Thermodynamics

458 | ThermodynamicsWX workm ic iSurroundingsControlvolumeX CVTm ec eQX heatproportional to the amount of mass (Fig. 8–42). Again taking the positivedirection of heat transfer to be to the system and the positive direction of worktransfer to be from the system, the general exergy balance relations (Eqs. 8–36and 8–37) can be expressed for a control volume more explicitly asorX heat X work X mass,in X mass,out X destroyed 1X 2 X 1 2 CVa a1 T 0T kbQ k 3W P 0 1V 2 V 1 24 ainmc aoutmc X destroyed 1X 2 X 1 2 CVIt can also be expressed in the rate form as(8–44)(8–45)a a 1 T 0b Q # k a W # P dV CV0 b T k dt ainm # c aoutm # c X # destroyed dX CVdt·X inFIGURE 8–42Exergy is transferred into or out of acontrol volume by mass as well asheat and work transfer.HeatWorkMassSteady flowsystem·X destroyedHeatWorkMassFIGURE 8–43The exergy transfer to a steady-flowsystem is equal to the exergy transferfrom it plus the exergy destructionwithin the system.·X out(8–46)The exergy balance relation above can be stated as the rate of exergy changewithin the control volume during a process is equal to the rate of net exergytransfer through the control volume boundary by heat, work, and mass flowminus the rate of exergy destruction within the boundaries of the controlvolume.When the initial and final states of the control volume are specified, theexergy change of the control volume is X 2 X 1 m 2 f 2 m 1 f 1 .Exergy Balance for Steady-Flow SystemsMost control volumes encountered in practice such as turbines, compressors,nozzles, diffusers, heat exchangers, pipes, and ducts operate steadily,and thus they experience no changes in their mass, energy, entropy, andexergy contents as well as their volumes. Therefore, dV CV /dt 0 anddX CV /dt 0 for such systems, and the amount of exergy entering a steadyflowsystem in all forms (heat, work, mass transfer) must be equal to theamount of exergy leaving plus the exergy destroyed. Then the rate form ofthe general exergy balance (Eq. 8–46) reduces for a steady-flow process to(Fig. 8–43)Steady-flow: a a 1 T 0b Q # k W # (8–47)T ainm # c aoutm # c X # destroyed 0kFor a single-stream (one-inlet, one-exit) steady-flow device, the relationabove further reduces toSingle-stream: a a 1 T 0b Q # k W # m # 1c 1 c 2 2 X # destroyed 0 (8–48)T kwhere the subscripts 1 and 2 represent inlet and exit states, ṁ is the massflow rate, and the change in the flow exergy is given by Eq. 8–23 asc 1 c 2 1h 1 h 2 2 T 0 1s 1 s 2 2 V 1 2 2 V 2 g 1z 1 z 2 22