E.T.D PATEL DARSHAN EXERGY

Topics:  Exergy of closed system  Irreversibility  Gouy-Stodola theorem  Second Law Efficiency

EXERGY:  “The useful work potential of the system at the specified state and is called exergy.”  It is important to realize that exergy does not represent the amount of work that a work-producing device will actually deliver upon installation.  Rather, it represents the upper limit on the amount of work a device can deliver without violating any thermodynamic laws.  For more understanding of exergy see this fig.

Exergy of closed system:  A system at a given state can attain a new state through work and heat interactions with its surroundings. Since the exergy value associated with the new state would generally differ from the value at the initial state, transfers of exergy across the system boundary can be inferred to accompany heat and work interactions.  The change in exergy of a system during a process would not necessarily equal the net exergy transferred, for exergy would be destroyed if irreversibilities were present within the system during the process.

 Exergy of a closed system, per unit mass j, can be found be adding all the terms  This gives us the maximum work we could possibly get out of a system.  Usually we will be more interested in the change in exergy from the beginning to end of a process.  Note that  = 0 at dead state.

 When properties are not uniform, exergy can be determined by integration:  Where V is the volume of the system and  is density.

 Note that exergy is a property, and the value of a property does not change unless the state changes.  If the state of system or the state of the environment do not change, the exergy does not change.  Therefore, the exergy change of a system is zero if the state of the system or the environment does not change during the process. For example, the exergy change of steady flow devices such as nozzles, compressors, turbines, pumps, and heat exchangers in a given environment is zero during steady operation.  The exergy of a closed system is either positive or zero. It is never negative.

Irreversibility:  It represents energy that could have been converted into work but was instead wasted  Difference between reversible work and useful work is called irreversibility  Irreversibility is equal to the exergy destroyed  Totally reversible process, I = 0  I, a positive quantity for actual, irreversible processes  To have high system efficiency, we want I to be as small as possible.

 (work output device, like a turbine) OR  (work input device, like a pump)  W u= useful work; the amount of work done that can actually be used for something desirable.  where W=actual work done.

Gouy-Stodola theorem:  We seen that,  The Gouy stodola theorem states that the rate of loss of exergy in a process is proportional to the rate of entropy generation,  This is known as the Gouy-stodola eqn. A thermody- namically efficient process would involve minimum exergy loss with minimum rate of entropy generation.

Second Law Efficiency  II  The first-law efficiency alone is not a realistic measure of performance of engineering devices. To overcome this deficiency, we define a second-law efficiency  II as the ratio of the actual thermal efficiency to the maximum possible (reversible) thermal efficiency.  For understand this point see this eg.

Eg.:  Consider two heat engines, both having a thermal efficiency of 30 percent as shown in Fig.  One of the engines (engine A) is supplied with heat from a source at 600 K, and the other one (engine B) from a source at 1000 K. Both engines reject heat to a medium at 300 K. At first glance, both engines seem to convert to work the same fraction of heat that they receive; thus they are performing equally well.  When we take a second look at these engines in light of the second law of thermodynamics, however, we see a totally different picture. These engines, at best, can perform as reversible engines, in which case their efficiencies would be

 Now it is becoming apparent that engine B has a greater work potential available to it (70 percent of the heat supplied as compared to 50 percent for engine A), and thus should do a lot better than engine A.  Therefore, we can say that engine B is performing poorly relative to engine A even though both have the same thermal efficiency.

 Based on definition of the second-law efficiencies,  Now for the two heat engines discussed above are:  That is, engine A is converting 60% of the available work potential to useful work. This ratio is only 43% for engine B.

 The second-law efficiency can also be expressed as the ratio of the useful work output and the maximum possible (reversible) work output:  This definition is more general since it can be applied to processes (in turbines, piston–cylinder devices, etc.) as well as to cycles.  Note that the second law efficiency cannot exceed 100%.

 We can also define a second-law efficiency for work- consuming noncyclic (such as compressors) and cyclic (such as refrigerators) devices as the ratio of the minimum (reversible) work input to the useful work input  For cyclic devices such as refrigerators and heat pumps, it can also be expressed in terms of the coefficients of performance as

 The general definition,

Reference:  Fundamentals of engineering thermodynamics (Moran J., Shapiro N.M. - 5th ed Wiley)  Thermodynamics An Engineering Approach 5th Edition - Yunus Cengel, Boles - Book  Thermodynamics by PK Nag