Quetion 8. Noting tt ( or idel ge, ence, ince 5. From te tedy energy eqution: Q & & 5 k e rte o entroy cnge o ir i: Q Q& ir 5 k ΔS& AIR ir 0.0889 k/k 98 K cont. 0 y Quetion 8. e roertie o te ter re 00 k v v 60 @60 @60 0.0007m /kg 0.8 kj/kg K ( ( 0.0007 0.000 m /kg v v 0 k v 0.000 m /kg v v 0.000 0.0006 0.0005 v.99 0.0006 +.06 +.5 kg comreed liquid 00 k 60 ( 0.0005( 6.60.078 kj/kg K Vcuum en te entroy cnge o te ter: ( ( kg(.078 0.8 ΔS m kj/kg K 0.5895 kj/k Quetion 8. e initil tte i uereted vor: 6 M 00 78. kj/kg 6.5 kj/kg K (ble A - 6 e entroy i contnt during te roce. e inl tte i miture ince te entroy i beteen nd g or 00 k. e roertie t ti tte re: + (6.5.08 kj/kg K 0.865 6.056 kj/kg K 7.5+ (0.865(57.5 70.9 kj/kg e cnge in te ently cro te turbine: Δ 70.9 78. 807. kj/kg
Quetion 8. N n idel g. Nitrogen contnt eciic et t room temerture: R 0.968 kj/kg.k nd c v 0.7 kj/kg.k. From te olytroic reltion, v v n n v v en te entroy cnge o nitrogen:. ( 0 K( 8.7 K N Δ S N m c ( 0.50 kg ( 0.7 kj/kg K ln + ( 0.968 kj/kg K ln( 0.5 0.0557 kj/k + v, vg ln R V ln V 8.7 K 0 K Quetion 8.5 e roce i ientroic. For tedy tte: m & m& m&. From te energy blnce or ti tedy-lo ytem: m & m & + M m& ( 60 e inlet tte roertie re urbine M 59. 9 kj/kg 60 6. 998 kj/kg K 00 k For ti ientroic roce, te inl tte roertie re 00 k 6. 998 kj/kg K Subtituting, + ( 59. 9 58. 9 kj/kg 6.0 kj/kg 6. 998. 08 0. 997 6. 056 7. 5+ ( 0. 997( 57. 5 58. 9 kj/kg V.
Quetion 8.6 From ble: du δq δ 600 k u 566. 8 kj/kg 6. 759 kj/kg K ΔU m( u u (ince Q KE E 0 700 kj u u + 566. 8 kj/kg + 6. 8 kj/kg m kg e entroy t te inl tte i: u u 6. 8 7. 0 00 k 0. 867 u 088. u 6. 8 kj/kg +. 08 + 0. 867 6. 056 6. 55 kj/kg K e entroy cnge i Δ 6. 55 6. 759 0.8 kj/kg K e roce i not relitic ince entroy cnnot decree during n dibtic roce. In te limiting ce o reverible (nd dibtic roce, te entroy remin contnt. Quetion 8.7 Air i n idel g it contnt eciic et. At room temerture re c.005 n kj/kg K nd k.. For te olytroic roce v ontnt : ( n / n 0. /. 80 k (7 K 6. K 800 k For tedy tte: m & m& m&. e energy blnce or ti tedy-lo ytem i: V m& + m& V + Solving or te eit velocity, V 0. 5 [ V + ( ] [ V + c ( ] ( 5 m/ 68 m/ V + 0. 5 V + 700 k 00 0 m/ 000 m / + (. 005 kj/kg K(7 6. K kj/kg Air 0. 5 00 k
Quetion 8.8 Air i n idel g it contnt eciic et. e roertie o ir t 00 K re c.005 kj/kg K, c v 0.78 kj/kg K nd k.. Alo, R 0.87 kj/kg K du δq δ ΔU m( u u (ince Q KE E 0 mc ( v 550 kj mcv ( ( 0 + 7 K 59. 8 K mcv ( 5 kg ( 0. 78 kj/kg K From te entroy cnge reltion o n idel g, Δ ir c ln R ln 59. 8 K 00 k (.005 kj/kg Kln (0.87 kj/kg Kln 68 K 600 k 0.59 kj/kg K Since te entroy cnge i oitive or ti dibtic roce, te roce i irreverible nd relitic. Quetion 8.9 From te tem tble: 7 M 650.6 kj/kg 600 7.090 kj/kg K 50 k 50 780. kj/kg For tedy tte: m& m& m&. e energy blnce or ti tedy-lo ytem i: m& ( + V / + m& ( + V / V V m& + Subtituting, te m lo rte o te tem i: ( 0 m/ 5000 kj/ m& 780. 650.6 + m& 5.78 kg/ (ince Q& Δe 0 ( 75 m/ kj/kg 000 m / e ientroic eit ently o te tem nd te oer outut o te ientroic turbine: nd 50 k + 7.090.09 0.98 6.509 0.5 + ( 0.98( 0.7 67. kj/kg
m& ( + {( V V / } ( 0 m/ ( 75 m/ ( 5. 78kg/ 67. 650.6 + 6807 k en te ientroic eiciency o te turbine become 5000 k 0.75 7.5% 6807 k kj/kg 000 m / Quetion 8.0 Air i n idel g it contnt eciic et. e roertie o ir t te nticited verge temerture o 00 K re c.0 kj/kg nd k.95 m & + m & (ince Q& Δke Δe 0 m& ( mc & ( e ientroic eit temerture i ( k 00 k ( 0 + 7 K 800 k From te deinition o te ientroic eiciency, 0.95/.95 6 6 K.,out,out c ( c ( 59 7 0.966 96.6% 59 6. 6.8 M 0 Air turbine 00 k Quetion 8. Air i n idel g it contnt eciic et (k. e ientroic eit temerture i ( k 0./. 600 k ( 7 + 7 K 95 k 508 K en te ientroic eiciency become ( c 0. 8 8. % c ( AIR
Quetion 8. From te rerigernt tble g@ 00 k g@ 00 t. vor v v 00 k k g@ 00 k. kj/kg 0.958 kj/kg K 0.95 m /kg R- 87% M 8.5 kj/kg 0.7 m /min From te ientroic eiciency reltion, + ( + ( /. 8.5. /0.87 89.69 kj/kg u, M 56.5 89.69 kj/kg e m lo rte o te rerigernt i determined rom V 0.7/60 m / &m & 0.06059 kg/ v 0.95 m /kg For tedy tte: m& m& m& : + m & m & (ince Q& Δke Δe 0 m& ( Subtituting, te oer inut to te comreor become, & ( 0.06059 kg/(. - 89.69 kj/kg.5 k
Quetion 8. Air i n idel g it contnt eciic et. e roertie o ir t room temerture re c.005 kj/kg K nd k.. For te comreion roce, ( k 0./. (88 K( 585.8 K c c For te enion roce, ( + ( 585.8 88 88 + 68.9 K 0.90 87 K 88 K q in q ou ( k 0./. (87 K 9. K c ( ( c ( 87 (0.90(87 9. 7.6 K e ientroic nd ctul ork o comreor nd turbine re om, c ( (.005 kj/kg K(585.8 88K 99. kj/kg om c ( (.005 kj/kg K(68.9 88K.6 kj/kg urb, c ( (.005 kj/kg K(87 9.K 6.0 kj/kg urb c ( (.005 kj/kg K(87 7.6K 0. kj/kg e bck ork rtio or 90% eicient comreor nd ientroic turbine ce i r b om urb,.6 kj/kg 6.0 kj/kg 0.757 e bck ork rtio or 90% eicient turbine nd ientroic comreor ce i r b om, urb 99. kj/kg 0. kj/kg e to reult re lmot identicl. 0.756
Quetion 8. From te tem tble, 50 k t @ 50 k 6 0 kj/kg,. 6. 8. 6. 75 v v @ 75 @ 75.0 kj/kg 0.0006 m /kg 50 50 k. 6000 k. 0 ( 6. 0 0 kj/kg 0. 9 kj/kg 6. 79 kj/kg K + 6. 79. 09 0. 8660 6. 509 0. 5 + ( 0. 8660( 0. 7 6. kj/kg ( 0. 9 ( 0. 9( 0. 9 6. 9. kj/kg u, Q& in,out net m& ( m& ( m &,out ( 0 kg/(0.9 0. kj/kg 59,660 k ( 0 kg/(0.9 9. kj/kg 8,70 k ( 0 kg/(-6.0 kj/kg k + 8, 70 + ( 8,050 k nd t Q& net in 8, 050 59, 660 0.05
Quetion 8.5 From te tem tble, v v t @ 0 t @ 00 @ 0 @ 0 8. 65 kj/kg 7. 85 k 8588 k 67. 5 kj/kg 0. 00008 m /kg 67. 5 ( 8. 65 76. 8 kj/kg 00 0 in 79.6 kj/kg 5.7059 kj/kg K + 5.7059 0.57 0.668 7.68 67.5 + (0.668(06.0 775. kj/kg u, 79. 6 775. 97.5 kj/kg qin 79. 6 76. 8 57. kj/kg qout 67. 5 775. 607. 6 kj/kg e terml eiciency o te cycle i qout 607. 6 t 0.75 q 57.
Quetion 8.6 Air i n idel g it contnt eciic et. e roertie o ir t room temerture re c.005 kj/kg K nd k.. Uing te ientroic reltion,,,,,net, m&, net,,net, + ( k ( k c c, ( 00 K( ( 000 K ( (.005 kj/kg K( 00-60. K ( (.005 kj/kg K( 000 9.7 50. 8 + (. 75 99. kj/kg 70,000 kj/ 5 99. kj/kg 0./. kg/ e net ork outut i determined to be,net m&, ( 0. 85( 50. 8 net,net, +,, + 60. K 0./., + (.75 9.7 K / 70,000 kj/ 07 67.5 kj/kg 0.85 67.5 kj/kg kg/.75 kj/kg K 50.8 kj/kg