Thermodynamics

Q # net,in W # shaft,net out d erdV dt aoutm # a P r u V 22 gz b CVChapter 5 | 255where e u V 2 /2 gz is the total energy per unit mass for both the controlvolume and flow streams. Then,orQ # net,in W # shaft,net out d dtCV ainm # a P r u V 22 gz berdV aoutm # a h V 22 gz b(5–58) ainm # a h V 22 gz b(5–59)where we used the definition of enthalpy h u Pv u P/r. The lasttwo equations are fairly general expressions of conservation of energy, buttheir use is still limited to uniform flow at inlets and outlets and negligiblework due to viscous forces and other effects. Also, the subscript “net,in” standsfor “net input,” and thus any heat or work transfer is positive if to the systemand negative if from the system.SUMMARYThe conservation of mass principle states that the net masstransfer to or from a system during a process is equal to thenet change (increase or decrease) in the total mass of the systemduring that process, and is expressed asm in m out ¢m system andm # in m # out dm system >dtwhere m system m final m initial is the change in the mass ofthe system during the process, m . in and m . out are the total ratesof mass flow into and out of the system, and dm system /dt is therate of change of mass within the system boundaries. Therelations above are also referred to as the mass balance andare applicable to any system undergoing any kind of process.The amount of mass flowing through a cross section perunit time is called the mass flow rate, and is expressed asm # rVAwhere r density of fluid, V average fluid velocity normalto A, and A cross-sectional area normal to flow direction.The volume of the fluid flowing through a cross sectionper unit time is called the volume flow rate and is expressed asV # VA m # >rThe work required to push a unit mass of fluid into or outof a control volume is called flow work or flow energy, and isexpressed as w flow Pv. In the analysis of control volumes,it is convenient to combine the flow energy and internalenergy into enthalpy. Then the total energy of a flowing fluidis expressed asu h ke pe h V 2The total energy transported by a flowing fluid of mass mwith uniform properties is mu. The rate of energy transportby a fluid with a mass flow rate of m . is m . u. When the kineticand potential energies of a fluid stream are negligible, theamount and rate of energy transport become E mass mh andE . mass m . h, respectively.The first law of thermodynamics is essentially an expressionof the conservation of energy principle, also called theenergy balance. The general mass and energy balances forany system undergoing any process can be expressed asE in E out ¢E system⎫⎪⎬⎪⎭⎫⎪⎬⎪⎭⎫⎪⎪⎬⎪⎪⎭⎫⎪⎪⎬⎪⎪⎭Net energy transferby heat, work, and massIt can also be expressed in the rate form asRate of net energy transferby heat, work, and mass2 gzChanges in internal, kinetic,potential, etc., energiesE # in E # out dE system >dtRate of change in internal, kinetic,potential, etc., energiesThermodynamic processes involving control volumes canbe considered in two groups: steady-flow processes and