Thermodynamics

ple, m i 0 if no mass enters the control volume during the process, m e 0if no mass leaves, and m 1 0 if the control volume is initially evacuated.The energy content of a control volume changes with time during anunsteady-flow process. The magnitude of change depends on the amount ofenergy transfer across the system boundaries as heat and work as well as onthe amount of energy transported into and out of the control volume bymass during the process. When analyzing an unsteady-flow process, wemust keep track of the energy content of the control volume as well as theenergies of the incoming and outgoing flow streams.The general energy balance was given earlier asEnergy balance: E in E out ¢E system 1kJ2 (5–44)Net energy transferby heat, work, and mass⎫⎪⎬⎪⎭⎫⎪⎬⎪⎭Change in internal, kinetic,potential, etc., energiesThe general unsteady-flow process, in general, is difficult to analyze becausethe properties of the mass at the inlets and exits may change during aprocess. Most unsteady-flow processes, however, can be represented reasonablywell by the uniform-flow process, which involves the following idealization:The fluid flow at any inlet or exit is uniform and steady, and thusthe fluid properties do not change with time or position over the cross sectionof an inlet or exit. If they do, they are averaged and treated as constantsfor the entire process.Note that unlike the steady-flow systems, the state of an unsteady-flowsystem may change with time, and that the state of the mass leaving thecontrol volume at any instant is the same as the state of the mass in the controlvolume at that instant. The initial and final properties of the control volumecan be determined from the knowledge of the initial and final states,which are completely specified by two independent intensive properties forsimple compressible systems.Then the energy balance for a uniform-flow system can be expressedexplicitly asClosedChapter 5 | 247QClosedsystemQ – W = ∆UClosedFIGURE 5–45The energy equation of a uniform-flowsystem reduces to that of a closedsystem when all the inlets and exitsare closed.Wa Q in W in ainmu b a Q out W out aoutmu b 1m 2 e 2 m 1 e 1 2 system(5–45)where u h ke pe is the energy of a fluid stream at any inlet or exitper unit mass, and e u ke pe is the energy of the nonflowing fluidwithin the control volume per unit mass. When the kinetic and potentialenergy changes associated with the control volume and fluid streams arenegligible, as is usually the case, the energy balance above simplifies toW bMovingboundaryW eQ W aoutmh ainmh 1m 2 u 2 m 1 u 1 2 system(5–46)where Q Q net,in Q in Q out is the net heat input and W W net,out W out W in is the net work output. Note that if no mass enters or leaves the controlvolume during a process (m i m e 0, and m 1 m 2 m), this equationreduces to the energy balance relation for closed systems (Fig. 5–45).Also note that an unsteady-flow system may involve boundary work as wellas electrical and shaft work (Fig. 5–46).Although both the steady-flow and uniform-flow processes are somewhatidealized, many actual processes can be approximated reasonably well byW shFIGURE 5–46A uniform-flow system may involveelectrical, shaft, and boundary workall at once.