6-5. H 2 O 200 kpa 200 C Q. Entropy Changes of Pure Substances

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1 Canges f ure Substances 6-0C Yes, because an ternally reversible, adiabatic prcess vlves n irreversibilities r eat transfer. 6- e radiatr f a steam eatg system is itially filled wit supereated steam. e valves are clsed, and steam is allwed t cl until te temperature drps t a specified value by transferrg eat t te rm. e entrpy cange f te steam durg tis prcess is t be determed. Analysis Frm te steam tables, 00ka v.080m /kg 00 C s kJ/kg K 80 C v v s x e mass f te steam is v v f v fg s f + xs fg kj/kg K V 0.00m m kg v.080m /kg ( 0.7)( 6.569) en te entrpy cange f te steam durg tis prcess becmes S m s ( s ) ( kg)( ) kj/kg K kj/k H O 00 ka 00 C Q 6-5

2 6-8 An sulated cylder is itially filled wit saturated liquid water at a specified pressure. e water is eated electrically at cnstant pressure. e entrpy cange f te water durg tis prcess is t be determed. Assumpts e ketic and ptential energy canges are negligible. e cylder is well-sulated and tus eat transfer is negligible. e termal energy stred te cylder itself is negligible. 4 e cmpress r expans prcess is quasi-equilibrium. Analysis Frm te steam tables, v v m /kg 50ka H O 467.kJ/kg sat. liquid 50 ka s s K 00 kj Sat. liquid Als, m V m kg v m / kg We take te cntents f te cylder as te system. is is a clsed system sce n mass enters r leaves. e energy balance fr tis statary clsed system can be expressed as E E E 4 4 system 4 4 Net energy transfer by eat, wrk, and mass Cange ternal, ketic, ptential, etc. energies We, Wb, U We, m( ) sce U + W b H durg a cnstant pressure quasi-equilibrium prcess. Slvg fr, We, 00 kj kj / kg m kg us, f ka x 0.08 fg kJ/kg s s + x s kJ/kg en te entrpy cange f te water becmes f fg ( )( ) K ( ) ( 4.748kg)(.68.46) kj/kg K 5.7 kj/k S m s s 6-9

3 6-6 Oxygen gas is cmpressed frm a specified itial state t a specified fal state. e entrpy cange f xygen durg tis prcess is t be determed fr te case f cnstant specific eats. Assumpts At specified cndits, xygen can be treated as an ideal gas. rperties e gas cnstant and mlar mass f xygen are R kj/kg.k and M kg/kml (able A-). Analysis e cnstant vlume specific eat f xygen at te average temperature is (able A-) ave 49 K Cv, ave kj / kg K us, V s s Cv, ave + R V O 560K 0.m /kg 0.8 m ( 0.690kJ/kg K) + ( 0.598kJ/kg K) /kg 98K 5 C 0.8m /kg 0.05kJ/kg K 6-6 An sulated tank cntas CO gas at a specified pressure and vlume. A paddle-weel te tank stirs te gas, and te pressure and temperature f CO rises. e entrpy cange f CO durg tis prcess is t be determed usg cnstant specific eats. Assumpts At specified cndits, CO can be treated as an ideal gas wit cnstant specific eats at rm temperature. rperties e specific eat f CO is C v kj/kg.k (able A-). Analysis Usg te ideal gas relat, te entrpy cange is determed t be us, V V S m( s ) s m C 0. kj/k v, ave 0ka. 00ka (.7 kg)( 0.657kJ/kg K) (.) V + R V mc v, ave CO.5 m 00 ka. kg 6-0

4 6-67 Air is cmpressed a pistn-cylder device a reversible and istermal manner. e entrpy cange f air and te wrk dne are t be determed. Assumpts At specified cndits, air can be treated as an ideal gas. e prcess is specified t be reversible. rperties e gas cnstant f air is R 0.87 kj/kg.k (able A-). Analysis (a) Ntg tat te temperature remas cnstant, te entrpy cange f air is determed frm S air C p, ave R R 400ka 90ka ( 0.87kJ/kg K) 0.48kJ/kg K Als, fr a reversible istermal prcess, ( 9 K)( 0.48kJ/kg K) 5.4kJ/kg q 5.4 kj/kg q s (b) e wrk dne durg tis prcess is determed frm te clsed system energy balance, E E 44 Net energy transfer by eat, wrk, and mass W Q w U mc q Esystem 44 Cange ternal, ketic, ptential, etc.energies v ( ) kj/kg AIR cnst Q 6-68 Air is cmpressed steadily by a 5-kW cmpressr frm ne specified state t anter specified state. e rate f entrpy cange f air is t be determed. Assumpts At specified cndits, air can be treated as an ideal gas. Air as variable specific eats. rperties e gas cnstant f air is R 0.87 kj/kg.k (able A-). Analysis Frm te air table (able A-7), 90 K s 00 ka 440 K s 600 ka.6680 kj/kg K.0887 kj/kg K en te rate f entrpy cange f air becmes & S sys m& s s R kw/k (.6/60kg/s) ( 0.87kJ/kg K) 600ka 00ka 600 ka 440 K AIR COMRESSOR 00 ka 90 K 5 kw 6-

5 Reversible Steady-Flw Wrk 6-78C e wrk assciated wit steady-flw devices is prprtal t te specific vlume f te gas. Clg a gas durg cmpress will reduce its specific vlume, and tus te pwer cnsumed by te cmpressr. 6-79C Clg te steam as it expands a turbe will reduce its specific vlume, and tus te wrk put f te turbe. erefre, tis is nt a gd prpsal. 6-80C We wuld nt supprt tis prpsal sce te steady-flw wrk put t te pump is prprtal t te specific vlume f te liquid, and clg will nt affect te specific vlume f a liquid significantly. 6-0

6 6-84 A steam pwer plant perates between te pressure limits f 0 Ma and 0 ka. e rati f te turbe wrk t te pump wrk is t be determed. Assumpts Liquid water is an cmpressible substance. Ketic and ptential energy canges are negligible. e prcess is reversible. 4 e pump and te turbe are adiabatic. rperties e specific vlume f saturated liquid water at 0 ka is v v 0 ka m /kg (able A-5). Analysis Bt te cmpress and expans prcesses are reversible and adiabatic, and tus isentrpic, s s and s s 4. en te prperties f te steam are 4 0 ka 4 sat. vapr s4 s 0 Ma s s kj/kg Als, v v 0 ka m /kg kj/kg kj/kg K e wrk put t tis isentrpic turbe is determed frm te steady-flw energy balance t be 0 (steady) E E Esystem 0 & 44 & & Rate f net energy transfer by eat, wrk, and mass Rate f cange ternal, ketic, ptential, etc.energies E& E& m & m & 4 + m& ( 4 ) Substitutg, wturb, kj / kg e pump wrk put is determed frm te steady-flw wrk relat t be H O H O 4 us, w w w pump, turb, pump, ( ) vd + ke + pe v kj (0.0007m /kg)(0,000 0)ka ka m kJ/kg 6-85 EES slut f tis (and ter cmpreensive prblems designated wit te cmputer icn) is available t structrs at te Instructr Manual sect f te Onle Learng Center (OLC) at See te reface fr access frmat. 6-

7 6-97 Steam enters an adiabatic turbe at a specified state, and leaves at a specified state. e mass flw rate f te steam and te isentrpic efficiency are t be determed. Assumpts is is a steady-flw prcess sce tere is n cange wit time. tential energy canges are negligible. e device is adiabatic and tus eat transfer is negligible. Analysis (a) Frm te steam tables (ables A-4 and A-6), 6Ma 658.4kJ/kg 600 C 7.677kJ/kg K s 50ka 00 C a 68.5kJ/kg ere is nly ne let and ne exit, and tus m& m& m&. We take te actual turbe as te system, wic is a cntrl vlume sce mass crsses te bundary. e energy balance fr tis steady-flw system can be expressed te rate frm as E E E & 44 & & (steady) system Rate f net energy transfer by eat, wrk, and mass m& ( + V E& E& / ) + m& ( a, m& Rate f cange ternal, ketic, ptential, etc.energies a, + V V + V /) (sce Q& pe 0) Substitutg, te mass flw rate f te steam is determed t be (40 m/s) (80 m/s) kj/kg 8000 kj/s m& m /s m& 8.5 kg/s (b) e isentrpic exit entalpy f te steam and te pwer put f te isentrpic turbe are and s s, s s 50ka s m& s f x s + x s s ( + {( V V )/ } ) s fg s s f s fg (40 m/s) (80 m/s) ( 8.5 kg/s) s, kw en te isentrpic efficiency f te turbe becmes η a 8000 kw % 9554 kw s ( 0.94)( 05.4) 49.7 kj/kg kj/kg 000 m /s H O 8 MW 6-40

8 6-00 [Als slved by EES n enclsed CD] Refrigerant-4a enters an adiabatic cmpressr wit an isentrpic efficiency f 0.80 at a specified state wit a specified vlume flw rate, and leaves at a specified pressure. e cmpressr exit temperature and pwer put t te cmpressr are t be determed. Assumpts is is a steady-flw prcess sce tere is n cange wit time. Ketic and ptential energy canges are negligible. e device is adiabatic and tus eat transfer is negligible. Analysis (a) Frm te refrigerant tables, 0ka s s g sat. vapr v v Ma ss s s g@0ka 77.84kJ/kg Frm te isentrpic efficiency relat, us, η C a a s a Ma 88.84kJ/kg a a C.86kJ/kg 0.954kJ/kg K 0.64m /kg ( )/η.86 + ( ) s C / kJ/kg (b) e mass flw rate f te refrigerant is determed frm & m& V 0./60 m / s 0.0 kg / s v 0.64 m / kg ere is nly ne let and ne exit, and tus m& m& m&. We take te actual cmpressr as te system, wic is a cntrl vlume sce mass crsses te bundary. e energy balance fr tis steady-flw system can be expressed as E E & 44 & Rate f net energy transfer by eat, wrk, and mass E & (steady) system a, E& Rate f cange ternal, ketic, ptential, etc.energies E& a, m& ( ) Substitutg, te pwer put t te cmpressr becmes, W & a, 0.0kg/s kj/kg.70 + m & m & (sce Q& ke pe 0) ( )( ) kw R-4a η C 80% 0. m /m 6-0 EES slut f tis (and ter cmpreensive prblems designated wit te cmputer icn) is available t structrs at te Instructr Manual sect f te Onle Learng Center (OLC) at See te reface fr access frmat. 6-4

Department of Civil Engineering & Applied Mechanics McGill University, Montreal, Quebec Canada

Department of Civil Engineering & Applied Mechanics McGill University, Montreal, Quebec Canada Department f Ciil ngeerg Applied Mechanics McGill Uniersity, Mntreal, Quebec Canada CI 90 THRMODYNAMICS HAT TRANSFR Assignment #4 SOLUTIONS. A 68-kg man whse aerage bdy temperature is 9 C drks L f cld