where V is the velocity of the system relative to the environment.

Transcription

1 Exergy Exergy is the theoretical limit for the wor potential that can be obtaed from a source or a system at a given state when teractg with a reference (environment) at a constant condition. A system is said to be the dead state when it is thermodynamic equilibrium with its environment. Unless otherwise stated, assume the dead state to be: P = atm and = 5 C A system delivers the maximum possible wor as it undergoes a ersible process from the specified itial state to the state of its environment (dead state). his represents the useful wor potential, or exergy, or availability. Exergy is a property of the system-environment combation (not the system alone). Exergy of Ketic Energy Ketic energy can be converted to wor entirely; thus: V x KE e J / g where V is the velocity of the system relative to the environment. Exergy of Potential Energy Potential energy is also a form of mechanical energy and can be converted to wor entirely; thus: Some Defitions x PE pe gz J / g Surroundgs wor: is the wor done by or agast the surroundgs durg a process. his wor cannot be recovered and utilized. For a cylder-piston assembly, one can write: surr P V V he difference between the actual wor and the surroundgs wor surr is called the useful u : u = surr = - P (V V ) Reversible or: is the max amount of useful wor that can be produced (or the m wor needs to be supplied) as the system undergoes a process between the itial and fal states. hen the fal state is the dead state, the ersible wor equals exergy. Irersibility: I is equal to the exergy destroyed; thus for a ersible process the irersibility or exergy destruction is zero. I =, u, M. Bahrami ENSC 46 (S ) Exergy

2 or, I = u,, Example A 5-g iron bloc is itially at C and is allowed to cool to 7 C by transferrg heat to the surroundgs air at 7 C. Determe the ersible wor and the irersibility for this process. Assumption: ) the etic potential energies are negligible. ) the process volves no wor teractions. Analysis: he ersible wor is determed by considerg a series of imagary ersible heat enges operatg between the source (at a variable temperature ) and the s. th, Q Q Q Usg the first law for the iron bloc, a relationship for the heat transfer can be found: Q then Q du mc mc he ersible net wor is determed to be: ave ave ave 89 ave d ave mc d mc mc ln J Note that the first term the above equation, mc ave ( ) = 38,95 J, is the total heat transfer from the iron bloc to the enge. his means that only % of the heat transferred from the iron bloc could have been converted to wor. he irersibility for the process is determed from: I = u = 89 = 89 J he entire wor potential is wasted. he Second Law Efficiency he second law efficiency, η is the ratio of actual thermal efficiency to the maximum possible (ersible) thermal efficiency under the same conditions: d M. Bahrami ENSC 46 (S ) Exergy

3 th th, u Exergy recovered Exergy supplied Exergy destroyed Exergy supplied u heat enges or - producg devices or - consumg devices refrigerators and heat pumps COP COP he second law efficiency serves as a measure of approximation to ersible operation; thus its value should range from to. s, = 6 K s, = K net, HEA ENGINE η th = 35% HEA ENGINE η th = 35% net, η = 5% η = 7% η = 73% η = 48% S = 3K Exergy of A Fixed Mass Consider a stationary cylder-piston assembly that contas a fluid of mass m at, P, U, and S. he system is allowed to undergo a differential change. he energy balance for the system durg this differential process can be expressed as: he system volves some boundary wor: Q du () P P dv P dv P dv PdV () b, useful For a system, which is at temperature, to have a ersible heat transfer with the surroundgs at, heat transfer must occur through a ersible heat enge (η th = L / H ). For the ersible heat enge, one can write: M. Bahrami ENSC 46 (S ) Exergy 3

4 Q Q Q For a ersible process, we have; HE HE Q Q HE ds ds 3 ds Q ; thus : P P δ b, useful P δq Heat enge δ HE Usg Eqs. (), (), and (3); one can fd:, useful HE b, useful du P dv ds total Integratg from itial state to dead state gives: U U P V V S total, useful S where total,useful is the total useful wor delivered as the system undergoes a ersible process from the given state to the dead state which is the exergy of the system. otal exergy for a closed system cludg the potential and etic energies can be written as: V U U P V V S S m mgz on a unit mass basis, the closed system exergy is : V u - u P v v s s gz where subscript denotes the state of the system at the dead state. M. Bahrami ENSC 46 (S ) Exergy 4

5 Exergy of a Flow Stream A flowg fluid has flow energy; that is the energy needed to mata flow a pipe or le; w flow = Pv he flow wor is the boundary wor done by a fluid on the fluid downstream. he exergy associated with flow energy can be written as x flow = PV P V = (P P ) V he exergy of a flow stream can be found from: x flowg fluid = x nonflowg fluid + x flow x flowg fluid =(u u ) + P (V V ) (s s ) + V / +gz + (P - P )V where V is the velocity of the system and V is the volume. x flowg fluid = (u + PV) ( u P V ) (s s ) + V / +gz x flowg fluid = ψ = (h h ) (s s ) + V / +gz he flow exergy is represented by symbol ψ. Exergy by Heat ransfer Heat is a form of disorganized energy, thus only a portion of it can be converted to wor. Heat transfer Q at a location at thermodynamic temperature is accompanied by exergy transfer: heat Q J If the temperature of the heat source is changg with time, use: heat Q J Exergy ransfer by or surr for boundary wor wor for other forms of wor where surr = P (V V ). herefore the exergy transfer with wor such as shaft wor and electrical wor is equal to the wor. Note that the wor done or agast atmosphere is not available for any useful purpose, and should be excluded from available wor. he Decrease of Exergy Prciple Entropy and exergy for an isolated closed system can be related through an energy balance and entropy balance as follows: M. Bahrami ENSC 46 (S ) Exergy 5

6 ) Energy balance: E E = E = E E () ) Entropy balance: S S + S gen = S system S gen = S S () Multiplyg Eq. () by and subtractg it from Eq. (), one fds: - S gen = E E (S S ) For a closed system, we now that: E E P V V S S sce V = V for an isolated system. Combg these two equations gives: - S gen = Sce is a positive value, we have: isolated = ( ) isolated he exergy of an isolated system durg a process always decreases or, the limitg case of a ersible process, remas constant. Irersibilities such as friction, mixg, chemical reaction, heat transfer, unrestraed expansion always generate entropy (or destroy exergy). destroyed = S gen Exergy destruction cannot be negative. he decrease of exergy prciple can also be expressed as: destroyed Irersible process Reversible process Impossible process Exergy Balance: Closed System destroyed = system where; destroyed = S gen For a closed system that does not volve any mass flow. he exergy balance can be written as: or the rate form: P V V S Q gen Q P dv system gen S d system M. Bahrami ENSC 46 (S ) Exergy 6

7 Exergy Balance: Control Volumes Exergy balance relations for control volumes volve mass flow across the boundaries. he general exergy balance relationship can be expressed as: heat wor + mass, mass, destroyed = ( ) CV Or, Q the rate form: dvcv d Q P m m destroyed P V V m m destroyed CV where the itial and fal states of the control volume are specified, the exergy change of the control volume is: m m Steady-flow devices such as: turbes, compressors, nozzles, diffusers, heat exchangers, pipes, and ducts do not experience no changes their mass, energy, entropy, and exergy content as well as their volumes. herefore: and hus, one can write: Q dv CV / = d CV / = m m destroyed CV M. Bahrami ENSC 46 (S ) Exergy 7