Thermodynamics

Chapter 7 | 387Under the stated assumptions and observations, the mass and energybalances for this steady-flow system can be expressed in the rate form asfollows:Mass balance:Energy balance:Rate of net energy transferby heat, work, and massRate of change in internal, kinetic,potential, etc., energiesE # in E # outm # 1h 1 m # 2h 2 m # 3h 3 Q # out 1since W # 0, ke pe 02Combining the mass and energy balances givesThe desired properties at the specified states are determined from the steamtables to beState 1:m # in m # out dm system >dt 0 S m # 1 m # 2 m # 3E # in E # out dE system /dt 0⎫⎪⎪⎬⎪⎪⎭⎫⎪⎪⎬⎪⎪⎭¡ 0 (steady)¡ 0 (steady)Q # out m # 1h 1 m # 2h 2 1m # 1 m # 22h 3P 1 20 psiaT 1 50°Ffh 1 h f @ 50°F 18.07 Btu>lbms 1 s f @ 50°F 0.03609 Btu>lbm # RState 2:P 2 20 psiaT 2 240°F fh 2 1162.3 Btu>lbms 2 1.7406 Btu>lbm # RState 3:Substituting,180 Btu>min 3300 18.07 m # 2 1162.3 1300 m # 22 97.994 Btu>minwhich givesP 3 20 psiaT 3 130°F fh 3 h f @ 130°F 97.99 Btu>lbms 3 s f @ 130°F 0.18174 Btu>lbm # Rm # 2 22.7 lbm>minThe rate of entropy generation during this process can be determined byapplying the rate form of the entropy balance on an extended system thatincludes the mixing chamber and its immediate surroundings so that theboundary temperature of the extended system is 70F 530 R:S # in S # out S # gen dS system >dt123Rate of net entropytransfer by heatand mass123Rate of entropygeneration123Rate of changein entropym # 1s 1 m # 2s 2 m # 3s 3 Q# outT b S # gen 0