Question 8.1 Noting that h = h(t) for ideal gases, hence, h 1 = h 2 since T 1 = T 2 = 25 C. From the steady energy equation: P 2

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1 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 k/k 98 K cont. 0 y Quetion 8. e roertie o te ter re 00 k v m /kg 0.8 kj/kg K ( ( m /kg v v 0 k v m /kg v v v kg comreed liquid 00 k 60 ( ( kj/kg K Vcuum en te entroy cnge o te ter: ( ( kg( ΔS m kj/kg K kj/k Quetion 8. e initil tte i uereted vor: 6 M 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: + ( kj/kg K kj/kg K 7.5+ (0.865( kj/kg e cnge in te ently cro te turbine: Δ kj/kg

2 Quetion 8. N n idel g. Nitrogen contnt eciic et t room temerture: R 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 + ( kj/kg K ln( 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 kj/kg kj/kg K 00 k For ti ientroic roce, te inl tte roertie re 00 k kj/kg K Subtituting, + ( kj/kg 6.0 kj/kg ( ( kj/kg V.

3 Quetion 8.6 From ble: du δq δ 600 k u kj/kg kj/kg K ΔU m( u u (ince Q KE E kj u u kj/kg kj/kg m kg e entroy t te inl tte i: u u k u 088. u 6. 8 kj/kg kj/kg K e entroy cnge i Δ 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 V k 00 0 m/ 000 m / + (. 005 kj/kg K(7 6. K kj/kg Air k

4 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 ( ( K K mcv ( 5 kg ( kj/kg K From te entroy cnge reltion o n idel g, Δ ir c ln R ln 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 kj/kg kj/kg K 50 k 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& 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 ( 0.98( kj/kg

5 m& ( + {( V V / } ( 0 m/ ( 75 m/ ( 5. 78kg/ k en te ientroic eiciency o te turbine become 5000 k % 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 ( K 800 k From te deinition o te ientroic eiciency, 0.95/ K.,out,out c ( c ( % 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 ( K 95 k 508 K en te ientroic eiciency become ( c % c ( AIR

6 Quetion 8. From te rerigernt tble 00 k g@ 00 t. vor v v 00 k k g@ 00 k. kj/kg kj/kg K 0.95 m /kg R- 87% M 8.5 kj/kg 0.7 m /min From te ientroic eiciency reltion, + ( + ( / / kj/kg u, M kj/kg e m lo rte o te rerigernt i determined rom V 0.7/60 m / &m & 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, & ( kg/( kj/kg.5 k

7 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( K c c For te enion roce, ( + ( K K 88 K q in q ou ( k 0./. (87 K 9. K c ( ( c ( 87 (0.90( K e ientroic nd ctul ork o comreor nd turbine re om, c ( (.005 kj/kg K( K 99. kj/kg om c ( (.005 kj/kg K( K.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 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

8 Quetion 8. From te tem tble, 50 k 50 k 6 0 kj/kg, v kj/kg m /kg k k. 0 ( kj/kg 0. 9 kj/kg kj/kg K ( ( kj/kg ( 0. 9 ( 0. 9( kj/kg u, Q& in,out net m& ( m& ( m &,out ( 0 kg/( kj/kg 59,660 k ( 0 kg/( kj/kg 8,70 k ( 0 kg/(-6.0 kj/kg k + 8, 70 + ( 8,050 k nd t Q& net in 8, ,

9 Quetion 8.5 From te tem tble, v v kj/kg k 8588 k kj/kg m /kg ( kj/kg 00 0 in 79.6 kj/kg kj/kg K (0.668( kj/kg u, kj/kg qin kj/kg qout kj/kg e terml eiciency o te cycle i qout t 0.75 q 57.

10 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( K ( (.005 kj/kg K( ( kj/kg 70,000 kj/ kj/kg 0./. kg/ e net ork outut i determined to be,net m&, ( 0. 85( net,net, +,, K 0./., + ( K / 70,000 kj/ kj/kg kj/kg kg/.75 kj/kg K 50.8 kj/kg

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