v v ¬­ ­­ ­ ®­ ¸ v ¨ V V V V V ­­¬ ­® ¸ ¬­ ­ ®­ V ¸ v V v V V ¨ ¸ V V V V ¸ ¬ ­­­ ®­ ² ¦ ¦ »v n ¦ ¦ ¼ v v v v v ² ¦ ¦ »v n ¦ ¦ ¼ q ²¦ ¦ » ¦¦ ¦¼ n q n n ² ¦ ¦v v » ¦ ¦ ¼ ² ¦ ¦v » ¦ ¦ ¼ V ¨ V V V v v ¸ ¬ ­­­ ®­ n ² ¦ ¦v » ¦ ¦ ¼ ² ¦ ¦v v » ¦ ¦ ¼ v ¨ V V V v v v ¸ ¬­ ­ ®­ n v v n v v v V V V v v ¨ V V V ­­¬ ­­ ® v v ¬­ ­ ®­ ¸ ¬­ ­ ®­ q V V V V V V V ¨ V ¨ V V ¸ V V ¬­ ­ ®­ V V V V ¨ V V V V ¸ n V V ¬­ ­ V ®­­ ¨ V q ¬­ ­­ ®­ V V q V ¸ ¸ ¬­ ­ ®­ V V ¨ P1 100 kPa b P2 700 kPa V2 Wb,out V V V V ¸ aV1 b V (1220 kPa/m )(0.2 m ) b P (kPa) 144 kPa 700 aV 2 b 100 3 3 P = aV+b 2 1 (1220 kPa/m 3 )V 2 (144 kPa) 0.692 m 3 Area P1 P2 (V 2 V1 ) 2 197 kJ 7 § 1 kJ · (100 700)kPa ¸ (0.692 0.2)ft 3 ¨ ¨ 1 kPa m 3 ¸ 2 © ¹ V (m3 ) V V V V ­¬ ­ V ­­® ­­¬ ­­ ® V V V V ¬­ ­ V ®­­ V V V ¶¶ lV ­­¬ ­­ ® V V n V V ¶¶ l n V n v v v v v v v ¸ ¬­ ­ ®­ V V ¨ V V V V V ¨ V V V V V V ¬­ ¬ ­­ ­­­ ® V ®­ V V V V V V V V V n ² ¦ ¦v !v » ¦ ¦ ¼ ¬­ ­ ®­ P V v V V V v V v v v V V v v v n V V ¬ ­­ ­ ® ¸ ¬­ ­ ®­ V P ¨ V ¨ ¸ V ¬ ¬­ ­ V ­­­ ­® V V ­® ¬ ­­ ­­ ¸ ­ ® 2 P = aVƄ-2 ¬­ ­­ ­ ®­ 1 0.1 0.3 V (m3) Closed System Energy Analysis % % ¸ % % % % ¸ % % ¸ ¸ % % % % v % % ²v ¦ ¦ » ¦ ¦ ¼ v v v ² ¦ ¦ » ¦ ¦ ¼ v v v V v v E E out in 'E system Net energy transfer by heat, work, and mass Change in internal, kinetic, potential, etc. energies Qout 'U m(u 2 u1 ) Qout m(u1 u 2 ) (since W KE = PE = 0) 1200 kPa ½ v 1 v g @1200 kPa 0.01672 m 3 /kg ¾ sat. vapor ¿ u1 u g @1200 kPa 253.81 kJ/kg P1 P2 (v 2 400 kPa ½ v f 0.0007907, v g 0.05120 m /kg ¾ v1) u fg 171.45 kJ/kg ¿ u f 63.623, q m V1 v1 0.6 m 3 0.01672 m 3 /kg v 2 v f P 1 35.90 kg v fg 0.01672 0.0007907 0.3159 0.05120 0.0007907 mf (1 x 2 )m (1 0.3159)(35.90 kg u2 u f x 2 u fg 63.623 0.3159(171.45) 117.78 kJ/kg x2 Qout R-134a 1200 kPa Sat. vapor 3 m(u1 u 2 ) (35.90 kg)(253.81 117.78) kJ/kg = 4883 kJ 24.56 kg 2 v % % n n ² ¦ ¦v v » ¦ ¦ ¼ v v V v v ² ¦ ¦ » ¦ ¦ ¦ ¼ v % % ' ' n n ²¦ ¦ » ¦¦ ¼ ²¦ ¦ » ¦¦ ¼ ! n v % % ' ' v V ² ¦ ¦ » ¦ ¦ ¼ v ² ¦ ¦ » ¦ ¦ ¼ v v % % ' ' n v % % % % ² ¦ ¦ » ¦ ¦ ¼v v ² ¦ ¦ » ¦ ¦ ¼ V v % % q v % q ¬­ ®­­ n ! ! v n n % % ! V % % v ¸ ¸ S V % ¶¶ l% ¸n ¸n % n % n % % v v v v V v V v V V ¸ ­­¬ ­® v % % ² ¦ ¦v v » ¦ ¦ ¼ V v V v ² ¦ ¦ » ¦ ¦ ¦ ¼ v n v V ¨ V V V ¸ ¬ ­­­ ®­ % % n n n ² ¦ ¦v » ¦ ¦ ¼ ²v !v ¦ ¦ » ¦ ! ¦ ¼ v n v v v V v < q > q q % % n n ¢ ² ¦ ¦v » ¦ ¦ ¼ v V V V v V ¯ ± v ¢¡ v q ² ¦ ¦ » ¦ ¦ ¼ v % ¢ ¯ ±° q % v ¯ ± ¢ ² v ¦ ¦ » ¦ ¦ ¼ v v % v v v v ¯ ± ¢ q ¯ ± % % % % % % v % v v % v% ¸ v q ¸ % ¸ v% v % v% q v v ¸ ¸ ¸ ¸ v %v v v % % ¸ % % ¸ ¸ n ¸ % % ¸ % % ¸ n ! v V ¸ ¸ v V V v Q V V Q V V V V V V q ¸ ¸ % v% ¸ % ¸ % v v v q % ¨ v q ¨ q ¯ ±° ¢¡ q q q % v v % v % v v % v ¸ ¸ ¸ ¸ % % 'ke # 'pe # 0 % % % v % v % % v v ¸ !% ! n % !% ! v V V ¶¶ l % % % V ¸ ! ¸ % !% q v % % % v % % % ' ' V ¸ ¸ v ! 'ke # 'pe # 0 E E out in Net energy transfer by heat, work, and mass W pw,in Qout W pw,in 'E system O2 101 kPa 27qC Change in internal, kinetic, potential, etc. energies 'U Qout m(u 2 u1 ) # Qout mcv (T2 T1 ) P1V T1 m P2V o T2 T2 P1V RT1 P2 T1 P1 140 kPa (300 K) 101 kPa (101 kPa)(0.285 m 3 ) (0.2598 kPa m 3 /kmol K)(300 K) 415.8 K 0.3693 kg Wpw,in = (20 kJ) + (0.3693 kg)(0.670 kJ/kg.K)(415.8 ± 300) K = 48.7 kJ 20 kJ % n !% ! v % % ! % v q v V q q V ¸ ¸ v ¢ ¯% ± ¸D % % % D q % % % n n V ¶¶ l ! V !% V V 'ke # 'pe # 0 v % % ¨ V ¨ V v V V V V V V V V V ­­¬ V ­­ ® V V V V V ¬­ ­­ ®­ ¬­ ­ ®­­ ¶¶ l V V % n !% ! v % % ! % v q q n v V q q V ¸ ¸ ¸n q n % % q % % ' ! ' V V q V ¶¶ l V% ¸ q q ¸ q V V ­­¬ ­® % ¸ % !% ! ¸ % n v ¡ ¡ ¡ ¢ ¬­ ­­ ®­ ¯ °° °± ¬­ ­­ ®­ v ¸ ¡ ¡ ¢ ¬­ ®­­ ¯ °° ± v ­­¬ ­® ¸ % ¶¶ l % % % V ¸ ¸ ¸n n ! ¸n n % % v v % v ¸ !% ! % ¶¶ l % % % ¬ ­­­ ­® n ¸n ¬­ ­ ®­­ n n 'ke # 'pe # 0 E E out in Net energy transfer by heat, work, and mass 0 P1V1 AIR 0.1 m3 700 kPa 37qC 'E system Change in internal, kinetic, potential, etc. energies 'U P2V 2 o P2 mcv (T2 T1 ) P1 V1 V2 P1 V2 / 2 V2 P1 2 700 kPa 2 350 kPa Vacuum 0.1 m3 v % % v n V V V V V ¬ ­­­ V ­® ¶¶ l ¶¶ l ¨ V V V ¸ V V q v q V V % % v % !% ! % V V % v ¸ ¸ ¸ ¸ V V V ¸ ¬­ ­ ®­ v ¸ % !% ! v V V % % ¶¶ l v q 'ke # 'pe # 0 V % % ¸ V V q V V ¸ ¶¶ l V V V ¨ V V V q q V v ! v % % % ¸ q q E E out in 'E system Net energy transfer by heat, work, and mass Change in internal, kinetic, potential, etc. energies Qout m UV 'U canned drink m(u 2 u1 ) o Qout (998 kg/m 3 )(0.35 u10 3 m 3 /can) Qout mc (T1 T2 ) mice Qout hif 0.349 kg/can (0.349 kg/can )(4.20 kJ/kg. qC) (30 3)qC 39.58 kJ/can 39.58 kJ/can 333.7 kJ/kg mc (T1 T2 ) 0.119 kg (per can of drink) Cola 30qC U U % % SV S Q q q Q n n S SV S ¸n n q % % ¶¶ l % % % % n n S SV S n % n % Q Q n ¸n q n U E Eout in 'Esystem Net energy transfer by heat, work, and mass Change in internal, kinetic, potential, etc. energies 'U plate Qin m(u2 u1 ) Plates 24qC mc (T2 T1 ) ULA (8530 kg/m 3 )(0.04 m)(0.6 m)(0.6 m) 122.8 kg m UV Qin mc (T2 T1 ) Q total q (122.8 kg/plate )(0.38 kJ/kg. qC) (500 24)qC n plateQin, per plate (300 plates/min) u (22,218 kJ/plate) 22,218 kJ/plate 6,665,356kJ/min = 111,090kW S SV S S Q Q ¸n n % n % % n n n n % % q % n % n n n n l n % % q n n n % % % % % % ¸n n ¬­ ­­ ®­ % % % q n n % % n n n % % % ­­¬ ­­ ® ! ¬­ ­ ®­ ­­¬ ­­ ® % ¬­ ­­ ®­ ­­¬ ­® ¬ ­­­ ® ­­¬ ­­ ® q % ­­¬ ­® ­­¬ ­® ¬­ ­­ ®­ % q % % ¬­ ­ ®­ q q q q q q q q ­­¬ ­® q q q q v ¨ v ¨v v v ¡v ¬­­ ¡ ­­ ¡v ® ¢ ¯ ° ¡ ° ¡ ¡ ° ± ¢ ¬­ ­­ ®­ ¯ ° ° ° ± ¯ ° ° ° ± v ¨ v ¨v v v ¡v ¬­­ ¡ ­­ ¡v ® ¢ ¯ ° ¡ ° ¡ ¡ ° ± ¢ ¬­ ­­ ®­ ¬­ ­ ®­ n ¸n % v% n % % % % n n l n l l ¶¶ l ¶¶ l ¬­ l ­ ¶¶ ®­ ¬­ l ­ ¶¶ ®­ % v % % v v v ¸ % % n !% ! ¦²¦ v » ¦¦ ¼ v v v v q q V v ² ¦ ¦ v v » ¦ ¦ ¼ ¨ V V V v v % % ¸ ¬­ ­ ®­ v 'ke # 'pe # 0 E E out in Net energy transfer by heat, work, and mass W pw,in T2 T1 P2 P1 'E system Change in internal, kinetic, potential, etc. energies 'U (288 K) ­­¬ ­­ ® Air 1 kg 210 kPa 15C mcv (T2 T1 ) 280 kPa 210 kPa mcv (T2 T1 ) Wpw,in 384 K Wpw 111qC (1 kg) (0.718 kJ/kg K)(384 288)K 68.9 kJ ¬­ ­ ®­ n n % ¸ v % % v v ¸ !% ! % % n v v n q ¶¶ l v v ²¦ ¦ » ¦¦ ¦¼ ! % n n ¬­ ®­­ v V v v q V V q v V n q ¦²¦ » ¦¦ ¦¼ v n V v V V v v V ¨ V V V V ¸ ­­¬ ­® v % % % % % n ² ¦ ¦ » ¦ ¦ ¼ ² ¦ ¦ » ¦ ¦ ¼ v q ­­¬ ­® % v n v v n n n v v n n % v v ¸ ¬­ ­ ®­ v V V V ¸ ¶¶ lV ¨ V V V V q ¸ q ¬­ V ¬­ ­­ ­­ ¶¶ l ®­ V ®­ V V ¶¶ l ¸ ¬ l ­­­® ¶¶ % % v V v V V V ¸ ­­¬ ­® ¨ V V V ¸ ¬­ ­ ®­ V ' % % % ¸ v % v % ¸ % V ' n n % % n % l% % % P P n v v v v v n q q V v n n ¸n n n % S SV q % n % % % % n % ¸n % % % % % n n n ¸n n n % % l n n % l % % q % ¸n n n v n v % ¢ % l % ¢ v ¯ ± ¸n % n % ¬­ ­­ ®­ ¯ ± ¸P P n SV ¢ % % % ¢ ¯ ± ¸P n % n % ¯ ± P ¸P P n ² ¦ ¦ » ¦ ¦ ¼ v % % % % % % V v V v V v ² ¦ ¦ » ¦ ¦ ¦ ¼ q n % ²v n ¦ ¦ » ¦ ¦ ¼ % % V v V v V ¦²¦ » ¦¦ ¦¼ v % q n n n n n % % % P % P ¸n n ¸n ¸n n n n n n SV n % n % % P % P n n ¸n n n ¸n n n ¸n ¸n n ¸n n % ¢ % ¯ ± ¢ ¸n n ¯ ± ¸n n n n % % n v v v v v n q ² ¦ ¦v » ¦ ¦ ¼ ²v ¦ ¦ » ¦ ¦ ¦ ¼ v q V v V V ¸ q % q ¸ % q % % ! % % % n n n n n q % % 0% V V ¶¶ l !% q v V V ! q % % % % v ² ¦ ¦v » ¦ ¦ ¼ v ²¦ v ¦ » ¦¦ ¼ n < q q > V v V v V v v ²¦ v ¦ » ¦¦ ¦¼ n v v v n v v v q v v % !% ! n % % ! v V Q V Q V ­¬ ­ V ­­ ® V V ¶¶ l V % Q ­­¬ ¶¶ lV ­­® ¶¶ l V Q ¶¶ l ¶¶ l ! % % % n n ² ¦ ¦v » ¦ ¦ ¼ ² ¦ ¦v » ¦ ¦ ¼ ²¦ ¦ » ¦¦ ¦¼ n n v v ! v v % % v v % % ¸n n % SV % ¸n n ¸n n % SV % ¸n n n n n n n n n n q n n n n ¸n n n n n n n n n n n n n n n ¸n q q ¸n n n ¸n n n n n q q q q q ¸ n v ¸ P2=1200 [kPa] T2=700 [C] T3=1200 [C] P3=P2 "1" v2=volume(steam_iapws, P=P2, T=T2) v1=v2 P1=pressure(steam_iapws, x=1, v=v1) "2" v3=volume(steam_iapws, P=P3, T=T3) w_b=P2*(v3-v2) "3" u1=intenergy(steam_iapws, x=1, v=v1) u3=intenergy(steam_iapws, P=P3, T=T3) q=u3-u1+w_b ô ò V V V V ¨ v v v v v v ¶¶ l v
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