Chpter 14 Gs-Vpor Mixtures nd Air-Conditioning Study Guide in PowerPoint to ccopny Therodynics: An Engineering Approch, 5th edition by Yunus A. Çengel nd Michel A. Boles
We will be concerned with the ixture of dry ir nd wter por. This ixture is often clled tospheric ir. The teperture of the tospheric ir in ir-conditioning pplictions rnges fro bout 10 to bout 50 o C. Under these conditions, we tret ir s n idel gs with constnt specific hets. Tking C p = 1.005 /K, the enthlpy of the dry ir is gien by (ssuing the reference stte to be 0 o C where the reference enthlpy is tken to be 0 /) The ssuption tht the wter por is n idel gs is lid when the ixture teperture is below 50 o C. This ens tht the sturtion pressure of the wter por in the ir-por ixture is below 12.3 kp. For these conditions, the enthlpy of the wter por is pproxited by h (T) = hg t ixture teperture T. The following T-s digr for wter illustrtes the idel-gs behior t low por pressures. See Figure A-9 for the ctul T-s digr. 2
The sturted por lue of the enthlpy is function of teperture nd cn be expressed s Note: For the dry ir-wter por ixture, the prtil pressure of the wter por in the ixture is less tht its sturtion pressure t the teperture. P P st @ T ix 3
Consider incresing the totl pressure of n ir-wter por ixture while the teperture of the ixture is held constnt. See if you cn sketch the process on the P- digr reltie to the sturtion lines for the wter lone gien below. Assue tht the wter por is initilly superheted. P When the ixture pressure is incresed while keeping the ixture teperture constnt, the por prtil pressure increses up to the por sturtion pressure t the ixture teperture nd condenstion begins. Therefore, the prtil pressure of the wter por cn neer be greter thn its sturtion pressure corresponding to the teperture of the ixture. 4
Definitions Dew Point, Tdp The dew point is the teperture t which por condenses or solidifies when cooled t constnt pressure. Consider cooling n ir-wter por ixture while the ixture totl pressure is held constnt. When the ixture is cooled to teperture equl to the sturtion teperture for the wter-por prtil pressure, condenstion begins. When n tospheric ir-por ixture is cooled t constnt pressure such tht the prtil pressure of the wter por is 1.491 kp, then the dew point teperture of tht ixture is 12.95 o C. 375 325 275 225 Ste T [C] 175 125 75 1.491 kp T DP 25-25 0 2 4 6 8 10 12 s [/-K] 5
Reltie Huidity, ϕ Mss of por in ir Mss of in sturted ir P P g g P nd P g re shown on the following T-s digr for the wter-por lone. 125 Ste 75 T [C] T T dp 25 P g = 3.169 kp P = 1.491 kp o Vpor Stte -25 0 2 4 6 8 10 12 s [/-K] P 1491. kp Since Pg P, 1 or 100%, 0. 47 P 3169. kp g 6
Absolute huidity or specific huidity (soeties clled huidity rtio), Mss of wter por in ir Mss of dry ir PVM PVM / ( R T) / ( R T) u u P 0. 622 0. 622 P P M P M P P P Using the definition of the specific huidity, the reltie huidity y be expressed s P P nd 0. 622 Pg ( 0. 622 ) P P Volue of ixture per ss of dry ir, V g R T P / g After seerl steps, we cn show (you should try this) V RT P 7
So the olue of the ixture per unit ss of dry ir is the specific olue of the dry ir clculted t the ixture teperture nd the prtil pressure of the dry ir. Mss of ixture ( 1 ) ( 1) Mss flow rte of dry ir, Bsed on the olue flow rte of ixture t gien stte, the ss flow rte of dry ir is V 3 / s 3 / s Enthlpy of ixture per ss dry ir, h H H h h h H h h 8
Exple 14-1 Atospheric ir t 30 o C, 100 kp, hs dew point of 21.3 o C. Find the reltie huidity, huidity rtio, nd h of the ixture per ss of dry ir. P 2.548 kp 0.6 or 60% P 4.247 kp g 2. 548kP 0. 622 0. 01626 ( 100 2. 548) kp h h h Cp, T ( 25013. 182. T) o o 1005. ( 30 C) 0. 01626 ( 25013. 182. ( 30 C)) o C 7171. 9
Exple 14-2 If the tospheric ir in the lst exple is conditioned to 20 o C, 40 percent reltie huidity, wht ss of wter is dded or reoed per unit ss of dry ir? At 20 o C, Pg = 2.339 kp. P P 0. 4( 2. 339 kp) 0. 936kP g P 0. 936kP w 0. 622 0. 622 P P ( 100 0. 936) kp 0. 00588 The chnge in ss of wter per ss of dry ir is, 2, 1, 2, 1 2 1 ( 0. 00588 0. 01626) 0. 01038 10
Or, s the ixture chnges fro stte 1 to stte 2, 0.01038 of wter por is condensed for ech of dry ir. Exple 14-3 Atospheric ir is t 25 o C, 0.1 MP, 50 percent reltie huidity. If the ixture is cooled t constnt pressure to 10 o C, find the ount of wter reoed per ss of dry ir. Sketch the wter-por sttes reltie to the sturtion lines on the following T-s digr. T At 25 o C, P st = 3.170 kp, nd with 1 = 50% s P P 0.5(3.170 kp) 1.585 kp,1 1 g,1 o T T 13.8 C dp,1 st @ P 11
w 1 P, 1 15845. kp 0. 622 0. 622 P P ( 100 15845. ) kp 0. 01001, 1 Therefore, when the ixture gets cooled to T 2 = 10 o C < T dp,1, the ixture is sturted, nd = 100%. Then P,2 = P g,2 = 1.228 kp. 2 w 2 P,2 1.228 kp 0.622 0.622 P P (100 1.228) kp 0.00773,2 The chnge in ss of wter per ss of dry ir is, 2, 1 2 1 ( 0. 00773 0. 01001) 0. 00228 12
Or s the ixture chnges fro stte 1 to stte 2, 0.00228 of wter por is condensed for ech of dry ir. Stedy-Flow Anlysis Applied to Gs-Vpor Mixtures We will reiew the consertion of ss nd consertion of energy principles s they pply to gs-por ixtures in the following exple. Exple 14-3 Gien the inlet nd exit conditions to n ir conditioner shown below. Wht is the het trnsfer to be reoed per dry ir flowing through the deice? If the olue flow rte of the inlet tospheric ir is 200 3 /in, deterine the required rte of het trnsfer. 13
Before we pply the stedy-flow consertion of ss nd energy, we need to decide if ny wter is condensed in the process. Is the ixture cooled below the dew point for stte 1? P P 0.8(4.247 kp) 3.398 kp,1 1 g,1 o T T 26.01 C dp,1 st @ P So for T 2 = 20 o C < T dp, 1, soe wter-por will condense. Let's ssue tht the condensed wter lees the ir conditioner t 20 o C. Soe sy the wter lees t the erge of 26 nd 20 o C; howeer, 20 o C is dequte for our use here. Apply the consertion of energy to the stedy-flow control olue Q ( h V gz) W ( h V 2 2 net i i net e gz) 2 2 inlets Neglecting the kinetic nd potentil energies nd noting tht the work is zero, we get Q h h h h h net 1 1 1 1 2 2 2 2 l2 l2 Consertion of ss for the stedy-flow control olue is inlets i exits e exits e 14
For the dry ir: For the wter por: 1 2 1 2 l2 The ss of wter tht is condensed nd lees the control olue is l2 1 2 ( 1 2), then Q net h 1 1h 1 h 2 2h 2 ( 1 2) hl 2 Q net h 2 h 1 2h 2 1h 1 ( 1 2) hl 2 Q net C ( T T ) h h ( ) h Diide the consertion of energy eqution by p 2 1 2 2 1 1 1 2 l2 15
Now to find the 's nd h's. P 0.622P 1 0.622(3.398) 1 P P 100 3.398 1 1 0.02188 P 2 2 g2 2 ( 0. 95)( 2. 339 kp) 2. 222 kp 0. 622P 2 0. 622( 2. 222) P P 98 2. 222 2 2 0. 01443 16
Using the ste tbles, the h's for the wter re h 1 2555.6 h 2 2537.4 h l 2 83.91 The required het trnsfer per unit ss of dry ir becoes Q net C ( T T ) h h ( ) h p 2 1 2 2 1 1 1 2 l 2 o 1.005 (20 30) C 0.01443 (2537.4 ) o C 0.02188 (2555.6 ) (0.02188 0.01443) (83.91 ) 8.627 17
The het trnsfer fro the tospheric ir is q out Q net 8.627 The ss flow rte of dry ir is gien by V 1 1 1 0.287 (30 273) K P (100 3.398) kp 3 RT1 K kp 1 0.90 3 3 200 in 222.2 3 in 0.90 18
Q q out out 1in 1kWs 222.2 (8.627 ) in 60s 31.95kW 9.08Tons The Adibtic Sturtion Process Air hing reltie huidity less thn 100 percent flows oer wter contined in well-insulted duct. Since the ir hs < 100 percent, soe of the wter will eporte nd the teperture of the ir-por ixture will decrese. 19
If the ixture leing the duct is sturted nd if the process is dibtic, the teperture of the ixture on leing the deice is known s the dibtic sturtion teperture. For this to be stedy-flow process, keup wter t the dibtic sturtion teperture is dded t the se rte t which wter is eported. We ssue tht the totl pressure is constnt during the process. Apply the consertion of energy to the stedy-flow control olue Q ( h V gz) W ( h V 2 2 net i i net e gz) 2 2 inlets Neglecting the kinetic nd potentil energies nd noting tht the het trnsfer nd work re zero, we get exits h h h h h 1 1 1 1 l2 l2 2 2 2 2 Consertion of ss for the stedy-flow control olue is inlets i exits e e 20
For the dry ir: For the wter por: 1 2 1 l2 2 The ss flow rte wter tht ust be supplied to intin stedy-flow is, l2 2 1 ( ) 2 1 Diide the consertion of energy eqution by, then h h ( ) h h h 1 1 1 2 1 l2 2 2 2 Wht re the knowns nd unknowns in this eqution? Soling for 1 1 h 2 h 1 2( h 2 hl 2) ( h h ) 1 l2 C ( T T ) h p 2 1 2 fg2 ( h h ) g1 f 2 21
Since 1 is lso defined by We cn sole for P 1. P P P 1 1 0. 622 P 1 1 1 1P1 0. 622 1 Then the reltie huidity t stte 1 is 1 1 P Pg 1 22
Exple 14-4 For the dibtic sturtion process shown below, deterine the reltie huidity, huidity rtio (specific huidity), nd enthlpy of the tospheric ir per ss of dry ir t stte 1. 23
Using the ste tbles: Fro the boe nlysis 1 h h f 2 h 1 fg 2 C ( T T ) h p 2 1 2 fg 2 ( h h ) g1 f 2 67.2 2544.7 2463.0 o 1.005 16 24 C 0.0115 (2463.0 ) o C (2544.7 67.2) 0.00822 24
We cn sole for P 1. Then the reltie huidity t stte 1 is 1 P P P 1 1P1 0.622 0.00822(100 kp) 0.622 0.00822 1.3kP P 1 1 P g1 o st @24 C The enthlpy of the ixture t stte 1 is h h h 1.3kP 0.433 or 43.3% 3.004 kp 1 1 1 1 C T p h 1 1 1 o 1.005 (24 C) 0.00822 2544.7 o C 45.04 1 25
Wet-Bulb nd Dry-Bulb Tepertures In norl prctice, the stte of tospheric ir is specified by deterining the wetbulb nd dry-bulb tepertures. These tepertures re esured by using deice clled psychroeter. The psychroeter is coposed of two theroeters ounted on sling. One theroeter is fitted with wet guze nd reds the wetbulb teperture. The other theroeter reds the dry-bulb, or ordinry, teperture. As the psychroeter is slung through the ir, wter porizes fro the wet guze, resulting in lower teperture to be registered by the theroeter. The dryer the tospheric ir, the lower the wet-bulb teperture will be. When the reltie huidity of the ir is ner 100 percent, there will be little difference between the wet-bulb nd dry-bulb tepertures. The wet-bulb teperture is pproxitely equl to the dibtic sturtion teperture. The wet-bulb nd dry-bulb tepertures nd the tospheric pressure uniquely deterine the stte of the tospheric ir. 26
The Psychroetric Chrt For gien, fixed, totl ir-por pressure, the properties of the ixture re gien in grphicl for on psychroetric chrt. The ir-conditioning processes: 27
28
Exple 14-5 Deterine the reltie huidity, huidity rtio (specific huidity), enthlpy of the tospheric ir per ss of dry ir, nd the specific olue of the ixture per ss of dry ir t stte where the dry-bulb teperture is 24 o C, the wet-bulb teperture is 16 o C, nd tospheric pressure is 100 kp. Fro the psychroetric chrt red 44% g 8. 0 0. 008 h 46 3 0. 853 29
Exple 14-6 For the ir-conditioning syste shown below in which tospheric ir is first heted nd then huidified with ste spry, deterine the required het trnsfer rte in the heting section nd the required ste teperture in the huidifiction section when the ste pressure is 1 MP. 30
The psychroetric digr is 0.050 Psychroetric Digr 0.045 0.040 Pressure = 101.3 [kp] Huidity Rtio 0.035 0.030 0.025 0.020 0.015 0.010 0.005 h 1 =17 / 1 0 C h 3 =48 / h 2 =37 / 10 C 0.000-10 -5 0 5 10 15 20 25 30 35 40 1 =0.793 ^3/ T [C] 20 C 3 2 0.8 30 C 0.6 0.4 0.2 3 =0.0091/ 1 = 2 =0.0049 / Apply consertion of ss nd consertion of energy for stedy-flow to process 1-2. Consertion of ss for the stedy-flow control olue is inlets i exits e 31
For the dry ir 1 2 For the wter por (note: no wter is dded or condensed during siple heting) Thus, 1 2 2 1 Neglecting the kinetic nd potentil energies nd noting tht the work is zero, nd letting the enthlpy of the ixture per unit ss of ir h be defined s we obtin h h h E in E out Q in h1 h2 Q ( h h ) in 2 1 32
Now to find the nd h's using the psychroetric chrt. At T 1 = 5oC, 1 = 90%, nd T 2 = 24 o C: The ss flow rte of dry ir is gien by V 1 1 33
3 60 in 1in 7566. 1261. 3 in 60s s 0. 793 The required het trnsfer rte for the heting section is Qin 1261. ( 37 17) s 2522. kw 1kWs This is the required het trnsfer to the tospheric ir. List soe wys in which this ount of het cn be supplied. At the exit, stte 3, T 3 = 25 o C nd 3 = 45%. The psychroetric chrt gies 34
Apply consertion of ss nd consertion of energy to process 2-3. Consertion of ss for the stedy-flow control olue is inlets i exits e For the dry ir 2 3 For the wter por (note: wter is dded during the huidifiction process) 2 s 3 s 3 2 ( ) s 3 2 1261. ( 0. 0089 0. 0049) s 0. 00504 s 35
Neglecting the kinetic nd potentil energies nd noting tht the het trnsfer nd work re zero, the consertion of energy yields Soling for the enthlpy of the ste, E in E out h h h 2 s s 3 h ( h h ) s s 3 2 ( ) h ( h h ) h 3 2 s 3 2 s 2750 h s h h 3 2 3 2 (48 37) (0.0089 0.0049) 36
At P s = 1 MP nd h s = 2750 /, T s = 179.88 o C nd the qulity x s = 0.985. See the text for pplictions inoling cooling with dehuidifiction, eportie cooling, dibtic ixing of irstres, nd wet cooling towers. 37