergy of kinetic energy independent of the temperature and pressure of the environment Chapter 81 Student Study Guide for 5 edition ofThen nodynamics by Y A Qengel amp M A Boles 82 2 xke ke V kJkg Exergy of kinetic energy Exergy of potential energy Potential energy is a form of mechanical energy and can be converted directly into work Potential energy itself is the work potential or exergy of potential energy independent of the temperature and pressure of the environment Exergy of potential energy xpe pe g2 klkg Useful Work The work done by work producing deVices is not always entirely in a useable form Consider the pistoncylinder deVice shown in the following gure Chapter 82 Student Study Guide for 5 edition ofThen nodynamics by Y A Qengel amp M A Boles 83 allhischil SHm The work done by the gas expanding in the pistoncylinder device is the boundary work and can be written as 6W PdVP PodVPodV 6Wbuseful R The actual work done by the gas is W VVbuse Jl busefulRI2I1 The word done on the surroundings is WmJadValtV2 Vgt Any useful work delivered by a pistoncylinder device is due to the pressure above the atmospheric level Wu Chapter 83 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 84 Reversible Work Reversible work Wrev is de ned as the maximum amount of useful work that can be produced or the minimum work that needs to be supplied as a system undergoes a process between the specified initial and final states This is the useful work output or input obtained when the process between the initial and final states is executed in a totally reversible manner Irreversibility The difference between the reversible work Wrev and the useful work Wu is due to the irreversibilities present during the process and is called the irreversibility I It is equivalent to the exergy destroyed and is expressed as IX W W destroyed TOSgen Wrevout u out u1n rev in where Sgen is the entropy generated during the process For a totally reversible process the useful and reversible work terms are identical and thus irreversibility is zero Irreversibility can be viewed as the wasted work potential or the lost opportunity to do work It represents the energy that could have been converted to work but was not Exergy destroyed represents the lost work potential and is also called the wasted work or lost work Chapter 84 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 85 SecondLaw Efficiency The secondlaw e cz ency is a measure of the performance of a device relative to the performance under reversible conditions for the same end states and is given by 77th W 77 H Um rev Wrev for heat engines and other workproducing devices and COP W ICV 77 COP W rev u for refrigerators heat pumps and other workconsuming devices In general the secondlaw efficiency is expressed as Exergy recovered 1 Exergy destroyed H Exergy supplied Exergy supplied Exergy of change of a system Consider heat transferred to or from a closed system Whenever there is a temperature difference across the system boundary The exergy for a Chapter 85 Student Study Guide for 5 edition ofThen nodynamics by Y A Qengel amp M A Boles 86 system may be determined by considering how much of this heat transfer is converted to work entirely Let s take a second look at the following gure Taking the heat transfer to be from the system to its surroundings the conservation of energy is 6Ein 6Eout dly lsystem 0 6Q 6W dU The work is the boundary work and can be written as 6W PdV 13 130anP0 dV 6Wb useful R Any useful work delivered by a pistoncylinder device is due to the pressure above the atmospheric level To assure the reversibility of the process the heat transfer occurs through a reversible heat engine Chapter 86 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 87 2 5Q 5WHE 77th5Q 1 T5Q 5Q To T dS 5Qnet T T 5WHE 5Q YgdS 5Q 5WHE T0dS 5WHE T0 dS 5W mm PO dV dU 5Vthal useful 5VVb useful dU RdVT0dS Integrating from the given state no subscript to the dead state 0 subscript we have VVtotaluseful U0 UUoPoVVoYBS So This is the total useful work due to a system undergoing a reversible process from a given state to the dead state which is the definition of exergy Including the kinetic energy and potential energy the exergy of a closed system is Chapter 87 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 88 V2 X U U0RV K YBS SOm7mgz on a unit mass basis the closed system or non ow exergy is V2 uu0RVV07bsso7gz eeoPoVV0T0SSO Here uo v0 and so are the properties of the system evaluated at the dead state Note that the exergy of the internal energy of a system is zero at the dead state is zero since u uo v v0 and s so at that state The exergy change of a closed system during a process is simply the difference between the final and initial exergies of the system A XVZAXz AXH177 2 1 EE0P0VVbbSSo V2V2 ZUU0POVVlT0SS0mmg22Zl On a unit mass basis the exergy change of a closed system is Chapter 88 Student Study Guide for 539h edition of Thermodynamics by Y A Qengel amp M A Boles 89 A 2 1 eeoPoVV0T0SSo V2I72 uu0RVV07bssogzzZ1 Exergyof ow The energy needed to force mass to ow into or out of a control volume is the ow work per unit mass given by see Chapter 3 w ow Pv Imaginary piston represents the uid downstream w shaft Atmospheric D air displaced PVP0VWSha The exergy of ow work is the excess of ow work done against atmospheric air at P0 to displace it by volume v According to the above gure the useful work potential due to ow work is Pv Pov w ow energy Thus the exergy of ow energy is Chapter 89 Student Study Guide for 53911 edition of Thermod namics by Y A Qengel amp M A Boles 810 Pv PovP Pov x ow energy Flow Exergy Since ow energy is the sum of non ow energy and the ow energy the exergy of ow is the sum of the exergies of non ow exergy and ow exergy x owing uid xnon owing uid x ow exergy a2 u um1v vogt 73lts sogtgzP 1w V2 uPvuo PovoToSSo7gZ V2 hhoTosSo7gZ The ow or stream exergy is given by V2 Whh0T0sso7gZ The exergy of ow can be negative if the pressure is lower than atmospheric pressure The exergy change of a uid stream as it undergoes a process from state 1 to state 2 is Chapter 810 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 8ll T2 V2 42 AWZW2l1hzhliszsiTgZ2Z1 Exergy Transfer by Heat Work and Mass Exergy can be transferred by heat work and mass ow and exergy transfer accompanied by heat work and mass transfer are given by the following Exergy transfer by heat transfer By the second law we know that only a portion of heat transfer at a temperature above the environment temperature can be converted into work The maximum useful work is produced from it by passing this heat transfer through a reversible heat engine The exergy transfer by heat is Exergy transfer heal Xheat Chapter 81 1 Student Study Guide for 5 edition ofThen nodynamics by Y A Qengel amp M A Boles 812 MEDIUM I MEDIIM 2 Wzill Ti 399 Q muster Entropy generated 1 bnlrupx g muster Ti desu mi 1 lxergy hamster gt gt I 5 1 ag T 71 itQ Note in the above figure that entropy generation is always by exergy destruction and that heat transfer Q at a location at temperature T is always accompanied by entropy transfer in the amount of QT and exergy transfer in the amount of lToDQ Note that exergy transfer by heat is zero for adiabatic systems Exergy transfer by work Exergy is the useful work potential and the exergy transfer by work can simply be expressed as W Wm for boundary work X Exergy transfer by work39 wmk W for other forms of work where W5 n PUUZ 41 P0 is atmospheric pressure and V1 and V2 are the initial and final volumes of the system The exergy transfer for shaft work and electrical work is equal to the work W itself Chapter 812 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 813 Note that exergy transfer by work is zero for systems that have no work Exergy transfer by mass Mass ow is a mechanism to transport exergy entropy and energy into or out of a system As mass in the amount n1 enters or leaves a system the exergy transfer is given by Exergy transfer by mass X mass 2 m W Note that exergy transfer by mass is zero for systems that involve no ow Chapter 813 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 814 The Decrease of Exergy Principle and Exergy Destruction The exergy of an isolated system during a process always decreases or in the limiting case of a reversible process remains constant This is known as the decrease ofexergy principle and is expressed as lt0 isolated AX isolated X2 X1 Exergy Destruction Irreversibilities such as friction mixing chemical reactions heat transfer through finite temperature difference unrestrained expansion nonquasi equilibrium compression or expansion always generate entropy and anything that generates entropy always destroys exergy The exergy destroyed is proportional to the entropy generated as expressed as X destroyed 2735 gen The decrease of exergy principle does not imply that the exergy of a system cannot increase The exergy change of a system can be positive or negative during a process but exergy destroyed cannot be negative The decrease of exergy principle can be summarized as follows gt 0 Irreversible proces X destroyed 0 Reversible process lt 0 Impossible process Chapter 814 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 815 Exergy Balances Exergy balance for any system undergoing any process can be expressed as Total Total Total Change in the exergy exergy exergy total exergy entering leaving destroyed of the system General X in X out X destroyed AX system Ef J f Net exergy transfer Exergy Change by heat work and mass destruction in exergy General rate form X in X out X destroyed AX system J Rate 0f net exergy tranSfer Rate of exergy Rate of change by heat work and mass destruction of exergy General unitmass basis xin Xout xdestroyed Ax system Where To X heat Q X work Wuseful X mass V AX system system Chapter 815 Student Study Guide for 53911 edition of Thermodynamics by Y A Cengel amp M A Boles 816 For a reversible process the exergy destruction term Xdestroyed is zero Considering the system to be a general control volume and taking the positive direction of heat transfer to be to the system and the positive direction of work transfer to be from the system the general exergy balance relations can be expressed more explicitly as T Vmelji Zmelje Xdestroyed 2X2 X1 k T dV dX W1307CVZmilIi Zmele Xdestroyed 27W where the subscripts are i inlet e exit 1 initial state and 2 final state of the system For closed systems no mass crosses the boundaries and we omit the terms containing the sum over the inlets and exits Example 81 Oxygen gas is compressed in a pistoncylinder device from an initial state of 08 m3kg and 25 C to a nal state of 01 m3kg and 287 C Determine the reversible work input and the increase in the exergy of the oxygen during this process Assume the surroundings to be at 25 C and 100 kPa We assume that oxygen is an ideal gas with constant specific heats From Table A2 R 02598 kJkgK The specific heat is determined at the average temperature T Z T 7 25287 C av 2 156 273K 2 429K 156 C Table A2b gives CV ave 0690 kJkgK Chapter 816 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles The entropy change of oxygen is s2 s1CV ave ln RlnV 2 T1 V1 01111 3 0690i1n 287273K 02508 k In kg kgK 25273K gK 08m kg 0105i kgK We calculate the reversible work input which represents the minimum work input Wme in this case from the exergy balance by setting the exergy destruction equal to zero 0 X in X out destroyed A system E f f Net exergy transfer Exergy Change by heat work and mass destruction in exergy VVrevin X2 X1 Therefore the change in exergy and the reversible work are identical in this case Substituting the closed system exergy relation the reversible work input during this process is determined to be Chapter 817 Student Study Guide for 53911 edition of Thermodynamics by Y A Cengel amp M A Boles 818 wrevin 2 1 M2 uiPoV2 V1TOS2 S1 CvaveT2 iPoV2 V1TOS2 S1 m3 H Em3kPa 0690i287 25K100kPa01 08 kgK 25 273K 0 105 i kg K 21421E kg The increase in exergy of the oxygen is k x2 x1 Z 2 l wrev in gt Example 82 Steam enters an adiabatic turbine at 6 MPa 600 C and 80 ms and leaves at 50 kPa 100 C and 140 ms The surroundings to the turbine are at 25 C If the power output of the turbine is 5MW determine a the power potential of the steam at its inlet conditions in MW b the reversible power in MW c the second law efficiency We assume steady ow and neglect changes in potential energy Chapter 81 8 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles V1 80 ms Steam turbine P1 6 MPa quot T1 600 C Wm 5 MW 2 V2 140 ms P2 50 kPa T2 100 C The mass ow rate of the steam is determined from the steady ow energy equation applied to the actual process Ein Eout systems 0 steady Rate of net energy transfer Rate of change by heat work and mass of energy V12 V22 quot110A m2h2 Wom 0 2 2 Conservation of mass for the steady ow gives min mout Anlsystem r Rate of net mass transfer Rate of change mass ml m20 m1m2m Chapter 819 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 820 The work done by the turbine and the mass ow rate are I I72 I72 W m L 2 out 2 2 mm m Ill h2 Ake Where 2 2 2 2 140 ms2 80ms2 lkJkg 2 1000 m252 66 kg Chapter 820 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 821 From the steam tables h1 36588 Pi 6MPa kg T1 2 600 C 12 71693i kg K I22 26824E P2 50kPa kg TZ ZIOOOC 76953i N Po 100kPa ho hf25 c 10433 kg To 25 C s0 2 SmC 03672k JK h h2 Ake 5 MW 1000 kJs 36588 26824 66E MW kg k 516 g S The power potential of the steam at the inlet conditions is equivalent to its exergy at the inlet state Recall that we neglect the potential energy of the ow Chapter 821 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 822 0 LI11771W12m h0T0S1SoigZ1 36588 10483 298K71693 03672l kg kg kgK T12516 2 s 80ms kJkg 2 1000m252 25161 g15333E 5 kg lOOOkJs 791MW The power output of the turbine if there are no irreversibilities is the reversible power and is determined from the rate form of the exergy balance applied on the turbine and setting the exergy destruction term equal to zero 0 0 steady X in X out X destroyed Asyzem Ef J Rate 0f net exergy tranSfef Rate of exergy Rate of change by heat work and mass destruction of exergy X in X out mwl Wrev out mWZ Wrev out mW2 W1 0 mlth h2gt lts s2gt AkeApej Chapter 822 Student Study Guide for 53911 edition of Thermodynamics by Y A Qengel amp M A Boles 36588 26824E 298K7 1693 76953i kg kgK Wrev0ut S 66 kg 2516k g11265E 5 kg IOOOkJs 581MW The secondlaw efficiency is detennined from NH KZMZEggm W 581MW 78V Chapter 823

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