INDUSTRIAL AND ENGINEERING CHEMISTRY
968
-
1
-7-j
-
AT,< TG
-.:ilt chnngw the equilibrium conditions, because each concentra. tion of a salt solution has its own vapor pressure-temperature relntion which is different from that of pure m t c r , and it also add> the heat of solution for the ,salt. The equilibrium condition? rill continue to change until the bulb-m-etting liquid become2 wturnted with salt. At this point a ne!\- equilibrium condition exists a t an entirely different n-et-bulb temperature, which is called n saturated salt solution net-bulb tempcrature, t,. If t>he solution 011 the n-r:t bult) is not saturated. its composition nil! ' clianx stc~nclilyas evaporation proceeds. .In equation for this condition nould he too dificult to use because the salt Concentration arid v:ipor pressure for that solution n.ould have to be knowr-n lor each \\-et-bulb tcmperature readinq. If n-et-bulh memurements arc made with 3 baturated salt solw tion, diffusion of water vapor into the air stream will cause parr 8)f the salt to crystallize out of solution. This crystallization is A continuous equilibrium pror.css in menswing a salt-bulb temperat u r e and must be considered in the heat balance as the heat o: cryitallization. q,: A,Tr
h,k,.4
ill'
50
70
60
80
CA LCUL AT E D
90
100
110
T E M PE R AT UR E
120
balances may be arranged. On the one hand, heat is removed from the \\--et bulb by vaporization of the 11-ater; on the other. heat is gained by convection and radiation from the surrounding air and walls. It was shown that, with a sufficiently high air velocity, the radiation effect on an unshielded bulb is negligihli~ (I, 4 , 6 , 10) and \Till be neglected in this derivation. I n the case of a bulb wet wit,h pure water, the heat transferrcil hy vaporization of the rvater 111
q =
+ qc
c;
h=litE -
fi)
7
t q,
q' = f Y k , A ( / h - pL.. =
Aik,d(
, tr
0:
2'
llization per pCJulld of i\-attA* heat evolved by cr evaporatrd from saturated iolution
'The equ:ition tlicii
I w i
/'i - / I 9 )
(Xi
-
)mea:
=
/?.a(fG- fi!
Ck,ds PI - pg!
I !t
1 .
ii k,
/ ' ) Ipj - pol = - [ i, - iii
i
10
S i n c e the interface conditions pi, t t ! and X i are for saturated salt solutions, t,hey are indicated as p r , is, and A,. Therefore, the final Corm of the equation hecomes:
'As -
and under equilibrium conditions must equal the sensible hen1 rwansierred to the wet bulb from the air: fi)
=
/I,)
Thtb quantity of qc is dependent upon the rate of evaporation thc \\-ater and is related to that rate as follows:
wlierc f '
q = hdit, -
-
I /Ib
130
Ts -'F.
Figure 1. Comparison of Derived and Experimental W e t Rulb Temperatures with Saturated Sodium Xitrate Solutions
q = XiTV
Vol. 38, No. 9
c')
(TI4
-
/IQ)
=
' / k,
- t.)
Ill
(21
Therefore (2, I l ) , X j W = hd(t0 - ti)
(31
Since W is the rate of vaporization, the following relation may I)(, jet up according t o Fourier's law (8):
w = k,A(pi
1
- p,)
The heat, relation then becomes: Xi(pi
- p G ) k p 4 = hA(i, - ti)
1,
51
Let us suppose that a water-soluble salt is being dried in a rotary dryer, and the bulk of the air contains some entrained particlch of salt. If these particles of salt come in contact with the wet bulb of the thermometer, the standard humidity equations will not be valid until corrections have been made for the effect of the 3alt ( 2 2 ) . The first effect t o be considered is the transfer of 3ensible heat from the particles of salt to the lvet bulb. Since the sensible heat in the salt striking the wet bulb is such a small percentage of the total sensible heat transferred by conrection from the air stream, it can be neglected or ronsidered as being a part of the air. In either case the t,otal heat, q, transferred t o the a e t bulb will be such that adiabatic conditions are maintained. The second effect t o be considered is the heat of solution. .is the particles of salt impinge on the wet bulb, they tend to dissolve as long as the bulb-wetting liquid is not saturated. The dissolvrd
Figure 2.
Relation of 3Ieasured Vet-Bulb Temperature*
w ith Values Calculated from the 3Iethod for Salt Solution.
by Williams ( 1 2 )
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1946
969
p is small in comparison t o unity, and Equation 12 becomes, approximately,
H =
Thej also say: " n i t h i n a smaller error, humidities are proportional to partial pressures, and humidity diherences are proportional t o partial pressure differences." In the condition of this work, p a is lower than p , and this s u b stitution will be even more accurate, Replacing partial presures p , and p s b! the corresponding humidities H and H,, Equation 11 becomes:
----t
fl, - H
Figure 3.
18 p0 2n
idiabatic R et-Bulb Lines with Saturated Sodium Xitrate Solution-
=
_ _ - ~h_-
/,.,,
c') ( t o -
f8'
'131
K i t h Equations 11 and 13 it is possible t o calculate data for constructing humidity chartq for various saturated salt bolutions. .ictual substitution of Equation 12 in Equation 11 results in the folloiring:
[(;:?J]+;;Hj] -[(,
H H \Then pure water is used as the bulb-netting liquid, the partial 11 uressure of \rater vapor a t the interface, p,, is greater than the = ~ - I ~ l- 'I L 14) partial pressure of n a t e r vapor in the main body of the air c nhere the t n o partial prer-tream, except at 1 0 0 ~ satmation, Honever, this equation is rather cumbersome and is unnecessary -ures are equal. Pllder leas than saturated nater tor most purposes. vaporizes from the net-bulb thermometer continually; p , 1% Values of C may be obtained from the literature (3, ;, 41 o r ilwa>s greater than p,, and tu 1' alryays above t t . physlco-chemical techniques. 'nay be If, hojyever, a saturate& >alt solution 1s used as the bulb-netring liquid, the partial pressure of nater vapor a t the interface, EXPERIVEhTAL PROCEDURE u,, is lower than nhen pule n a t e r is ubed as the bulb-netting iiquid. K i t h the loner partial pieswre for the saturated salt A forced circulation dryer was used to produce a high air velocaolution, p , becomes equal t o and finally greater than PS as th( ity for the n e t - and dry-bulb temperature readings. The dryer u r approaches 100% saturation. Simultaneouqly the t c m p r i ~ a eqq u i p p d Kith steam heat 50 that the temperature could hfa cure of the saturated salt solution wethulb thermometer, tr, becomes equal T U and finally greater than the temptwT . ~ B LI.E wre of the air, f,. P,, \Then p . is less than p o , Tvater vapoi. 11m. P;. B.T.U./ Xu, As. Mm. Run T, n.T.cT.r Tu. T., Giiffuses frQm the air stream to t h e So. F. F. F. Hg Lb. Lh. Hg salt solution xet-bulb thermometer. 71.2 67.5 73.8 17.2 16.8 1054.1 1050 7 16.1 53.9 73 7 zo.9 63 7 15.1 69.8 13.3 1056.1 1052 8 14.2 52.8 ii9 0 Therefore, with a n excess of salt on 13.2 65.6 71.8 16.1 14.2 1055.1 1051 7 15.1 53.4 71 1 73.2 67.2 73.4 17.1 15.5 1054.3 10.50 9 15.9 53.8 72.9 the wet bulb and water vapor diffu572.5 68.4 74.6 17.8 1050.2 16.5 e4.1 74.0 16 2 1053.6 ing t o the wet bulb, part of the eweas 71.9 69.4 75.7 18.4 17.i 1053.1 1049.7 17.1 04.4 75.2 73.2 6 7 . 1 73.6 17.0 15.4 1054.3 1030.8 1 6 . 0 53.9 72.8 ialt must dissolve if the bulb-netting 79.5 72.1 20.2 79,l 18.3 1051.5 1047.8 18.9 5S.2 78.3 80.1 22.9 75.9 83.0 20.9 1049.6 1045,6 21.4 56.4 81.6 liquid is t o remain saturated. This in81.1 77.5 84.7 24.1 23.4 1048.7 1044.7 22.5 56.8 84.7 troduces the heat of solution effect on 11 86.7 81.9 9 2 . 8 30.7 30.3 1044.7 1040.3 28.8' 59.1 92.6 :he wet-bulb thermometer instead of 12 83.1 81.3 89.0 27.4 26.9 1046.6 1042.4 25.7 58.0 88.6 13 8 8 . 2 8 7 . t 9 4 . 8 3 2 . 6 3 2 . 2 1043.6 1039.2 3 0 . 6 5 9 . 5 94.6 The heat of crystallization. However. 14 92.1 '31.0 99.9 37.5 37.0 1041.3 1036.4 35.1 61.0 99.7 15 91.9 90.9 99.5 37.1 36.6 1041.4 1036.5 34.7 60.8 99.2 d l other heat and weight effects are 16 94.5 9 3 . 5 102.7 40.2 40.0 1039.9 1034.8 37.8 61.8 102.6 17 also in the reverse direction, and Equa99.1 9 8 . 2 108.0 46.2 46.4 1037.3 1035.9 43.2 63.3 108.4 18 9 4 . 3 104.2 98.3 41.3 40.0 1039',5 1034.0 39.3 62.2 103.5 rion 11 holds for diffusion in either di19 101.7 9 5 . 5 105.8 42.9 41.3 1038.8 1033.1 40.7 62.5 105.3 rection, since the signs of the quanti20 105.8 96.8 107.1 44.6 42.2 1038.1 1032.4 42.2 63.0 106.8 21 1 0 7 . 8 9 0 . 5 100.9 36.7 32.1 1041.6 Lies mutually cancel. 1036,8 36.1 61.3 99.2 22 106.7 9 2 . 3 102.7 38.8 35.1 1040.6 1034.8 37.8 6 1 . 8 101.4 Qince humidity H m-as defined ( 2 , 11 I 23 1 0 9 . 4 107.4 118.9 61.2 60.7 1032.2 1025.7 58.2 66.6 118.9 24 1 0 6 . 5 102.9 1 1 3 . 9 53.6 52.6 1034.7 1028,6 50.6 65.0 113.2 2s pounds of water vapor per pound nf 23 1 0 7 . 8 1 0 6 . 3 117.7 61.8 58,9 1032.8 1026.4 56.3 66.1 117.r 26 116.0 108.3 1 2 0 . 4 62.8 60.8 1031.7 1024.9 'try air, it follow that 60.7 67.0 119.8
H =
18 Pa 29 (1 - poi
121
Badger and McCabe ( 2 ) state that under ordinary temperature conditions,
27 28
118.8 1 0 6 . , 122.2 1 0 8 . 9
118.8 121.5
.59 9 63.8
56.8 60.4
1032.6 1031.4
1023.7 1024.3
58.0 62.5
66.4 67.8
118.1 120.3
29 30 31 32 33 34 35 36 37
122.2 121.5 120.7 122.2 75.0 125.4 127.9 124.0 126.0
117.5 118.6 106.5 123.3 74.7 113.4 117.7 123.4 112.8
57.1 50.2 41.9 67.2 17.6 52.2 58,7 69.3 50.2
02.8 45.0 37.6 64.3 l5,9 46.1 33.1 65.1 44.9
1033.5 1035.9 1039.2 1030.4 1058.3 1035.2 1033.0 1029.8 1033.6
1026.5 1029.3 1032.7 1023.3 1050.2 1028.9 1026.4 1023.2 1029.2
.56.0 48.8 11.7 65.8 16.6 49.8 j6.8 66.0 49.1
66.1 64.6 62.8 67.8 54.1 64.9 66.1 67.9 64.7
116.5 111.7 106.4 122.6 73.9 113.2 117.3 123.1 112.5
105,l 100 8 94 8 110.7 68 2 102.0 106.0 111.7 104.8
970
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 38, No. 9
SODIUlI NITRATE SOLUTION
I n order to compare this work with the previous incestigation using qaturated salt solutions (I$j, experimc,nts \vc:re rc~1ii::lted using ,saturated sodium Ilitrat(' .solutions as t h t l tiulb-u-cstting liquid for net-hulb trmp e ~ t i i r emrasurc~mcnta. This s:ilt solution exerts a vapor iirt's6urc Io!vcr than that of pure bvater, and the hear of cry6talliz:tt ion nmounts to approximately 5Cb of the Intcwt heat o f cwporation of water. S o hydrates of sodium nitrat>e arc formed over the trmperatiirc: rnngc used in these determinations. 'I'hc experimental data arc givcri in Table I and corrc'I:itecl in Figure I . The data .cover a dry-bulb range from ? l o to 120" F. and a corresponding wet-bult) r:ingc: from 64' to 112" F. The wet-bulb temperature dcpresuion.. varied from 1" to 26' F., and the temperaturr ri.w ni t h e salt solutioii effect varied from 6.1" to 12.6" F. TEMPERATURE -OF. I.;xcellent agreement vas obtained in the rorrelatioii Figure 4.. Vapor Pressure Curves for Saturated Solri tione rif the experimental values for t s with those dtlrived by of Salts using Equation 11. The agreements Tsere good when t,lic ridt solution n et-bulb temperatures iwre both u b o w : i r d tielon. the air miwn .temperatures. K h e n cxperimeriial I , adjusted to the desired range. To vary tlic v a ~ i o r~ J H 'Y! (JI \vas lirlon t)he air temperature, the values were 0.1" to 1.7" F. water in the air stream, water was sprayed upon ihc, sur of a :ibovc. t,hosc calculated from Equation 11. With t a above the *team-heated preheater located at the air intakc of t h r dryer. air. temperature, the experimental values were from 1.4' l o w x Thus the humidity of the :iir as well as the tempernture could he to 0.45" F. higher than the calculated ones. This correlation adjustrd. is good and tends to subistantiate the correctnesp of the portuThree t,liermomett.rs for measuring the dry-bulb, n : i t e r \vc.t,in lated equ:ition. bulb, and salt solution net-bulb temperatures were m T O T h e ~ edata vivert: further oorrelated by the empirical mothuti t,he end of the 6-inch-diameter exhaust air duct of the d (18) proposed by IVilliams and Williams (Figure 2 ) . Good agreeprotect the thermometers against radiation, black sh td ment \vas obtained: The empirical results were from 0.1" to plates were soldered in the duct between each thermometer and 3.6"F.lon-er than the experimental water wet-bulb temperatui,es parallel to t>heair stream. The air velocity was maint:iiripd at I n this correlation the hrats of crystallization were neglected beapproximately 2100 feet pcr minute, which also minimized r:idiacause thv heat produced by salt crystallization was considered t,ion effects. nepligitilp cwmpiretl t r i thr lntmt, heat of vaporization for n-ater. The w a t v \vet bulb was u e t with distilled \sat,er a t thv \vetbulb temperature. The solution wet bulb was wet with a solution of a reagent grade salt; the salt had been 'raB1,E 11. I ) X ~ . XW K A M M O S I I : ~SITRATE SOLUTIOXS s a h r a t e d a t a temperature higher than Pu.. Po. XIL., XI Pa, C, T8 the solution wet-bulb temperature and Run T. T,, Ta, Mrn. \Im. H.T,Li./ B . T . ~ . / M m . B.T.U.; Calcd., No. a F. F. ' F. Ng Fie Lh. Lb. Hg Lb. F. then cooled to the solution wet-bulb 107.2 30.4 219.5 1041.8 1033.1 36.3 * 3 X 4 100.8 90.1 105.8 temperature. The salt solutions used 1 106.1 1033.5 29.8 218.9 32 -7 1042.3 35.3 89.2 104.9 100.0 2 112.6 1030.0 33.3 226.0 in this research were sodium nitrate, 3 105.0 93.8 110.3 1039.5 $0.3 3 7 . 4 114.6 1029.6 34.6 229.0 1039.c 42.4 39.2 112.1 95.2 107.R 4 ' ammonium nitrate, and magnesium 230.2 115.6 1029.1 35.1 1038., 3 Y . Y 43.1 108.0 9 5 . 7 112.9 5 114.9 1029.3 35.0 229.5 1039.0 42.4 39.9 chloride hexahydrate. 6 104.7 9 5 , 2 112.7 220.3 107.2 30.9 1034.6 10 . 8 32.5 103.6 90.0 106.7 1.!? 7 125.2 10 . O 1023.2 44.1 2 5 5 . 4 .52:1 I n taking the experimental data, the 8 106.5 104.2 123.3 .ia.H 127.7 1022.9 44.6 246.3 IO .8 S.6 56.2 9 106.7 104.5 123.8 dry-bulb, water wet-bulb, and satu127.9 1022.5 45.3 247.5 56.0 10 .i 56.5 10 106.7 104.7 124.5 rated salt solution wet-bulb tempera65.3 10.3 156.0 1055.4 1059.6 12.1 8.7 11 7 0 . 5 57.4 6 5 . 1 156.6 65.6 10.5 1055.1 8.9 10,59.,5 tures were determined simultaneously 12 70.9 57.8 65.7 12.2 67.8 1053.9 11.2 IbO.5 1058.4 13.1 10.0 67.8 59.6 1 3 71.8 and under the same heat and air con162.0 68.8 1 1 . 5 10.58.0 1053.4 lo.,; 1 3 . : 68.9 60.3 72.0 14 163.0 69.5 11.7 1053.0 1057.6 10.9 13., 72.2 61.0 69.5 ditions. Before a solution wet-bulb 13 162.3 68.9 11.6 1053.3 1057.Y 10.5 13.5 6 9 . 1 6 0 . 5 72.3 16 114.2 34.3 228.0 1029.8 $0.8 1039.1 temperature was taken, the bulb was li 100.5 9.5.0 111.7 42.2 252.5 131.0 48.5 1032.4 1020.6 59.8 60.2 I8 108.6 106.9 127.8 wetted several times and the salt solu236.6 119.2 38.6 1026.8 1037.1 45.8 47.1 103.5 48.6 117.1 19 119.0 38.2 235.8 1027.0 1087.2 45.5 46.8 tion allowed to evaporate until free 20 103.3 98.4 106.6 salt was present. This ensured the 21 88.3 7 1 . f i 83.6 lY.8 13.6 1051.9 1045.3 17.8 185.5 82.: 22 84.7 70.9 82.6 19.3 13.8 1052.3 1045.9 17.2 183.8 81.1 presence of excess salt when the t,em23 91.8 7 7 . 0 90.0 23.8 20.0 1048.9 1041.8 21.1 195.0 89.3 90.3 21.5 196 04 1041.4 1048.fi 20.2 24.2 93.8 77.7 90.7 p e r a t u r e d e t e r m i n a t i o n was made. 24 92.7 1040.2 22.8 200.0 IO4i.i 25,, 21.0 97.3 79.3 93.0 25 195.0 89.6 1041.8 2 1 . 1 1048.8 When the salt solution wet-bulb tem26 20.4 90.7 77.2 90.0 23.9 96.2 24.3 204.0 1038.7 1045.8 26.7 28.5 95.8 82.6 27 89.4 perature was above the exhaust air 208.0 99.0 25.8 1037.1 1044.E 2 9 . 2 30.4 89.2 84.6 98.5 28 29 89.4 84.8 98.8 30.6 29.4 1044.t 1037.0 26.0 208.8 99,l temperature, i t was impossible t o main30 108.6 103.6 124.8 R4.7 53.4 1034.2 1022.4 45.5 246.7 126.5 tain a n excess of salt for any long ,
period of time on the u e t bulb by this method, because water condensed on the bulb. Therefore, readings for the salt Jolution wet-bulb temperatures that iverc above the exhaust air temperature may be slightly low because of the difficulty of maintaining saturated conditions.
31 32 33 34 35
36 37 38 39 40
108.5
109.3 109.2 86.5 86.1 71.6 73.6 75.4 78.1 80,s
95.0 113.5
100.0 102.0
76.8 77.0 64.8 137.8 69.8 74.4 77.5
120.0
121.9 89.1 88.9 23.4 (6.8 79.5
85.1 89.2
42.2
38.i
49.2 *52.2 23.6 23.8 15.7 17.3
46.7 50.3 21.1 21.4 13.8 15.8 17.2 20.8 23..3
18.7
21.8 24.2
1038.1 1036.3 1033.2 1049.0 lo&%(! 105t5.L, 1054.0 1052.8 1050.4 1048.7
1028.8 1025.1 1024.1 1042.2 1043.0 1050.9 1049.0 1047.6 1044.5 1042.3
35.7 41.2 42.7 20.6
231.0 240.8 243.5 1P3.8 193.5 20.5 13.2 169.3 14.6 174.4 15.8 179.0 18.5 187.8 20.7 194.0
114.7 121.6
124.3 88.7 88.9 23.6 (7.2 79,s
85.2 89.2
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1946
I
Figure 5.
1 Heat of Cryatallisat ion.. from Aqueous Solutions
'This ;issumption is applicable to salts having loiv heats of crystallization, but it does not apply when the lient of rrystallization is large in comparison t o the latent heat 01 w i t e r . The purpose of the empirical relation (12) is to convert the experimental salt solution wet-bulb temper:iturw t o water wetI,ulb temperatures by isobaric reading.- from the respective vapor pressure curves; this relation is R sitisfactory :ipproximation for dalt solutions with small vapor pressure lowerings, but is not satisfactory when the vapor pressure lowering is large. .\ humidity chart (Figure 3) was constructed for satur:tted solutions of sodium nitrate, using derived Equation 11 as the basis of calculation. This new humidity chart is of considerable value when it becomes necessary t o make heat or moisture halances in clrying the salt.
37 1
temperatures varied from 65.1' to 127.8' F., : i d the tcmperature rise due to the salt solution effect varied from 7.7" t'tr '20.9' F. The salt solution net-bulb temperatures varied from less than the air temperature to as much as 18.3" F. iibove the air strenm temperature, f,, If a wet-bulb thermometer became coated with ammonium nitrate or a similar salt during psyclirometric measurements, the wet-bulb temperature n-ould indicatc :in :Ihsolutc humidity which would be in error by :tpproximatcly 300"; for the lowest vxt-bulb temperature reziding, and it would hi, irnposqihle t o determine the humidity for tho maximum \vetl)ulIi temperature hrc.:iusc it would read 18.3" F. :iI)ovt>t l i ( , drybrill^ rc.mperature of 109.t30F. By applying the t hrory devvioped earlier, it ctil~rchtio1iof the cxl)ei,imental salt solution ivct-bulb trmperaturc~with t h c t ~ o r r ~ l -pon(liiig drrived values gave good agrermerit, :is indiwtcd i n Figiire 6. 'The agreement w:ts good ivhen the salt solution wt:tbull) temperatures, t,?,viere both :itiove and belon. the roi ing dry-bulb temperatures, t,. K h c n the expcrimcntal 1, valuw WI'C h d o w f,, they ranged from 0.2" less than to 0.9" F. greater thnn the d u e s calculated from the theoretical cquation. With tr above ,L the experimental values vnried from 0.3' greater thnn t o 3.8" F. less than the corresponding derived values. The gre:itest dcviutions occurred at higher wet-bulb temperatures xhen t s x i s greater than to. It is supposed that tvater vapor condensing on the wet bulb made it more difficult t o maintain H saturated salt solution on the wet-bulb thermometer. If the salt solution on the wet bulb is not saturated, i t gives R higher vapor pressure and, consequently, t s will be too low (Figure 6). \Then these data were correlated by the method of the previous investigators ( 1 2 ) , the results were not so satisfactory. I n this (,orrelation (Figure 2 ) the empirical results were from 3.7' to 7.4' F. lower than the Corresponding experirncntal w:itvr w e t bulb tcmperatures. In the correlation of the d:it:i :is proposed iii this report, the variation was from 0.2" less than t o 0.9" F. greater than the calculated theoretical values when ts was less than fs. When t. \v:iw greater t h m to, the experimental values varied from 0.3" greater than t o 3.8" F. less than the values calculated from the*
AhIMONIUM NITHA
.\iiinionium nitrate was chosen :is :I solutt. IIJI.wlt solut ion wet-bulb measurements bec:ius;e of it. high o f crystallization and the relatively Ioiv vapor urci obtained over its saturated solutions. T h t ~ cfftsrt the two variables could therefoi,c t)c combincd, :md a maximum deviation c ~ ~ u l lt lx c~spectcrl iron1 the‘ postulated equaticn. It. v:ipor 1)rt'sw-t.tenilwr:itru,e relation (Figure 4) is rnricli Icin.er th:in t t ~ : - i t I I ~water or sodium nitrate solutions. :ind thc h w r of crystallization (Figure 5j is liigIi--:i]~i)i,~)~im;itc,ly 20yc of the Intent heat of vaporimtioii for \v:iii,r, :'\lso, ammonium nitrate f(o~,nx-no h y h t t , . OI.iti,ln with values calculated hy naing Equntion 11 is -tiown in Figure 6. The data cover a'tlry-hulli t t ~ ~ ~ i p r a t nrange r c ~ from 70.Y to 109.5' F. and a ,.c,rr"si")ntliiiF wc,t-bulb temperature range from 57.4' t o 10ti.9° F. w i t h depressions varying from 1.7' t o 18.0" F. 'J'lita ~ i i i g c for ' thr, ~ i m u l t n n c o u ~d(,tc,rrniricd ly I\ iJt-hull)
.
Figure 6 . Coriiparihon of Deri\ed arid Euperitneiital U et-Bulb Temperat tires \* i t h '+atura tetl tnimoniir r i i K i t rate Solutions
INDUSTRIAL AND ENGINEERING CHEMISTRY
972
Vol. 38, No. 9
The heat of crystallization (Figure .iI on the order of 10 B.t.u. Der Dound and PW x Po, pa, C. Tat has no practical effect if it is ignored ii. nuI 31 m. .\Im. \1111. B.T.U., I3.T.U.; C$d.. B .T.V. so Hg Lh. Lh. F. psychrometric calculations. Over t h r He Lh. Hg 8.3 123.3 temperature range used in the experi,. 1 112.1 92 0 1 2 0 . 0 3 8 . .5 32.3 2i.3 1040.7 1024.8 2 108.5 93.4 123.3 40.1 36.2 29.4 1040.0 1023.3 8 .5 1 2 8 . 0 mental work, magnesium chloridr i.i i n 3 114.3 93.6 123.3 40.3 35.0 29.4 1039,Q 1023.3 8,: 126.3 4 1 1 4 . 4 9 3 . 9 122.9 40.8 29.1 35.5 1039.7 1023.5 the form of a hexahydrate. 8.5 126.8 5 111.2 9 6 . 8 126.0 44.6 40.8 31.6 1038.1 1021.7 8.5 130.8 The experimental data for Mg;CI,.GH,@ 6 1 1 0 . 8 9 6 . 6 126.7 44.3 40.6 32.2 1038,2 1021.3 8.5 130.6 7 110.1 9 6 . 4 126.3 44.1 40.5 31.9 1038,3 1021.6 8.5 130.3 3olutions are given in Table 111, and the 8 111.6 102.0 132.4 52.2 49.7 37.2 1035,2 1018.0 8.6 138.5 9 110.8 1 0 2 . 4 133.2 50 6 52.8 37.8 1035,O 1017.5 s i l t solution wet-bulb temperatures are 8.6 129.1 10 77.4 58.6 7 6 . 6 12.6 7.9 7.6 1059,o 1048.2 8.2 ,7.5 correlated with the theoretical values 11 84.6 69.4 88.5 18.4 11.2 14.6 1053.0 1047. i 8.3 92.6 (Figure 8 ) calculated by Equation 11. 94.3 73.8 96.1 21.3 18. I 13.8 1050.9 1038. ,5 8.3 99.0 94.6 81.5 104.4 27.5 24.2 17.6 1046 3 1033.9 The data cover a dry-bulb temperaturt8.4 109.7 92.5 81.0 104.4 27.1 24.: 17.6 1046,7 1033,9 8.4 108.8 r:Inge from 77.4" t o 130.8" F. iirid L 92.8 8 3 . 3 107.2 29.2 2G.t 19.0 1045,5 1032.3 8.4 112.1 94.8 8 6 . 2 111.4 32.0 21.4 29.8 1043.9 1030.0 1lG.Z twrresponding wet-bulb temperaturc. . 8 . 4 95,7 8 5 . 8 111.4 31.6 29,; 21.4 1044.2 1030.0 8.4 ll3,, 98.2 9 2 . 3 118.4 37.38.8 25.7 1040.8 8.5 124.5 r:mge from 38.6" t o 115.0" F., with &1026.0 96.8 9 1 . 6 117.9 36.6 37.9 25.4 1041 . 0 1026,s 8.3 123.6 prc5nsion;: varying from 5.0" to 42.2' 1.. 110.1 70.0 93.2 8.5 18.8 12.7 1052.7 1040.1 8.3 93.4 .. 98.1 63.7 87.1 16.2 7.9 10.7 1055.1 1043.4 1 r m z e for the simultnneously derfsr8.2 87.2 108.0 68.9 92.1 18.1 8.1 12.3 1053,s 104O.ii 8.3 91.9 mined t , values varied from i6.6" 23 113.5 9 6 . 3 124.3 43.8 3 9 . tj 30.2 1038.2 1022.15 8.5 130.3 1.52.8" F., and the temperaturcri 24 114.1 8 8 . 5 106.1 27.9 24.2 34.5 1042, , 1027.4 8.5 119.5 25 113 0 86.9 114.1 32.7 25.7 22.9 1043..j 1028.3 8 . 4 1 1 6 . 9 tirvaried from 18.0" to 36.8" F. The & i t 26 112.5 8 7 . 3 114.1 24.0 22.9 33.1 1043.3 1048.3 8.4 114.9 27 109.0 84.7 111.0 30.6 24.0 21.1 1030.2 1044,i lor t , varied from 16.9" below to X i 3F. 8.4 113.9 28 106 3 8 4 . 0 109.8 29.9 24.1 20.4 1045,o 1030.9 8.4 113.2 :ihove theair stream temperature, tu. I: 29 100.0 7 3 . 0 97.9 13.9 20.8 14.5 1051.1 1037,j 8.3 97.8 30 1 3 0 . 8 9 5 . 0 129.2 42.2 3 2 . $1 34.3 1039. 1 1019.8 8 . 6 128.3 n.oultl be impossible t o obtain acrurate 31 1 3 0 . 6 9 4 . 5 128.3 41.5 32.1 33.6 1039.3 1020 3 8.5 127.6 32 130 5 1 0 1 . 4 135.7 51.2 43.6 40.0 tvater et-bulb temperatures if llg['12,8.6 137.6 1035.6 1016.1 33 1 2 9 . 7 107.2 141.1 60.9 53 0 4.5.3 1032.3 1013.0 8.7 146.0 t i K O impinged on the wick during re:td84 129.9 108.5 141.4 63.1 57.3 45.7 1031 . t i 1012.7 8.7 147,s ings. Assuming t h a t t h e water on ttir35 127.2 9 3 . 7 126.3 40.6 31.; 31.9 1039.8 1021..j 8.3 126.5 36 1 2 5 . 6 102.4 1 3 4 . 8 52.7 4 6 . ~ 39.2 8.6 139.1 n-ct bulb became saturated with thi 1035.0 10IG.R 37 127.0 105.6 139.3 58,O 52.5 43.4 1033.2 1014.0 8.6 143.7 t h o lon-est 1%-et-bulbtemperature d : ~ t a 38 127.4 1 0 6 . 0 1 3 8 . 4 52.1 ?8.7 -12.9 1033.0 1014.5 8.G 143.4 39 121.5 1 0 3 . 5 135.3 49.8 04.4 39., 1010.3 1034.3 8.6 140.5 i ~ ~ r d ei nd this work would cauw : ~ n 40 119.8 9 6 . 4 127.4 44.1 38.0 32.8 1038.3 1020.'? 8.3 130.4 41 119.3 94.1 124.5 41.0 34.5 8.5 127.0 t w o r of approximately 3257, i n t h i b 30.4 1022.5 1039.6 42 90.0 z0.0 92.5 18.8 13.; 12.3 1052, i 1040.5 8.3 102.2 93.4 ;ibrolute humidity. 43 85.6 (6.2 98.8 23.1 20.7 14.9 1049.4 1037.0 44 83.8 7 8 . 3 101.1 24.8 23.3 15.9 1048.3 1035.7 8.3 105.1 The results w r e correlated as exp.rl45 82.8 l5,2 63.9 83.7 11.4 8.2 88.4 rneiital salt solution wet-bulb tempora9.5 1056.1 104i. 46 82.8 69.6 90.3 18.5 15.2 11.7 1053.0 1041., 8.3 92.8 tures with the corresponding salt solu47 81.7 70.7 91.2 19.2 16.4 12.0 1052.4 1041.2 8.3 94.6 48 79.7 73.6 95.0 21.2 19.9 13.4 1050.9 1039. I tion wet-bulb temperatures derived from 8 . 3 99.0 49 81.1 74.0 94.8 21.5 19.7 13.3 1039.2 1050.6 8.3 99.2 50 84.1 72.0 93.6 20.1 8.3 100.0 Equation 11. Good agreement wn.* ob19,s 12.8 1039 9 1051.6 51 83.5 76.3 99.1 23.3 21.5 l5,O 1049.2 8.3 102.6 1036.9 tnined from thi- correlation (Figure 8 , 52 82.9 7 7 . 9 100.2 23.2 24.5 14.7 1048 5 1036,2 8.3 104 5 53 83.3 74.4 96.6 19.5 21.8 14.0 1050.4 1038,2 8.3 93.7 \Then the temperatures t , were lower 54 12.81 115.0 1 5 2 . 8 72.6 76.0 58.7 1027.9 1006.0 8.8 157.5 55 130.3 8 8 . 1 118.9 8..5 118.9 than the air temperature t u , a n excellenr 23.1 34.0 26. I 1042.9 1025.7 wrrelition reaulted ~ i t ht h e \ariation ranging from 1.2" less than t o 0.9" F greater than the theoretical values. T W G ~ theoretical Equation 11. Cornpaling the t n o correlationz >lion thirds of thcae temperatures were practically equal to the calcuthat the greatest deviation (3 8" F.) indicatcd by t h r ne\\- theorv 1 ited valuez; this shoxved that the c o tion was better than t h e is appri..imately the same as the minimum deviation (3.7" F.) resulting from the method used by the previous investigators ( I d ) . Thii: s h o w a substantial improvement in t h r rorirIation. I n order t o make this work of somf' pia( tic.rl value, a humidity chart (Figure 7) \%asconstructed for saturated solutions of ammonium nitrate using Equation I 1 as the basi. of calculation.
TABLE 111. DATAFOR
b l A G X E S K \ I CHLORIDE H E X . 4 H Y D R i T E ~ o L C r I O S 5
~~
Jj.,
1 7 ,
tic3
-
VAGNESIUM CHLORIDE HEXAHYDRATE SOLUTIOYS
I n order t o check the validity of the empirical relation used by the previous investigdtors ( l e ) ,i t was necessary t o choose a salt nitli very low saturated-solution vapor pressures compared to water or saturated sodium nitrat? aolutions, and alao one that had a very lo\\ heat of crystallization. Solutions of lIgC1- 6H20 meet these requirements becauw tlics vapor pressures a t various temperatui es (Figure 4) are much loryer than for n , ~ t e ror solutions of sodium nitr,ite nnd ammonium nit1 i t c
60 Figure 7 .
70
80
90 100 TEMPERATURE
\IO
-E
120
130
140
Adiabatic K et-Bulb Lines 7s i t h Saturated Arnnioniurn Sitrate Solution3
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1946
913
Comparing the variations from the two methods of correlation shows that the maximum deviation of 6.5" F. shown by the ncv theory is approximately equal t o the minimum deviation of 6.4" F. obtained by the method of the previous investigators ( I d ) . K h e n t, is less than f,, the proposed method is accurate but becomes less accurate a t high humidities. I n either caSe considerable improvement is obtained in the correlation. -1humidity chart (Figure 9) was constructed for saturated solutions of lIgC12.6H,0, using Equation 11 for calculating the adiabatic wet-bulb lines. The curves showing per cent relative humidity are the same as for the standard air-water m p o r hi]midity chart. DISCUSSION OF RESULTS
I P: 1
7 o v 70
80
100 110 120 130 140 CALCULATED TEMPERATURE Ts-OF.
90
-
I
150
;,gure 8. Comparison of Derived and Experimental et-Bulb Temperatures w-ith Saturated Magnesium Chloride Hexahydrate Solutions
The results obtained n-ith the three saturated salt solutions correlated excellently when f, was less than t u (that is, a t lo^ humidities). V h e n t. was greater than fg, the correlations Kith the values of t s calculated with Equation 11 were good but inferior t o thc previous ease. I n general, where t ax i s greater than tu, the quality of the results decreased as fa increased. This decrease in accuracy is suspected t o be due to the difficulty of maintaining a saturated salt solution on the nick of the wet-bulb thermometer. Furthermore, the greater the temperahre difference for isobaric readings obtained from the water and salt solution vapor pressure curves when t, is greater than to, the greater the condensation of water vapor, bpcause the vapor pressure of the salt solution is lower. and ii greater driving force ( p , - p a ) for diffusion is set up. There are two factors which change the wet-bulb temperatures ivhen salt solutions are used. The most important factor is the change in vapor pressure of water caused by t,he addition of soluble salts. The lower the salt solution vapor pressure, the greater the difference between f w and t a becomes in order that equilibrium adiabatic conditions be maintained. This fact is readily observed by comparing the cxperimental data or humidity charts for the three salt solutions. The second factor to be considered is the heat of c,rystallization or solution. This heat must be considered for all salt solutions if adiabatic conditions are to be employed. The heat evolved per pound of water evaporated is shon-n in Figure 5 for saturated solutions of sodium nitrate, ammonium nitrate, and magnesium chloride hexahydrate. Comparison of the heats of crystallization with the latent heat of vaporization shows that the former cannot be neglected for any salt solution if accurate salt solution wet-bulb temperatures
above range of temperature variations indicated. R-hen fs n-a> above f,, the experimental values varied from 0.8" to 6.5' F. lek; chan the corresponding derived values. The variation oft, from the derived values of t , increased slightly n-ith increasing tempera-,ures. This is t o be expected because water vapor condenses on :he wet bulb a t a n increasing rate as t a increases, so that it i? difficult to keep the wick continually saturated with hIgCls.BH,O solution. As the salt solution concentration decreases, it gives an increased water vapor pressure and, simultaneously, t , approaches :to, the water \vet bulb temperature. I t is the slight change in salt concentration n-ith the corresponding change in the solution vapor pressure that makes the experimental values of t s lie belo\v :he derived values o f t , (Figure 8 ) . These data were correlated by the method of the previous investigators ( 1 2 ) ,and the results viere far worse. I n this correla:ion (Figure 2 ) the empirical results were from 6.4" to 14.4" F. l e s than the corresponding vater wet-bulb temperatures. I n this case the heat of crystallization amounted t o less than 10 B.t.u. per pound of Ivatc'r vapor tranqferreil and had no practical effect upon the temperalures. This indicates that vnpor pressure l o w r ing caused by the salt solutions is the primarv iactor t o be considered in the derivation of a xxv theory; it also s h o w definitely that the empirical relation (18) for conwrting the es__--. .. . .. perimental t a t o f v (by isohnric readings from :he respective rapor pressure cui 5alt solution and pure rvateri is in error. The empirical corrclution of espcrimentd ta values by the method of \T-illiams ant1 'A-illiams (12) pave a mi,i:ition of 6.4" t o 14.4' F. less than corresponding \v-ntcr net-bulb In a rorrclation of data as -emperahre t,. proposed in this report, the \-nri:ition was 1.2" ' . thnn to 0.09" F. greater t h a n the calcua t e d t,'values, m-hen t , was less thnn fg. IYlien T E M P E R A T U R E -OF. was greater than f2, the experimental value; d f, varied from 0.8" to 6.2' F. Figure 9. Adiabatic Wet-Bulb Lines w-ith Saturated llagnesium Chloride Hexahydrate Solutions values of t , calcu1:ited hy using
974
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 38, No. 9
muvh .maIlw, with a r t h t a n t 1 1 i ~v~i rw
in
~ ~ : i d t : i t ~ifTc.ct. oii