Chapter 7. (a) The compressor work is give by. = m (h 2 h 1 ) = (0.08 kg/s)( ) kj/kg = kw. (b) The refrigeration capacity, in tons, is

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1 apter 7 Exaple Refrigerant 4a i te working fluid in an ideal vapor-opreion refrigeration yle tat ouniate terally wit a old region at 0 and a war region at 6. Saturated vapor enter te opreor at 0 and aturated liquid leave te ondener at 6. e a flow rate of te refrigerant i 0.08 kg/. Deterine (a) te opreor power, in k, (b) te refrigeration apaity, in ton, () te oeffiient of perforane, and (d) te oeffiient of perforane of a arnot refrigeration yle operating between war and old region at 6 and 0, repetively. Solution H H ondener Expanion valve Evaporator 4 opreor iquid 4 a b Ientalp 6 o 0 o Vapor Speifi Internal Speifi Speifi ype ep reure Volue Energy Entalpy Entropy uality ae Ma /kg kj/kg kj/kg kj/kg/k R-4a Saturated Vapor R-4a Saturated iquid R-4a Supereated Vapor (a) e opreor work i give by ( ) (0.08 kg/)( ) kj/kg.408 k (b) e refrigeration apaity, in ton, i ( 4 ) (0.08 kg/)( ) kj/kg.0 k ton (.0 kj/)(60 /in).7 ton kj/in 6 Moran, M. J. and Sapiro H. N., Fundaental of Engineering erodynai, iley, 008, pg

region at 0 and a war region at 6. Saturated vapor enter te opreor at 0 and aturated liquid leave te ondener at 6. e a flow rate of te refrigerant i 0.08 kg/.

2 () te oeffiient of perforane i β (d) e oeffiient of perforane of a arnot refrigeration yle operating between war and old region at 6 and 0, repetively β H H H ondener iquid H Expanion valve Evaporator 4 opreor H 4 Ientalp Figure 7.- A vapor-opreion refrigeration wit irreveribilitie. Vapor Figure 7.- ow everal feature exited in atual vapor opreion yte. e eat tranfer between te refrigerant and te war and old region are not aoplied reveribly: te refrigerant teperature in te evaporator i le tan te low reervoir teperature,, and te refrigerant teperature in te ondener i greater tan te ig reervoir teperature, H. e opreor will not ave 00% effiieny o tat te fluid leaving te opreor will be at tate (), wi i at iger entropy tan te ientropi opreion tate (). e oeffiient of perforane dereae a te average teperature of te refrigerant in te evaporator dereae and a te average teperature of te refrigerant in te ondener inreae. If te teral effiieny of te opreor i known, te entapy at tate () an be deterined fro te following expreion: ( ) / η ( / ) Due to frition, tere will be preure drop a te refrigerant flow troug te evaporator, ondener, and piping onneting te variou oponent. e preure drop are ignored in ubequent alualtion for ipliity. 7-

- A vapor-opreion refrigeration wit irreveribilitie. Vapor Figure 7.- ow everal feature exited in atual vapor opreion yte.

3 Exaple Refrigerant 4a i te working fluid in an ideal vapor-opreion refrigeration yle tat ouniate terally wit a old region at 0. Saturated vapor enter te opreor at 0 and aturated liquid leave te ondener at 9 bar. e a flow rate of te refrigerant i 0.08 kg/. Deterine (a) te opreor power, in k, (b) te refrigeration apaity, in ton, () te oeffiient of perforane. Solution H H ondener Expanion valve Evaporator 4 opreor iquid 4 a b Ientalp 9 bar -0 o Vapor Speifi Internal Speifi Speifi ype ep reure Volue Energy Entalpy Entropy uality ae Ma /kg kj/kg kj/kg kj/kg/k R-4a Saturated Vapor R-4a Supereated Vapor R-4a Saturated iquid (a) e opreor work i give by ( ) (0.08 kg/)(4 9.7) kj/kg.44 k (b) e refrigeration apaity, in ton, i ( 4 ) (0.08 kg/)( ) kj/kg.4 k ton (.4 kj/)(60 /in).5 ton kj/in () e oeffiient of perforane i β Moran, M. J. and Sapiro H. N., Fundaental of Engineering erodynai, iley, 008, pg

region at 0. Saturated vapor enter te opreor at 0 and aturated liquid leave te ondener at 9 bar. e a flow rate of te refrigerant i 0.08 kg/.

4 Exaple Refrigerant 4a i te working fluid in an ideal vapor-opreion refrigeration yle tat ouniate terally wit a old region at 0. Saturated vapor enter te opreor at 0 and liquid leave te ondener at 9 bar and 0 o. e opreor a an effiieny of 80%. e a flow rate of te refrigerant i 0.08 kg/. Deterine (a) te opreor power, in k, (b) te refrigeration apaity, in ton, () te oeffiient of perforane. Solution Expanion valve H ondener Evaporator 4 opreor iquid 0 o -0 o 4 Ientalp 9 bar H Vapor Speifi Speifi Speifi ype ep reure Volue Entalpy Entropy uality ae Ma /kg kj/kg kj/kg/k R-4a Saturated Vapor R-4a Supereated Vapor R-4a opreed iquid 4 R-4a iquid Vapor Mixture (a) e opreor work i give by ( ) η (0.08 kg/) kj/kg. k (b) e refrigeration apaity, in ton, i ( 4 ) (0.08 kg/)( ) kj/kg.08 k ton (.08 kj/)(60 /in).44 ton kj/in () te oeffiient of perforane i β Moran, M. J. and Sapiro H. N., Fundaental of Engineering erodynai, iley, 008, pg

region at 0. Saturated vapor enter te opreor at 0 and liquid leave te ondener at 9 bar and 0 o. e opreor a an effiieny of 80%. e a flow rate of te refrigerant i 0.08 kg/.

5 Exaple Deign a refrigeration yte, wi upplie two level of aonia refrigerant at 0 o and at 0 o to two exanger requiring dutie of 850 and,500 k, repetively. Draw a proe flow diagra (FD) owing ajor equipent, flow rate in kg/ of refrigerant, duty of ea eat exanger, duty, and orepower of ea opreor. Alo, ow teperature and preure of all trea. ere are no inter-ooler between opreor. e opreed ga fro te lat tage opreor an be ooled to aturated liquid at 0 o. Ue 75% adiabati effiieny for all opreor. Solution ,, 4, 5 E, i F V F V E E Figure 7.- A two level refrigeration yte. A deign of a two level refrigeration yte i own in Figure 7.-. Saturated liquid aonia at i i partially vaporized troug a let-down valve V to and. art of te liquid eparated by te fla dru F i ued to provide te firt level refrigeration troug te eat exanger E. e reaining liquid pae troug a eond valve were it teperature and preure i redued to and. e liquid trea fro te eond fla dru F i ued for te eond level refrigeration troug te eat exanger E were it beoe aturated vapor. i trea i obined wit te aturated vapor fro te eond fla dru and opreed bak to preure. e proble an be olved eiter wit a reure-entalpy diagra of aonia a own in Figure 7.-4 or wit a progra olving an equation of tate to obtain terodynai propertie of a pure ubtane given any two oter propertie (for exaple, teperature and preure or aturation teperature). 7-5

dutie of 850 and,500 k, repetively. Draw a proe flow diagra (FD) owing ajor equipent, flow rate in kg/ of refrigerant, duty of ea eat exanger, duty, and orepower of ea opreor.

6 Ioter at i ritial point, i Saturated vapor Saturated liquid,,ideal Ientropi line,,, Entalpy Figure 7.-4 reure-entalpy diagra. e will ue te terodynai value fro a oputer progra a own in able 7.-. For ti exaple te preure drop aro te eat exanger and aro te fla dru will be negleted. Saturated liquid aonia at i 0 o i a defined tate at.67 Ma wit entalpy equal to.4 kj/kg a own in te firt line of te property table in Figure Siilarly, te aturated propertie of aonia at 0 o and 0 o an be obtained. e a flow rated of aturated liquid aonia,,, required to reove,500 k in eat exanger E i given by, 500k V,, kg/ In ti equation, V, and, are te entalpy of aturated vapor and liquid aonia at 0 o, repetively., i alo te liquid flow rate leaving fla dru F. e vapor flow rate, V,, leaving te eond fla dru F an be deterined fro te a and energy balane around valve V and fla dru F., + V, In ti equation i te aturated liquid aonia flow rate at and entering valve V. e energy balane i given by + ),,, + V, (, V, V, Solving for V, we ave 7-6

Siilarly, te aturated propertie of aonia at 0 o and 0 o an be obtained. e a flow rated of aturated liquid aonia,,, required to reove,500 k in eat exanger E i given by, 500k V,, 500 4

7 , V,, V,,, kg/ able 7.- erodynai propertie of aonia. Speifi Speifi Speifi ype ep reure Volue Entalpy Entropy uality ae Ma /kg kj/kg kj/kg/k Aonia Saturated iquid Aonia Saturated Vapor Aonia Saturated iquid 4 Aonia Saturated Vapor 5 Aonia Saturated iquid 6 Aonia Saturated Vapor 7 Aonia Supereated Vapor 8 Aonia Supereated Vapor 9 Aonia Supereated Vapor 0 Aonia Supereated Vapor Aonia Supereated Vapor e liquid flow rate troug valve V i ten kg/ e a flow rated of aturated liquid aonia, E,, required to reove 850 k in eat exanger E i given by E, 850k V,, kg/ In ti equation, V, and, are te entalpy of aturated vapor and liquid aonia at 0 o, repetively. e liquid flow rate,,, leaving fla dru F i te u of te liquid flow rate troug te eat exanger E and te liquid flow rate troug te valve V, E, kg/ Siilarly, te vapor flow rate, V,, leaving te firt fla dru F an be deterined fro te a and energy balane around valve V and fla dru F. V,, i V,, i kg/ e total a flow rate i of aonia required for te yte i ten i, + V, kg/ 7-7

467 Saturated Vapor 7 Aonia 9.4 0.65 0.4 50 5.467 Supereated Vapor 8 Aonia 5.64 0.65 0.465 56 5.57 Supereated Vapor 9 Aonia 8.85 0.65 0.8 59 5.46 Supereated Vapor 0 Aonia 87.57.67 0.47 68 5.

8 e vapor flow rate fro bot te exanger E and te fla dru F i given by, vap E, + V, kg/,vap e now deterine te orepower of te eond opreor. e aturated vapor leaving te eond exanger E and te fla dru F ut be opreed fro Ma to 0.65 Ma. For ientropi work, te ga entering and exiting te opreor will ave te ae entropy at kj/kg o K. e entalpy of te ga leaving te eond opreor due to ientropi opreion i 50 kj/kg. For 75% adiabati effiieny, te atual entalpy of te exiting ga i given by,atual 4 + (50 4)/ kj/kg e orepower required of te eond opreor i H.0764 (50 4)/ k 68 p e atual teperature of te exiting ga i obtained fro 0.65 Ma and,atual 56 kj/kg. e ave te ga leaving te eond opreor at 5.64 o tat ut be ixed wit te aturated ga leaving te firt eat exanger E and te firt fla dru F at 0 o. e entalpy of te ga entering te firt opreor i ten kj/kg At tee ondition ( 0.65 Ma, kj/kg) o and entropy kj/kg o K, te ga will be opreed to.67 Ma. e entalpy of te ga leaving te firt opreor due to ientropi opreion i 68 kj/kg. For 75% adiabati effiieny, te atual entalpy of te exiting ga i given by 5,atual ( )/ kj/kg e orepower required of te firt opreor i H.004 ( )/ k 54 p e ga leaving te firt opreor at.67 Ma, 5,atual 66. kj/kg, it teperature 5 i 00.8 o. e ga will be ondened to aturated liquid at 0 o (.67 Ma). e duty of te eat exanger E i given by.004 (66..4) 40 k 7-8

e entalpy of te ga leaving te eond opreor due to ientropi opreion i 50 kj/kg. For 75% adiabati effiieny, te atual entalpy of te exiting ga i given by,atual 4 + (50 4)/0.

Chapter 4. 4.3 Applications of Energy Balance

Chapter 4. 4.3 Applications of Energy Balance Capter 4 4. Appliation of Energy Balane We will diu exaple illutrating te analyi of erveral devie of interet in engineering, inluding nozzle and diffuer, turbine, opreor and pup, eat exanger, and trottling