Exergy

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

Exergy The maximum useful work that can be obtained from a system.The maximum useful work that can be obtained from a system. All irreversibilities are disregarded in finding exergyAll irreversibilities are disregarded in finding exergy System must be at a dead state at the end of the process.System must be at a dead state at the end of the process.

In a dead state when at equilibrium with its environment. Unless otherwise stated, the dead-state temp and pressure are those above.

Something already at its dead state has no potential for work. The properties of a system at its dead state are denoted by subscript 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?

Exergy Not the amount of work a work producing device will actually produce.Not the amount of work a work producing device will actually produce. It is the upper limit of workIt is the upper limit of work Difference is room for improvement.Difference is room for improvement. Can increase exergy by changing the environment, but not easy.Can increase exergy by changing the environment, but not easy.

The exergy of ke is the ke itself The exergy of pe is the pe itself. x pe = 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 is the work that a reversible (Carnot) heat engine can produce between 2000 R and the environment (77°F) Btu’s/s 2196 Btu’s/s Unavailable energy is the energy that must be discarded.

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

Example – expanding piston – some of the work is done to push the atmosphere out of the way. W surr = P 0 (V 2 – V 1 )Useful work = W u = W - W surr If compressed, W surr represents a gain.

Surroundings work has no significance for cyclic and constant volume devices.

Reversible Work The maximum amount of usable work that can be produced when a system undergoes a process between specified initial and final states.The maximum amount of usable work that can be produced when a system undergoes a process between specified initial and final states. How does this differ from exergy?How does this differ from exergy? Why is this more useful in evaluating a particular device?Why is this more useful in evaluating a particular device? Equal to exergy when the final state equals the dead state.Equal to exergy when the final state equals the dead state.

Irreversibility or I is the difference between reversible work and usable work. Always positive for an actual process. Equivalent to exergy destroyed. Can be viewed as the wasted work potential or lost opportunity to do work. Like reversible work, based on actual initial and final states, not dead state.

Example 7-3 Reversible Power and Rate of Irreversibility of a Heat Engine. W rev = η th,rev Q in = (1-T sink /T source )Q in W rev = 375 kW I = W rev,out – W u,out = 195 kW Is heat rejected, 125 kW, part of irreversibility? Heat rejected is not energy wasted since the rejected heat is required to get work out.

Example 7-4 Reversible Work and Irreversibility of the Cooling of an Iron Block. Is there reversible work here? Still has a potential for work so can calculate reversible work. W rev is the work you could get out of a Carnot heat engine with the two state available.

Source temperature varies as the iron cools, so have to integrate to get W rev as shown in example. W rev = 8191 kJ. Is this the total sensible heat of the iron block? Only 21% of the total sensible heat of the block, 38,925 kJ, can be turned into work. If 27°C is the lowest available environment temperature, what is the exergy of this iron block? What is the irreversibility of this process?

Is the sensible heat of the iron block, 38,925 kJ, the maximum heat 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 dump 38,925 – 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 with that work, you can transfer 13.6 times (the COP of the heat pump) that amount of energy, or 111,398 kJ to the house for a total of 142,132 kJ of heat! For this, irreversibility is zero.