Thermodynamics

382 | Thermodynamicsor, in the rate form, asQ # ka a m # is i a m # es e S # gen dS CV >dt1kW>K2T kThis entropy balance relation can be stated as:The rate of entropy change within the control volume during a process isequal to the sum of the rate of entropy transfer through the control volumeboundary by heat transfer, the net rate of entropy transfer into the controlvolume by mass flow, and the rate of entropy generation within theboundaries of the control volume as a result of irreversibilities.(7–83)s is e > s iFIGURE 7–64The entropy of a substance alwaysincreases (or remains constant in thecase of a reversible process) as it flowsthrough a single-stream, adiabatic,steady-flow device.Most control volumes encountered in practice such as turbines, compressors,nozzles, diffusers, heat exchangers, pipes, and ducts operate steadily,and thus they experience no change in their entropy. Therefore, the entropybalance relation for a general steady-flow process can be obtained from Eq.7–83 by setting dS CV /dt 0 and rearranging to giveSteady-flow: S # gen a m # es e a m # Q # kis i a (7–84)For single-stream (one inlet and one exit) steady-flow devices, the entropybalance relation simplifies toSteady-flow, single-stream: S # gen m # Q # k1s e s i 2 a (7–85)For the case of an adiabatic single-stream device, the entropy balance relationfurther simplifies toSteady-flow, single-stream, adiabatic: S # gen m # 1s e s i 2(7–86)which indicates that the specific entropy of the fluid must increase as itflows through an adiabatic device since S . gen 0 (Fig. 7–64). If the flowthrough the device is reversible and adiabatic, then the entropy remainsconstant, s e s i , regardless of the changes in other properties.T kT kEXAMPLE 7–17Entropy Generation in a WallConsider steady heat transfer through a 5-m 7-m brick wall of a house ofthickness 30 cm. On a day when the temperature of the outdoors is 0C, thehouse is maintained at 27C. The temperatures of the inner and outersurfaces of the brick wall are measured to be 20C and 5C, respectively, andthe rate of heat transfer through the wall is 1035 W. Determine the rate ofentropy generation in the wall, and the rate of total entropy generationassociated with this heat transfer process.Solution Steady heat transfer through a wall is considered. For specifiedheat transfer rate, wall temperatures, and environment temperatures, theentropy generation rate within the wall and the total entropy generation rateare to be determined.Assumptions 1 The process is steady, and thus the rate of heat transferthrough the wall is constant. 2 Heat transfer through the wall is onedimensional.