Thermodynamics

246 | ThermodynamicsSubstituting the known quantities, the exit temperature of the air is determinedto beDiscussionof air.115 kJ/s2 10.2 kJ/s2 13 kg/s211.005 kJ/kg # °C21T2 172°CT 2 21.9°CNote that heat loss from the duct reduces the exit temperatureSupply lineControlvolumeCV boundaryFIGURE 5–43Charging of a rigid tank from a supplyline is an unsteady-flow process sinceit involves changes within the controlvolume.FIGURE 5–44INTERACTIVETUTORIALSEE TUTORIAL CH. 5, SEC. 5 ON THE DVD.CV boundaryControlvolumeThe shape and size of a controlvolume may change during anunsteady-flow process.5–5 ■ ENERGY ANALYSIS OF UNSTEADY-FLOWPROCESSESDuring a steady-flow process, no changes occur within the control volume;thus, one does not need to be concerned about what is going on within theboundaries. Not having to worry about any changes within the control volumewith time greatly simplifies the analysis.Many processes of interest, however, involve changes within the controlvolume with time. Such processes are called unsteady-flow, or transientflow,processes. The steady-flow relations developed earlier are obviouslynot applicable to these processes. When an unsteady-flow process is analyzed,it is important to keep track of the mass and energy contents of thecontrol volume as well as the energy interactions across the boundary.Some familiar unsteady-flow processes are the charging of rigid vesselsfrom supply lines (Fig. 5–43), discharging a fluid from a pressurized vessel,driving a gas turbine with pressurized air stored in a large container, inflatingtires or balloons, and even cooking with an ordinary pressure cooker.Unlike steady-flow processes, unsteady-flow processes start and end oversome finite time period instead of continuing indefinitely. Therefore in thissection, we deal with changes that occur over some time interval t insteadof with the rate of changes (changes per unit time). An unsteady-flow system,in some respects, is similar to a closed system, except that the masswithin the system boundaries does not remain constant during a process.Another difference between steady- and unsteady-flow systems is thatsteady-flow systems are fixed in space, size, and shape. Unsteady-flowsystems, however, are not (Fig. 5–44). They are usually stationary; that is,they are fixed in space, but they may involve moving boundaries and thusboundary work.The mass balance for any system undergoing any process can be expressedas (see Sec. 5–1)m in m out ¢m system 1kg2(5–42)where m system m final m initial is the change in the mass of the system.For control volumes, it can also be expressed more explicitly asm i m e 1m 2 m 1 2 CV(5–43)where i inlet, e exit, 1 initial state, and 2 final state of the controlvolume. Often one or more terms in the equation above are zero. For exam-