Thermodynamics

428 | ThermodynamicsAtmosphericairP 0SYSTEMV 1AtmosphericairSYSTEMV 2FIGURE 8–8As a closed system expands, somework needs to be done to push theatmospheric air out of the way (W surr ).CyclicdevicesSteady-flowdevicesRigidtanksFIGURE 8–9For constant-volume systems, the totalactual and useful works are identical(W u W).InitialstateReversibleprocessW revI = W rev – W uP 0Actual processW u < W revFinal stateFIGURE 8–10The difference between reversiblework and actual useful work is theirreversibility.of the model (isentropic) process is not the same as the actual exit state and itis limited to adiabatic processes.In this section, we describe two quantities that are related to the actualinitial and final states of processes and serve as valuable tools in the thermodynamicanalysis of components or systems. These two quantities are thereversible work and irreversibility (or exergy destruction). But first weexamine the surroundings work, which is the work done by or against thesurroundings during a process.The work done by work-producing devices is not always entirely in ausable form. For example, when a gas in a piston–cylinder device expands,part of the work done by the gas is used to push the atmospheric air out ofthe way of the piston (Fig. 8–8). This work, which cannot be recovered andutilized for any useful purpose, is equal to the atmospheric pressure P 0times the volume change of the system,W surr P 0 1V 2 V 1 2(8–3)The difference between the actual work W and the surroundings work W surris called the useful work W u :W u W W surr W P 0 1V 2 V 1 2(8–4)When a system is expanding and doing work, part of the work done is usedto overcome the atmospheric pressure, and thus W surr represents a loss.When a system is compressed, however, the atmospheric pressure helps thecompression process, and thus W surr represents a gain.Note that the work done by or against the atmospheric pressure has significanceonly for systems whose volume changes during the process (i.e., systemsthat involve moving boundary work). It has no significance for cyclicdevices and systems whose boundaries remain fixed during a process suchas rigid tanks and steady-flow devices (turbines, compressors, nozzles, heatexchangers, etc.), as shown in Fig. 8–9.Reversible work W rev is defined as the maximum amount of useful workthat can be produced (or the minimum work that needs to be supplied) as asystem undergoes a process between the specified initial and final states. Thisis the useful work output (or input) obtained (or expended) when the processbetween the initial and final states is executed in a totally reversible manner.When the final state is the dead state, the reversible work equals exergy. Forprocesses that require work, reversible work represents the minimum amountof work necessary to carry out that process. For convenience in presentation,the term work is used to denote both work and power throughout this chapter.Any difference between the reversible work W rev and the useful work W uis due to the irreversibilities present during the process, and this differenceis called irreversibility I. It is expressed as (Fig. 8–10)I W rev,out W u,out orI W u,in W rev,in(8–5)The irreversibility is equivalent to the exergy destroyed, discussed in Sec.8–4. For a totally reversible process, the actual and reversible work termsare identical, and thus the irreversibility is zero. This is expected sincetotally reversible processes generate no entropy. Irreversibility is a positivequantity for all actual (irreversible) processes since W rev W u for workproducingdevices and W rev W u for work-consuming devices.