ExergyExergy

ExergyExergy

• The maximum amount of The maximum amount of work that can be extracted work that can be extracted from a system at a given state from a system at a given state in a specified environment.in a specified environment.• Also called:Also called:–AvailabilityAvailability–Available energyAvailable energy–Work potentialWork potential

ExergyExergy

• The maximum useful work The maximum useful work that can be obtained from a that can be obtained from a system.system.• All irreversibilities are All irreversibilities are

disregarded in finding exergydisregarded in finding exergy• System must be at a dead state System must be at a dead state

at the end of the process.at the end of the process.

In a dead state when at equilibrium with its environment.

Unless otherwise stated, the dead-state temp and pressureare those above.

Something already at its dead state has no potential for work.

The properties of a system at its dead state are denoted bysubscript 0.

Distinction must be made between surroundings, environment, and immediate surroundings.

The environment is free from any irreversibilities.

The atmosphere contains a tremendous amount of energy,but no exergy or work potential. Why?

ExergyExergy

• Not the amount of work a work Not the amount of work a work producing device will actually producing device will actually produce.produce.• It is the upper limit of workIt is the upper limit of work• Difference is room for Difference is room for

improvement.improvement.• Can increase exergy by changing Can increase exergy by changing

the environment, but not easy.the environment, but not easy.

The exergy of ke is the ke itself

The exergy of pe is the pe itself. xpe = pe = gz

Example 7-1 The work potential or exergy is the ke of the air.

Exergy of a furnace that can supply 3000 Btu’s/s at 2000 R isthe work that a reversible (Carnot) heat engine can producebetween 2000 R and the environment (77°F).

3000 Btu’s/s

2196 Btu’s/s

Unavailableenergy is theenergy that must be discarded.

Surroundings WorkSurroundings Work

• The work done by or The work done by or against the surroundings against the surroundings during a process.during a process.

Example – expanding piston – some of the work is Example – expanding piston – some of the work is done to push the atmosphere out of the way.done to push the atmosphere out of the way.

Wsurr = P0(V2 – V1) Useful work = Wu = W - Wsurr

If compressed,Wsurr representsa gain.

Surroundings work has no significance for cyclic and constantvolume devices.

Reversible WorkReversible Work

• The maximum amount of usable The maximum amount of usable work that can be produced when a work that can be produced when a system undergoes a process between system undergoes a process between specified initial and final states.specified initial and final states.

• How does this differ from exergy?How does this differ from exergy?• Why is this more useful in evaluating Why is this more useful in evaluating

a particular device?a particular device?• Equal to exergy when the final state Equal to exergy when the final state

equals the dead state.equals the dead state.

Irreversibility or I is the difference between reversible work andusable work. Always positive for an actual process.

Equivalent to exergydestroyed.

Can be viewed as thewasted work potentialor lost opportunity to do work.

Like reversible work,based on actual initialand final states, not dead state.

Example 7-3 Reversible Power and Rate of Irreversibility of aHeat Engine.

Wrev = ηth,revQin = (1-Tsink/Tsource)Qin

Wrev = 375 kW

I = Wrev,out – Wu,out = 195 kW

Is heat rejected, 125 kW, part of irreversibility?

Heat rejected is not energy wastedsince the rejected heat is required to get work out.

Example 7-4 Reversible Work and Irreversibility of the Coolingof an Iron Block.

Is there reversible work here? Still has a potential for workso can calculate reversible work.

Wrev is the workyou could get out of a Carnot heatengine with thetwo state available.

Source temperature varies as the iron cools, so have to integrate toget Wrev as shown in example.

Wrev = 8191 kJ. Is this the total sensible heat of the iron block?

Only 21% of the total sensible heatof the block, 38,925 kJ, can be turnedinto work.

If 27°C is the lowest available environment temperature, what is theexergy of this iron block?

What is the irreversibility of this process?

Is the sensible heat of the iron block, 38,925 kJ, the maximumheat you can get out of it to heat this house?

Remember, this process has an irreversibility of 8191 kJ!So can run a heat engine between iron and inside air and dump38,925 – 8191 = 30,734 kJ of heat to house and generate 8191 kJ of work. What do you do with the work?

If you run a heat pump withthat work, you can transfer13.6 times (the COP of the heat pump) that amount ofenergy, or 111,398 kJ tothe house for a total of 142,132 kJ of heat!

For this, irreversibility iszero.