570651010

(254857)

2557

- 1 -

Halsey A B

Halsey (Least Square Method)

1.

1.1 (Least Square Method)

Halsey exp BeqA

RH MRT

RH ,

T , C

Meq , %db

R = 8.314 kJ/kg-K

A, B

Halsey

1 2Y C C X

ln ln ln ln eqA

T RH B MR

ln lnY T RH

ln eqX M

1 lnA

CR

( 1CA Re )

2C B ( 2B C )

1C 2C

21 21

n

i i

i

E Y C C X

- 2 -

1.1.1 1C E 1C

1

E

C

= 1 2

1

2 1n

i i

i

Y C C X

= 0

1 21

n

i i

i

Y C C X

= 0

1 2

1 1

n n

i i

i i

Y C n C X

= 0

1C = 2

1 1

n n

i i

i i

Y C X

n

1.1.2 2C E 2C

2

E

C

= 1 2

1

2n

i i i

i

Y C C X X

= 0

2

1 2

1 1 1

n n n

i i i i

i i i

X Y C X C X

= 0

1C = 2

1 1

n n

i i

i i

Y C X

n

2

21 12

1 1 1

n n

i in n ni i

i i i i

i i i

Y C X

X Y X C Xn

= 0

2C 2C

2C = 1 1 1 22

1 1

n n n

i i i i

i i i

n n

i i

i i

n X Y X Y

n X X

1.1.3 2R (Coefficient of determination)

2

model2 1

2

1

1

n

i

n

i

Y Y

R

Y Y

modelY Y

Y Y 1

n

i

i

Y

n

- 3 -

1.2

(dry basis)

100%dbw d

M xd

dbM

w ()

d ()

- 4 -

2. A B Halsey

2.1 50 C

2.1 50 C

(g)

(g) RH (%) Meq (%db)

1 LiCl 30.5500 28.6200 11.4000 6.7435

2 LiCl 32.4600 30.2600 11.4000 7.2703

3 MgCl2.6H2O 32.2700 29.6500 31.4000 8.8364

4 NaCl 35.6600 27.2500 75.2000 30.8624

5 NaCl 37.6700 28.5900 75.2000 31.7594

6 KNO3 37.7000 26.8400 84.9900 40.4620

7 KNO3 39.5100 28.2100 84.9900 40.0567

2.1.1 1C 2C

1C 1C = 2

1 1

n n

i i

i i

Y C X

n

2C 2C = 1 1 1 22

1 1

n n n

i i i i

i i i

n n

i i

i i

n X Y X Y

n X X

2.2 1C 2C

N lni eqX M ln lniY T RH i iX Y 2

iX

1 1.9086 4.6875 8.9464 3.6427

2 1.9838 4.6875 9.2990 3.9355

3 2.1789 4.0590 8.8441 4.7475

4 3.4295 2.6568 9.1117 11.7617

5 3.4582 2.6568 9.1878 11.9591

6 3.7004 2.0958 7.7552 13.6927

7 3.6903 2.0958 7.7341 13.6183

1

n

i

i

X

= 20.3497 1

n

i

i

Y

= 22.9392 1

n

i i

i

X Y

= 60.8783 21

n

i

i

X

= 63.3575

- 5 -

2C 2C =

2

60.8783 20.3497 22.9392

63.3575 20. 7

7

7 349

2C = 1.3832

2C 1C

1C = 22.9392 1.3832 20 7

7

.349

1C = 7.2980

1.3832 7.2980Y X

2.1.2 2R

1 22.9392 3.27707

n

i

i

Y

Yn

model 1.3832 7.2980XY

2.3 2R

N X Y modelY 2

modelY Y 2

Y Y

1 1.9086 4.6875 4.6581 0.0009 1.9893

2 1.9838 4.6875 4.5541 0.0178 1.9893

3 2.1789 4.0590 4.2843 0.0507 0.6115

4 3.4295 2.6568 2.5544 0.0105 0.3847

5 3.4582 2.6568 2.5148 0.0202 0.3847

6 3.7004 2.0958 2.1798 0.0071 1.3953

7 3.6903 2.0958 2.1937 0.0096 1.3953

1

n

i

i

Y

= 22.9392 2

model

1

n

i

Y Y

= 0.1167 2

1

n

i

Y Y

= 8.1502

2R

2

model2 1

2

1

0.1167

8. 5 21

1 01

n

i

n

i

Y Y

R

Y Y

2 0.9857R

- 6 -

X Y

2R = 0.9857 1

2.1.3 A B

1CA Re 2B C

8.3147.2980 12282.6851A e x

1.3832B

A B Halsey

1.383212282.exp6851

eqRH MRT

1

1.3832

12282.6851

lneq

RT RHM

Halsey 50

RH 1% 90% Halsey

y = -1.3832x + 7.298

R = 0.9857

0.00

1.00

2.00

3.00

4.00

5.00

1.50 2.00 2.50 3.00 3.50 4.00

- 7 -

2R Halsey

1 165.9907 23. 1 07

7 3

n

i

i

Y

Yn

1.

1

mode

3832

l12282.685

l

1

nRT XY

2.4 2R Halsey

N X =

Y =

modelY

2

modelY Y 2

1

n

i

Y Y

1 11.4000 6.7435 6.6020 0.0200 287.9615

2 11.4000 7.2703 6.6020 0.4467 270.3604

3 31.4000 8.8364 10.3991 2.4419 221.3114

4 75.2000 30.8624 28.6596 4.8523 51.1142

5 75.2000 31.7594 28.6596 9.6085 64.7444

6 84.9900 40.4620 42.9960 6.4214 280.5301

7 84.9900 40.0567 42.9960 8.6396 267.1183

1

n

i

i

Y

=

165.9907

2

model

1

n

i

Y Y

= 32.4305

2

model

1

n

i

Y Y

=

1443.1404

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

50 C

Halsey

- 8 -

2R

2

model2 1

2

1

32.4305

1443.141

41

0

n

i

n

i

Y Y

R

Y Y

2 0.9775R

- 9 -

2.2 57 C

2.5 57 C

N

(g)

(g) RH (%) Meq (%db)

1 LiCl 22.6600 21.2900 11.2600 6.4349

2 LiCl 23.9400 22.5300 11.2600 6.2583

3 MgCl2.6H2O 26.5300 24.5300 30.9100 8.1533

4 Mg(NO3)2.6H2O 24.4300 21.6300 45.1596 12.9450

5 Mg(NO3)2.6H2O 21.3800 19.0200 45.1596 12.4080

6 NaCl 25.0300 18.9300 75.0600 32.2240

7 NaCl 23.0900 17.5200 75.0600 31.7922

8 KNO3 28.7600 20.4100 82.2363 40.9113

9 KNO3 26.6500 18.9500 82.2363 40.6332

2.2.1 1C 2C

1C 1C = 2

1 1

n n

i i

i i

Y C X

n

2C 2C = 1 1 1 22

1 1

n n n

i i i i

i i i

n n

i i

i i

n X Y X Y

n X X

2.6 1C 2C

N lni eqX M ln lniY T RH i iX Y 2

iX

1 1.8617 4.8242 8.9814 3.4661

2 1.8339 4.8242 8.8471 3.3632

3 2.0984 4.2035 8.8208 4.4034

4 2.5607 3.8136 9.7655 6.5572

5 2.5183 3.8136 9.6039 6.3420

6 3.4727 2.7944 9.7040 12.0597

7 3.4592 2.7944 9.6663 11.9662

8 3.7114 2.4112 8.9491 13.7745

9 3.7046 2.4112 8.9326 13.7240

1

n

i

i

X

= 25.2211 1

n

i

i

Y

= 31.8903 1

n

i i

i

X Y

= 83.2708 21

n

i

i

X

= 75.6564

- 10 -

2C 2C =

2

83.2708 25.2211 31.8903

75.6564 25. 1

9

9 221

2C = 1.2246

2C 1C

1C = 31.8903 1.2246 25 1

9

.221

1C = 6.9751

1.2246 6.9751Y X

2.2.2 2R

1 31.8903 3.54349

n

i

i

Y

Yn

model 1.2246 6.9751XY

2.7 2R

N X Y modelY 2

modelY Y 2

Y Y

1 1.8617 4.8242 4.6952 0.0166 1.6405

2 1.8339 4.8242 4.7293 0.0090 1.6405

3 2.0984 4.2035 4.4054 0.0407 0.4358

4 2.5607 3.8136 3.8393 0.0007 0.0730

5 2.5183 3.8136 3.8911 0.0060 0.0730

6 3.4727 2.7944 2.7224 0.0052 0.5610

7 3.4592 2.7944 2.7389 0.0031 0.5610

8 3.7114 2.4112 2.4301 0.0004 1.2817

9 3.7046 2.4112 2.4385 0.0007 1.2817

1

n

i

i

Y

= 31.8903 2

model

1

n

i

Y Y

= 0.0824 2

1

n

i

Y Y

= 7.5483

- 11 -

2R

2

model2 1

2

1

0.0824

7. 4 31

5 81

n

i

n

i

Y Y

R

Y Y

2 0.9891R X Y

2R = 0.9891 1

2.2.3 A B

1CA Re 2B C

8.3146.9751 8893.1465A e x

1.2246B

A B Halsey

1.22468893.1ex46

p5

eqRH MRT

1.2 6

1

24

8893.1465

lneq

RT RHM

y = -1.2246x + 6.9751

R = 0.9891

0.00

1.00

2.00

3.00

4.00

5.00

1.50 2.00 2.50 3.00 3.50 4.00

- 12 -

Halsey 57

RH 1% 90% Halsey

2R Halsey

1 191.7603 21. 0 79

3 6

n

i

i

Y

Yn

1.

1

mode

2246

l8893.1465

lnRT XY

2.8 2R Halsey

N X =

Y =

modelY

2

modelY Y 2

1

n

i

Y Y

1 11.2600 6.4349 5.7918 0.4137 221.1691

2 11.2600 6.2583 5.7918 0.2177 226.4537

3 30.9100 8.1533 9.6142 2.1342 173.0124

4 45.1596 12.9450 13.2192 0.0752 69.9183

5 45.1596 12.4080 13.2192 0.6580 79.1870

6 75.0600 32.2240 30.3855 3.3799 119.1870

7 75.0600 31.7922 30.3855 1.9788 109.9465

8 82.2363 40.9113 41.5474 0.4046 384.3410

9 82.2363 40.6332 41.5474 0.8356 373.5153

1

n

i

i

Y

= 191.7603

2

model

1

n

i

Y Y

= 10.0977

2

model

1

n

i

Y Y

= 1756.7304

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

57 C

Halsey

- 13 -

2R

2

model2 1

2

1

10.0977

1756.731

41

0

n

i

n

i

Y Y

R

Y Y

2 0.9943R

- 14 -

2.3 65 C

2.9 65 C

(g)

(g) RH (%) Meq (%db)

1 LiCl 36.1200 33.9900 11.1000 6.2665

2 LiCl 36.3100 34.3100 11.1000 5.8292

3 MgCl2.6H2O 36.8100 34.0300 30.3500 8.1693

4 MgCl2.6H2O 38.2600 35.4200 30.3500 8.0181

5 Mg(NO3)2.6H2O 39.5600 35.7700 43.0456 10.5955

6 Mg(NO3)2.6H2O 37.4600 33.7700 43.0456 10.9269

7 NaCl 44.7700 33.8200 74.9000 32.3773

8 NaCl 45.2900 34.1500 74.9000 32.6208

9 KNO3 48.7300 34.4700 79.2103 41.3693

10 KNO3 47.1200 33.3900 79.2103 41.1201

2.3.1 1C 2C

1C 1C = 2

1 1

n n

i i

i i

Y C X

n

2C 2C = 1 1 1 22

1 1

n n n

i i i i

i i i

n n

i i

i i

n X Y X Y

n X X

2.10 1C 2C

N lni eqX M ln lniY T RH i iX Y 2

iX

1 1.8352 4.962038 9.1065 3.3681

2 1.7629 4.962038 8.7475 3.1077

3 2.1004 4.350333 9.1373 4.4116

4 2.0817 4.350333 9.0561 4.3335

5 2.3604 4.003492 9.4500 5.5716

6 2.3912 4.003492 9.5732 5.7180

7 3.4775 2.933115 10.1998 12.0927

8 3.4849 2.933115 10.2218 12.1449

9 3.7225 2.717944 10.1177 13.8573

10 3.7165 2.717944 10.1012 13.8123

1

n

i

i

X

= 26.9333 1

n

i

i

Y

= 37.9338 1

n

i i

i

X Y

= 95.7110 21

n

i

i

X

= 78.4177

- 15 -

2C 2C =

2

95.7110 26.9333 37.9338

78.4177 26.9

1

10 3

0

33

2C = 1.0986

2C 1C

1C = 37.9338 1.0986 26.

10

9333

1C = 6.7524

1.0986 6.7524Y X

2.3.2 2R

1 37.93381

3.79340

n

i

i

Y

Yn

model 1.0986 6.7524XY

2.11 2R

N X Y modelY 2

modelY Y 2

Y Y

1 1.8352 4.9620 4.7361 0.0510 1.3657

2 1.7629 4.9620 4.8156 0.0214 1.3657

3 2.1004 4.3503 4.4448 0.0089 0.3102

4 2.0817 4.3503 4.4653 0.0132 0.3102

5 2.3604 4.0035 4.1591 0.0242 0.0441

6 2.3912 4.0035 4.1253 0.0148 0.0441

7 3.4775 2.9331 2.9319 0.0000 0.7401

8 3.4849 2.9331 2.9237 0.0001 0.7401

9 3.7225 2.7179 2.6626 0.0031 1.1566

10 3.7165 2.7179 2.6693 0.0024 1.1566

1

n

i

i

Y

= 37.9338 2

model

1

n

i

Y Y

= 0.1392 2

1

n

i

Y Y

= 7.2334

- 16 -

2R

2

model2 1

2

1

0.1392

7. 3 41

2 31

n

i

n

i

Y Y

R

Y Y

2 0.9808R X Y

2R = 0.9808 1

2.3.3 A B

1CA Re 2B C

8.3146.7524 7117.6105A e x

1.0986B

A B Halsey

1.09867117.6ex10

p5

eqRH MRT

1.0 6

1

98

7117.6105

lneq

RT RHM

y = -1.0986x + 6.7524

R = 0.9808

0.00

1.00

2.00

3.00

4.00

5.00

6.00

1.50 2.00 2.50 3.00 3.50 4.00

- 17 -

Halsey 65

RH 1% 90% Halsey

2R Halsey

1 197.29291

1 .72 30

9 9

n

i

i

Y

Yn

1.

1

mode

0986

l7117.6105

lnRT XY

2.12 2R

N X =

Y =

modelY

2

modelY Y 2

1

n

i

Y Y

1 11.1000 6.2665 5.1018 1.3565 181.2454

2 11.1000 5.8292 5.1018 0.5291 193.2124

3 30.3500 8.1693 8.9030 0.5383 133.6342

4 30.3500 8.0181 8.9030 0.7830 137.1527

5 43.0456 10.5955 12.2079 2.6000 83.4266

6 43.0456 10.9269 12.2079 1.6411 77.4828

7 74.9000 32.3773 32.3417 0.0013 159.9719

8 74.9000 32.6208 32.3417 0.0779 166.1908

9 79.2103 41.3693 39.3387 4.1233 468.2903

10 79.2103 41.1201 39.3387 3.1733 457.5666

1

n

i

i

Y

=

197.2929

2

model

1

n

i

Y Y

= 14.8238

2

model

1

n

i

Y Y

= 2058.1738

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

65 C

Halsey

- 18 -

2R

2

model2 1

2

1

14.8238

2058.171

81

3

n

i

n

i

Y Y

R

Y Y

2 0.9928R

- 19 -

2.4 72 C

2.13 72 C

(g)

(g) RH (%) Meq (%db)

1 LiCl 22.18 21.21 11.1000 4.5733

2 LiCl 28.67 27.51 11.1000 4.2166

3 MgCl2.6H2O 29.34 26.51 30.3500 10.6752

4 MgCl2.6H2O 26.77 24.46 30.3500 9.4440

5 Mg(NO3)2.6H2O 24.89 22.44 43.0456 10.9180

6 Mg(NO3)2.6H2O 27.32 24.76 43.0456 10.3393

7 NaCl 31.15 21.15 74.9000 47.2813

8 NaCl 27.58 18.76 74.9000 47.0149

9 KNO3 30.34 20.46 79.2103 48.2893

10 KNO3 29.06 19.05 79.2103 52.5459

2.4.1 1C 2C

1C 1C = 2

1 1

n n

i i

i i

Y C X

n

2C 2C = 1 1 1 22

1 1

n n n

i i i i

i i i

n n

i i

i i

n X Y X Y

n X X

2.14 1C 2C

N lni eqX M ln lniY T RH i iX Y 2

iX

1 1.5202 5.0643 7.6990 2.3111

2 1.4390 5.0643 7.2878 2.0708

3 2.3679 4.4526 10.5435 5.6071

4 2.2454 4.4526 9.9978 5.0417

5 2.3904 4.1058 9.8145 5.7141

6 2.3359 4.1058 9.5909 5.4567

7 3.8561 3.0354 11.7048 14.8696

8 3.8505 3.0354 11.6877 14.8261

9 3.8772 2.8202 10.9346 15.0328

10 3.9617 2.8202 11.1728 15.6950

1

n

i

i

X

= 27.8444 1

n

i

i

Y

= 38.9566 1

n

i i

i

X Y

= 100.4333 21

n

i

i

X

= 86.6249

- 20 -

2C 2C =

2

100.4333 27.8444 38.9566

86.6249 27.8

10

1 40 44

2C = 0.8840

2C 1C

1C = 38.9566 0.8840 27.

10

8444

1C = 6.3572

0.8840 6.3572Y X

2.4.2 2R

1 38.95661

3.89570

n

i

i

Y

Yn

model 0.8840 6.3572XY

2.15 2R

N X Y modelY 2

modelY Y 2

Y Y

1 1.5202 5.0643 5.0133 0.0026 1.3657

2 1.4390 5.0643 5.0850 0.0004 1.3657

3 2.3679 4.4526 4.2639 0.0356 0.3102

4 2.2454 4.4526 4.3722 0.0065 0.3102

5 2.3904 4.1058 4.2440 0.0191 0.0441

6 2.3359 4.1058 4.2921 0.0347 0.0441

7 3.8561 3.0354 2.9483 0.0076 0.7401

8 3.8505 3.0354 2.9533 0.0067 0.7401

9 3.8772 2.8202 2.9296 0.0120 1.1566

10 3.9617 2.8202 2.8549 0.0012 1.1566

1

n

i

i

Y

= 38.9566

2

model

1

n

i

Y Y

= 0.1265

2

1

n

i

Y Y

= 7.2334

- 21 -

2R

2

model2 1

2

1

0.1265

7. 3 41

2 31

n

i

n

i

Y Y

R

Y Y

2 0.9825R X Y

2R = 0.9808 1

2.4.3 A B

1CA Re 2B C

8.3146.3572 4794.1793A e x

0.8840B

A B Halsey

0.88404794.1ex79

p3

eqRH MRT

0.8 0

1

84

4794.1793

lneq

RT RHM

y = -0.8840x + 6.3572

R = 0.9825

0.00

1.00

2.00

3.00

4.00

5.00

6.00

1.50 2.00 2.50 3.00 3.50 4.00 4.50

- 22 -

Halsey 72

RH 1% 90% Halsey

2R Halsey

1 197.29291

1 .72 30

9 9

n

i

i

Y

Yn

1.

1

mode

0986

l7117.6105

lnRT XY

2.16 2R

N X =

Y =

modelY

2

modelY Y 2

1

n

i

Y Y

1 11.1000 4.5733 4.3167 0.0658 398.2611

2 11.1000 4.2166 4.3167 0.0100 412.6239

3 30.3500 10.6752 8.6230 4.2115 191.9494

4 30.3500 9.4440 8.6230 0.6740 227.5815

5 43.0456 10.9180 12.7659 3.4146 185.2809

6 43.0456 10.3393 12.7659 5.8884 201.3714

7 74.9000 47.2813 42.8436 19.6937 517.6320

8 74.9000 47.0149 42.8436 17.4002 505.5811

9 79.2103 48.2893 54.6501 40.4590 564.5162

10 79.2103 52.5459 54.6501 4.4275 784.9039

1

n

i

i

Y

=

245.2980

2

model

1

n

i

Y Y

= 96.2445

2

model

1

n

i

Y Y

= 3989.7014

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

72 C

Halsey

- 23 -

2R

2

model2 1

2

1

96.2445

3989.701

41

1

n

i

n

i

Y Y

R

Y Y

2 0.9759R

- 24 -

3.

50, 57, 65 72 C

11.11% 84.99%

Halsey 50, 57,

65 72 C

50 C R2 = 0.9775, 57 C R2 = 0.9943,

65 C R2 = 0.9928 72 C R2 = 0.9759 1

A, B R2 17

17 A, B R2

T ( C ) A B R2

50 12282.6851 -1.3832 0.9775

57 8893.1465 -1.2246 0.9943

65 7117.6105 -1.0986 0.9928

72 4794.1793 -0.8840 0.9759

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

50 C 57 C 65 C 72 C

- 25 -

Halsey

50, 57, 65 72 C ( 50 %)

Halsey

Halsey Halsey

R2 (0.97-0.99)

Halsey 50 C

Halsey 57 C

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

50 C

Halsey

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

57 C

Halsey

R2 = 0.9775

R2 = 0.9943

- 26 -

Halsey 65 C

Halsey 72 C

Halsey 50, 57, 65 72 C

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

65 C

Halsey

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

72 C

Halsey

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90

(%

db)

(%)

Halsey T = 50 C

Halsey T = 57 C

Halsey T = 65 C

Halsey T = 72 C

R2 = 0.9928

R2 = 0.9759