Exergy a Measure of Work Potential

Thermodynamics II Sciences/ Ch8 1 of 13 Dr. Nasser T. Ahmad

Ch 8 EXERGY: A MEASURE OF WORK POTENTIAL Objectives The objectives of Chapter 8 are to:

Examine the performance of engineering devices in light of the second law of thermodynamics.

Define exergy, which is the maximum useful work that could be obtained from the

system at a given state in a specified environment. Define reversible work, which is the maximum useful work that can be obtained as a system

undergoes a process between two specified states.

Define the exergy destruction, which is the wasted work potential during a process as a result of irreversibilities.

Define the second-law efficiency. Develop the exergy balance relation. Apply exergy balance to closed systems and control volumes.

81 Exergy: Work Potential of Energy

Exergy of kinetic energy:

xke = ke = V2 /2 (kJ/kg) (81)

Where V is the velocity in m/s of the system relative to the environment.

Exergy of potential energy:

xpe = pe = gz (kJ/kg) where g is the gravitational acceleration and z is the elevation of the system

relative to a reference level in the environment.

Example 81 Maximum Power Generation by a Wind Turbine A wind turbine with a 12-m-diameter rotor, as shown in Fig. 86, is to be installed at a location where the wind is blowing steadily at an average velocity of 10 m/s. Determine the maximum power

that can be generated by the wind turbine.


Solution:

Exergy = Maximum power =m

* (ke) = (1335 kg/s)(0.05 kJ/kg) = 66.8 kW

82 REVERSIBLE WORK AND IRREVERSIBILITY

Example 83 The Rate of Irreversibility of a Heat Engine A heat engine receives heat from a source at 1200 K at a rate of 500 kJ/s and rejects the waste heat

to a medium at 300 K. The power output of the heat engine is 180 kW.

Determine the reversible power and the irreversibility rate for this process.

Solution:

th,rev=1-300/1200=75 % Actual efficiency= 180/500= 0.36 = 36 %

Quiz on Sunday 13-10-2014 on Ch 8

83 SECOND-LAW EFFICIENCY, II

84 Exergy Change of a System : The expression is called flow (or stream) exergy


Example 88 Exergy Change during a Compression Process Refrigerant-134a is to be compressed from 0.14 MPa and -

10C to 0.8 MPa and 50C steadily by a compressor. Taking

the environment conditions to be T0= 20C and 95 kPa,

determine the exergy change of the refrigerant during this

process and the minimum work input that needs to be supplied

to the compressor per unit mass of the refrigerant.

The properties of the refrigerant at the inlet and the exit states are

85 EXERGY TRANSFER BY HEAT, WORK, AND MASS Exergy by Heat Transfer, Q

FIGURE 826 The Carnot efficiency c = 1 - T0 /T represents the fraction of the energy transferred from a heat source

at temperature T that can be converted to work in an environment at temperature T0.


This relation gives the exergy transfer accompanying heat transfer Q whether T is greater than or less than T0. When T

>T0, heat transfer to a system increases the exergy of that system and heat transfer from a system decreases it. But the opposite is true when T < T0. In this case, the heat transfer Q is the heat rejected to the cold medium (the waste heat), and

it should not be confused with the heat supplied by the environment at T0. The exergy transferred with heat is zero when T = T0 at the point of transfer.

FIGURE 827 The transfer and destruction of exergy during a heat transfer process through a finite temperature difference.


Exergy Transfer by Work, W

Exergy Transfer by Mass, m

Therefore, the exergy of a system increases by mc when mass in the amount of m enters, and decreases by the same

amount when the same amount of mass at the same state leaves the system (Fig. 829). Exergy flow associated with a fluid stream when the fluid properties are variable can be determined by integration from

where Ac is the cross-sectional area of the flow and Vn is the local velocity normal to dAc. Note that exergy transfer by heat Xheat is zero for adiabatic systems, and the exergy transfer by mass Xmass is zero for

systems that involve no mass flow across their boundaries (i.e., closed systems).

The total exergy transfer is zero for isolated systems since they involve no heat, work, or mass transfer.

FIGURE 829 Mass contains energy, entropy, and exergy, and thus mass flow into or out of a system is accompanied by energy, entropy, and exergy transfer.

86 THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION Exergy Destruction

Irreversibilities such as friction, mixing, chemical reactions, heat transfer through a

finite temperature difference, unrestrained expansion, nonquasiequilibrium

compression or expansion always generate entropy, and anything that generates

entropy always destroys exergy.

The exergy destroyed is proportional to the entropy generated, as can be seen from

Eq. 831, and is expressed as


FIGURE 831 The exergy change of a system can be negative, but the exergy destruction cannot.

Tuesday 30-09-2014

87 EXERGY BALANCE: CLOSED SYSTEMS

FIGURE 832 Mechanisms of exergy transfer.

EXAMPLE 811 Exergy Destruction during Expansion of Steam A pistoncylinder device contains 0.05 kg of steam at 1 MPa and 300C. Steam now expands to a final state of 200 kPa and 150C, doing work. Heat losses from the system to the surroundings are estimated to be 2 kJ during this process. Assuming the surroundings to be at T0 = 25C and P0 =100 kPa, determine (a) the exergy of the steam at the initial and the final states, (b) the exergy change of the steam, (c) the exergy destroyed, and (d) the second-law efficiency for the process.


88 EXERGY BALANCE: CONTROL VOLUMES

FIGURE 842 Exergy is transferred into or out of a control volume by mass as well as heat and work

transfer.

EXAMPLE 815 Second-Law Analysis of a Steam Turbine Steam enters a turbine steadily at 3 MPa and 450C at a rate of 8 kg/s and exits at 0.2 MPa and 150C, (Fig. 845). The steam is losing heat to the surrounding air at 100 kPa and 25C at a rate of 300 kW, and the kinetic and potential energy changes are negligible. Determine (a) the actual power output, (b) the maximum possible power output, (c) the second-law efficiency, (d) the exergy destroyed, and (e) the exergy of the steam at the inlet conditions.


Quiz on Ch 8 on Sunday 12-10-2014

Recommended Problems 836 An insulated pistoncylinder device contains 2 L of saturated liquid water at a constant pressure of 150 kPa. An

electric resistance heater inside the cylinder is turned on, and

electrical work is done on the water in the amount of 2200 kJ.


Assuming the surroundings to be at 25C and 100 kPa, determine

(a) the minimum work with which this process could be

accomplished and (b) the exergy destroyed during this

process. Answers: (a) 437.7 kJ, (b) 1705 kJ

Exergy a Measure of Work Potential

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