7 CHAPTER Exergy: A Measure of Work Potential

7-1 Irreversibility is the Difference Between Reversible Work and Actual Useful Work (fig. 7-9) © The McGraw-Hill Companies, Inc.,1998

7-2 Irreversible Heat Transfer Can be Made Reversible by a Reversible Heat Engine (Fig. 7-12)

Second Law of Efficiency 7-3 Second Law of Efficiency The second law of efficiency is a measure of the performance of a device relative to its performance under reversible conditions

The Second-Law Efficiency of All Reversible Devices is 100% 7-4 The Second-Law Efficiency of All Reversible Devices is 100% (Fig. 7-16)

7-5 The Work Potential or Exergy of Potential Energy Equals the Potential Energy Itself (Fig. 7-18)

The Exergy of a Specified Mass 7-6 The Exergy of a Specified Mass The exergy of a specified mass at a specified state is the useful work that can be produced as it undergoes a reversible process to the state of the environment (Fig. 7-19)

The Exergy of a Cold Medium 7-7 The Exergy of a Cold Medium (Fig. 7-20) The exergy of a cold medium is also a positive quantity since work can be produced by transferring heat to it

The Exergy of Flow of Work 7-8 The Exergy of Flow of Work The exergy of flow of work is the useful work that would be deliverd by an imaginary piston in the flow section (Fig. 7-21)

7-9 The Exergy of Enthalpy The exergy of enthalpy is the sum of the exergies of the internal energy and flow energy (Fig. 7-22)

7-10 The Energy and Exergy contents of (a) a Fixed Mass and (b) a Fluid System (Fig. 7-23)

The Transfer and Destruction of Exergy During Heat Transfer 7-11 The Transfer and Destruction of Exergy During Heat Transfer The transfer and destruction of exergy during a heat transfer process through a finite temperature difference (Fig. 7-27)

Mechanisms of Exergy Transfer for a General System 7-12 Mechanisms of Exergy Transfer for a General System (Fig. 7-32)

7-13 Exergy Transferrence Exergy is transferred into or out of a control volume by mass as well as by heat and work transfer (Fig. 7-42)

7-14 Chapter Summary 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.

7-15 Chapter Summary 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.

7-16 Chapter Summary Reversible work Wrev is defined 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.

I = Xdestroyed = ToSgen = Wrev,out - Wu,out = Wu,in - Wrev,in 7-17 Chapter Summary 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 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. I = Xdestroyed = ToSgen = Wrev,out - Wu,out = Wu,in - Wrev,in

7-18 Chapter Summary Exergy destroyed represents the lost work potential and is also called the wasted work or lost work.

7-19 Chapter Summary The second-law efficiency 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 for heat engines and other work-producing devices and for refrigerators, heat pumps, and other work-consuming devices.

Chapter Summary Exergy recovered Exergy destroyed 7-20 Chapter Summary In general, the second-law efficiency is expressed as Exergy recovered Exergy destroyed Exergy supplied Exergy supplied = = 1 -

Chapter Summary V2 2 The exergy of various forms of energy are 7-21 Chapter Summary The exergy of various forms of energy are V2 2 Exergy of kinetic energy: xke = ke = Exergy of potential energy: xpe = pe = gz Exergy of internal energy: xu = (u - uo) + Po(v - vo) - To(s - so) Exergy of flow energy: xpv = Pv - Pov = (P - Po)v Exergy of enthalpy: xh = (h - ho) - To(s - so)

7-22 Chapter Summary The exergies of a fixed mass (nonflow exergy) and of a flow stream are expressed as Nonflow exergy: Flow exergy:

7-23 Chapter Summary The exergy change of a fixed mass or fluid stream as it undergoes a process from state 1 to state 2 is given by

7-24 Chapter Summary Exergy can be transferred by heat, work, and mass flow, and exergy transfer accompanied by heat, work, and mass transfer are given by Exergy transfer by heat: Exergy transfer by work: Xwork = Exergy transfer by mass: W - Wsurr (for boundary work) W (for other forms of work

7-25 Chapter Summary 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 of exergy principle and is expressed as

7-26 Chapter Summary Exergy balance for any system undergoing any process can be expressed as General:

7-27 Chapter Summary Exergy balance for any system undergoing any process can be expressed as General, rate form:

Chapter Summary . . . (xin - xout) - xdestroyed = xsystem To T 7-28 Chapter Summary Exergy balance for any system undergoing any process can be expressed as General, unit-mass basis: (xin - xout) - xdestroyed = xsystem where . . To T Xheat = 1 - Q Xwork = Wuseful Xmass = m Xsystem - dXsystem / dt . For a reversible process, the exergy destruction term Xdestroyed drops out.

7-29 Chapter Summary 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 where the subscripts are i = inlet, e = exit, 1 = initial state, and 2 = final state of the system.