CHAPTER 1. PSYCHROMETRICS

Psychrometrics uses thermodynamic properties to analyze conditions and processes involving moist air. This chapter discusses perfect gas relations and their use in common heating, cooling, and humidity control problems. Formulas developed by Herrmann et al. (2009) may be used where greater precision is required.

Herrmann et al. (2009), Hyland and Wexler (1983a, 1983b), and Nelson and Sauer (2002) developed formulas for thermodynamic properties of moist air and water modeled as real gases. However, perfect gas relations can be substituted in most air-conditioning problems. Kuehn et al. (1998) showed that errors are less than 0.7% in calculating humidity ratio, enthalpy, and specific volume of saturated air at standard atmospheric pressure for a temperature range of −50 to 50°C. Furthermore, these errors decrease with decreasing pressure.

1. COMPOSITION OF DRY AND MOIST AIR

Atmospheric air contains many gaseous components as well as water vapor and miscellaneous contaminants (e.g., smoke, pollen, and gaseous pollutants not normally present in free air far from pollution sources).

Dry air is atmospheric air with all water vapor and contaminants removed. Its composition is relatively constant, but small variations in the amounts of individual components occur with time, geographic location, and altitude. Harrison (1965) lists the approximate percentage composition of dry air by volume as: nitrogen, 78.084; oxygen, 20.9476; argon, 0.934; neon, 0.001818; helium, 0.000524; methane, 0.00015; sulfur dioxide, 0 to 0.0001; hydrogen, 0.00005; and minor components such as krypton, xenon, and ozone, 0.0002. Harrison (1965) and Hyland and Wexler (1983a) used a value 0.0314 (circa 1955) for carbon dioxide. Carbon dioxide reached 0.0379 in 2005, is currently increasing by 0.00019 percent per year and is projected to reach 0.0438 in 2036 (Gatley et al. 2008; Keeling and Whorf 2005a, 2005b). Increases in carbon dioxide are offset by decreases in oxygen; consequently, the oxygen percentage in 2036 is projected to be 20.9352. Using the projected changes, the relative molecular mass for dry air for at least the first half of the 21st century is 28.966, based on the carbon-12 scale. The gas constant for dry air using the current Mohr and Taylor (2005) value for the universal gas constant is

(1)

Moist air is a binary (two-component) mixture of dry air and water vapor. The amount of water vapor varies from zero (dry air) to a maximum that depends on temperature and pressure. Saturation is a state of neutral equilibrium between moist air and the condensed water phase (liquid or solid); unless otherwise stated, it assumes a flat interface surface between moist air and the condensed phase. Saturation conditions change when the interface radius is very small (e.g., with ultrafine water droplets). The relative molecular mass of water is 18.015 268 on the carbon-12 scale. The gas constant for water vapor is

(2)

2. U.S. STANDARD ATMOSPHERE

The temperature and barometric pressure of atmospheric air vary considerably with altitude as well as with local geographic and weather conditions. The standard atmosphere gives a standard of reference for estimating properties at various altitudes. At sea level, standard temperature is 15°C; standard barometric pressure is 101.325 kPa. Temperature is assumed to decrease linearly with increasing altitude throughout the troposphere (lower atmosphere), and to be constant in the lower reaches of the stratosphere. The lower atmosphere is assumed to consist of dry air that behaves as a perfect gas. Gravity is also assumed constant at the standard value, 9.806 65 m/s2. Table 1 summarizes property data for altitudes to 10 000 m.

Pressure values in Table 1 may be calculated from

(3)

The equation for temperature as a function of altitude is

(4)

where

Z = altitude, m
p = barometric pressure, kPa
t = temperature, °C

Table 1 Standard Atmospheric Data for Altitudes to 10 000 m

Altitude, m

Temperature, °C

Pressure, kPa

−500

18.2

107.478

0

15.0

101.325

500

11.8

95.461

1000

8.5

89.875

1500

5.2

84.556

2000

2.0

79.495

2500

−1.2

74.682

3000

−4.5

70.108

4000

−11.0

61.640

5000

−17.5

54.020

6000

−24.0

47.181

7000

−30.5

41.061

8000

−37.0

35.600

9000

−43.5

30.742

10000

−50

26.436

Source: Adapted from NASA (1976).


Equations (3) and (4) are accurate from −5000 m to 11 000 m. For higher altitudes, comprehensive tables of barometric pressure and other physical properties of the standard atmosphere, in both SI and I-P units, can be found in NASA (1976).

3. THERMODYNAMIC PROPERTIES OF MOIST AIR

Table 2, developed from formulas by Herrmann et al. (2009), shows values of thermodynamic properties of moist air based on the International Temperature Scale of 1990 (ITS-90). This ideal scale differs slightly from practical temperature scales used for physical measurements. For example, the standard boiling point for water (at 101.325 kPa) occurs at 99.97°C on this scale rather than at the traditional 100°C. Most measurements are currently based on ITS-90 (Preston-Thomas 1990).

The following properties are shown in Table 2:

t =

Celsius temperature, based on the ITS-90 and expressed relative to absolute temperature T in kelvins (K) by the following relation:

 
 
Ws =

humidity ratio at saturation; gaseous phase (moist air) exists in equilibrium with condensed phase (liquid or solid) at given temperature and pressure (standard atmospheric pressure). At given values of temperature and pressure, humidity ratio W can have any value from zero to Ws.

vda =

specific volume of dry air, m3/kgda.

vas =

vsvda, difference between specific volume of moist air at saturation and that of dry air, m3/kgda, at same pressure and temperature.

vs =

specific volume of moist air at saturation, m3/kgda.

hda =

specific enthalpy of dry air, kJ/kgda. In Table 2, hda is assigned a value of 0 at 0°C and standard atmospheric pressure.

has =

hshda, difference between specific enthalpy of moist air at saturation and that of dry air, kJ/kgda, at same pressure and temperature.

hs =

specific enthalpy of moist air at saturation, kJ/kgda.

sda =

specific entropy of dry air, kJ/(kgda · K). In Table 2, sda is assigned a value of 0 at 0°C and standard atmospheric pressure.

ss =

specific entropy of moist air at saturation kJ/(kgda · K).

Table 2 Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 101.325 kPa

Temp., °C t

Humidity Ratio Ws, kgw/kgda

Specific Volume, m3/kgda

Specific Enthalpy, kJ/kgda

Specific Entropy, kJ/(kgda·K)

Temp., °C t

vda

vas

vs

hda

has

hs

sda

ss

−60

0.0000067

0.6027

0.0000

0.6027

−60.341

0.016

−60.325

−0.2494

−0.2494

−60

−59

0.0000076

0.6055

0.0000

0.6055

−59.335

0.018

−59.317

−0.2447

−0.2446

−59

−58

0.0000087

0.6084

0.0000

0.6084

−58.329

0.021

−58.308

−0.2400

−0.2399

−58

−57

0.0000100

0.6112

0.0000

0.6112

−57.323

0.024

−57.299

−0.2354

−0.2353

−57

−56

0.0000114

0.6141

0.0000

0.6141

−56.317

0.027

−56.289

−0.2307

−0.2306

−56

−55

0.0000129

0.6169

0.0000

0.6169

−55.311

0.031

−55.280

−0.2261

−0.2260

−55

−54

0.0000147

0.6198

0.0000

0.6198

−54.305

0.035

−54.269

−0.2215

−0.2213

−54

−53

0.0000167

0.6226

0.0000

0.6226

−53.299

0.040

−53.258

−0.2169

−0.2167

−53

−52

0.0000190

0.6255

0.0000

0.6255

−52.293

0.046

−52.247

−0.2124

−0.2121

−52

−51

0.0000215

0.6283

0.0000

0.6283

−51.287

0.052

−51.235

−0.2078

−0.2076

−51

−50

0.0000243

0.6312

0.0000

0.6312

−50.281

0.059

−50.222

−0.2033

−0.2030

−50

−49

0.0000275

0.6340

0.0000

0.6340

−49.275

0.066

−49.209

−0.1988

−0.1985

−49

−48

0.0000311

0.6369

0.0000

0.6369

−48.269

0.075

−48.194

−0.1943

−0.1940

−48

−47

0.0000350

0.6397

0.0000

0.6397

−47.263

0.085

−47.179

−0.1899

−0.1895

−47

−46

0.0000395

0.6425

0.0000

0.6426

−46.257

0.095

−46.162

−0.1854

−0.1850

−46

−45

0.0000445

0.6454

0.0000

0.6454

−45.252

0.107

−45.144

−0.1810

−0.1805

−45

−44

0.0000500

0.6482

0.0001

0.6483

−44.246

0.121

−44.125

−0.1766

−0.1761

−44

−43

0.0000562

0.6511

0.0001

0.6511

−43.240

0.136

−43.104

−0.1722

−0.1716

−43

−42

0.0000631

0.6539

0.0001

0.6540

−42.234

0.153

−42.081

−0.1679

−0.1672

−42

−41

0.0000708

0.6568

0.0001

0.6568

−41.229

0.172

−41.057

−0.1635

−0.1628

−41

−40

0.0000793

0.6596

0.0001

0.6597

−40.223

0.192

−40.031

−0.1592

−0.1583

−40

−39

0.0000887

0.6625

0.0001

0.6626

−39.217

0.215

−39.002

−0.1549

−0.1539

−39

−38

0.0000992

0.6653

0.0001

0.6654

−38.211

0.241

−37.970

−0.1506

−0.1495

−38

−37

0.0001108

0.6682

0.0001

0.6683

−37.206

0.269

−36.936

−0.1464

−0.1451

−37

−36

0.0001237

0.6710

0.0001

0.6711

−36.200

0.301

−35.899

−0.1421

−0.1408

−36

−35

0.0001379

0.6738

0.0001

0.6740

−35.195

0.336

−34.859

−0.1379

−0.1364

−35

−34

0.0001536

0.6767

0.0002

0.6769

−34.189

0.374

−33.815

−0.1337

−0.1320

−34

−33

0.0001710

0.6795

0.0002

0.6797

−33.183

0.417

−32.766

−0.1295

−0.1276

−33

−32

0.0001902

0.6824

0.0002

0.6826

−32.178

0.464

−31.714

−0.1253

−0.1232

−32

−31

0.0002113

0.6852

0.0002

0.6855

−31.172

0.516

−30.656

−0.1211

−0.1189

−31

−30

0.0002345

0.6881

0.0003

0.6883

−30.167

0.573

−29.593

−0.1170

−0.1145

−30

−29

0.0002602

0.6909

0.0003

0.6912

−29.161

0.636

−28.525

−0.1129

−0.1101

−29

−28

0.0002883

0.6938

0.0003

0.6941

−28.156

0.706

−27.450

−0.1088

−0.1057

−28

−27

0.0003193

0.6966

0.0004

0.6970

−27.150

0.782

−26.368

−0.1047

−0.1013

−27

−26

0.0003532

0.6994

0.0004

0.6998

−26.144

0.866

−25.278

−0.1006

−0.0969

−26

−25

0.0003905

0.7023

0.0004

0.7027

−25.139

0.958

−24.181

−0.0965

−0.0924

−25

−24

0.0004314

0.7051

0.0005

0.7056

−24.133

1.059

−23.074

−0.0925

−0.0880

−24

−23

0.0004761

0.7080

0.0005

0.7085

−23.128

1.170

−21.958

−0.0884

−0.0835

−23

−22

0.0005251

0.7108

0.0006

0.7114

−22.122

1.291

−20.831

−0.0844

−0.0790

−22

−21

0.0005787

0.7137

0.0007

0.7143

−21.117

1.424

−19.693

−0.0804

−0.0745

−21

−20

0.0006373

0.7165

0.0007

0.7172

−20.111

1.570

−18.542

−0.0765

−0.0699

−20

−19

0.0007013

0.7193

0.0008

0.7201

−19.106

1.728

−17.377

−0.0725

−0.0653

−19

−18

0.0007711

0.7222

0.0009

0.7231

−18.100

1.902

−16.198

−0.0685

−0.0607

−18

−17

0.0008473

0.7250

0.0010

0.7260

−17.095

2.091

−15.003

−0.0646

−0.0560

−17

−16

0.0009303

0.7279

0.0011

0.7290

−16.089

2.298

−13.791

−0.0607

−0.0513

−16

−15

0.0010207

0.7307

0.0012

0.7319

−15.084

2.523

−12.560

−0.0568

−0.0465

−15

−14

0.0011191

0.7336

0.0013

0.7349

−14.078

2.769

−11.310

−0.0529

−0.0416

−14

−13

0.0012261

0.7364

0.0014

0.7378

−13.073

3.036

−10.037

−0.0490

−0.0367

−13

−12

0.0013425

0.7392

0.0016

0.7408

−12.067

3.326

−8.741

−0.0452

−0.0317

−12

−11

0.0014689

0.7421

0.0017

0.7438

−11.062

3.642

−7.419

−0.0413

−0.0267

−11

−10

0.0016062

0.7449

0.0019

0.7468

−10.056

3.986

−6.070

−0.0375

−0.0215

−10

−9

0.0017551

0.7478

0.0021

0.7499

−9.050

4.358

−4.692

−0.0337

−0.0163

−9

−8

0.0019166

0.7506

0.0023

0.7529

−8.045

4.763

−3.282

−0.0299

−0.0110

−8

−7

0.0020916

0.7534

0.0025

0.7560

−7.039

5.202

−1.838

−0.0261

−0.0055

−7

−6

0.0022812

0.7563

0.0028

0.7591

−6.034

5.677

−0.356

−0.0223

0.0000

−6

−5

0.0024863

0.7591

0.0030

0.7622

−5.028

6.192

1.164

−0.0186

0.0057

−5

−4

0.0027083

0.7620

0.0033

0.7653

−4.023

6.750

2.728

−0.0148

0.0115

−4

−3

0.0029482

0.7648

0.0036

0.7684

−3.017

7.354

4.337

−0.0111

0.0175

−3

−2

0.0032076

0.7677

0.0039

0.7716

−2.011

8.007

5.995

−0.0074

0.0236

−2

−1

0.0034877

0.7705

0.0043

0.7748

−1.006

8.712

7.707

−0.0037

0.0299

−1

0

0.003790

0.7733

0.0047

0.7780

0.000

9.475

9.475

0.0000

0.0364

0

1

0.004076

0.7762

0.0051

0.7813

1.006

10.198

11.203

0.0037

0.0427

1

2

0.004382

0.7790

0.0055

0.7845

2.011

10.970

12.981

0.0073

0.0492

2

3

0.004708

0.7819

0.0059

0.7878

3.017

11.794

14.811

0.0110

0.0559

3

4

0.005055

0.7847

0.0064

0.7911

4.023

12.673

16.696

0.0146

0.0627

4

5

0.005425

0.7875

0.0068

0.7944

5.029

13.611

18.639

0.0182

0.0697

5

6

0.005819

0.7904

0.0074

0.7978

6.034

14.610

20.644

0.0219

0.0769

6

7

0.006238

0.7932

0.0079

0.8012

7.040

15.674

22.714

0.0254

0.0843

7

8

0.006684

0.7961

0.0085

0.8046

8.046

16.807

24.853

0.0290

0.0919

8

9

0.007158

0.7989

0.0092

0.8081

9.052

18.013

27.065

0.0326

0.0997

9

10

0.007663

0.8017

0.0098

0.8116

10.058

19.297

29.354

0.0362

0.1078

10

11

0.008199

0.8046

0.0106

0.8152

11.063

20.661

31.724

0.0397

0.1162

11

12

0.008768

0.8074

0.0113

0.8188

12.069

22.111

34.181

0.0432

0.1248

12

13

0.009372

0.8103

0.0122

0.8224

13.075

23.653

36.728

0.0468

0.1338

13

14

0.010013

0.8131

0.0131

0.8262

14.081

25.290

39.371

0.0503

0.1430

14

15

0.010694

0.8159

0.0140

0.8299

15.087

27.028

42.115

0.0538

0.1525

15

16

0.011415

0.8188

0.0150

0.8338

16.093

28.873

44.966

0.0573

0.1624

16

17

0.012181

0.8216

0.0160

0.8377

17.099

30.830

47.929

0.0607

0.1726

17

18

0.012991

0.8245

0.0172

0.8416

18.105

32.906

51.011

0.0642

0.1832

18

19

0.013851

0.8273

0.0184

0.8457

19.111

35.108

54.219

0.0676

0.1942

19

20

0.014761

0.8301

0.0196

0.8498

20.117

37.441

57.559

0.0711

0.2057

20

21

0.015724

0.8330

0.0210

0.8540

21.124

39.914

61.038

0.0745

0.2175

21

22

0.016744

0.8358

0.0224

0.8583

22.130

42.534

64.663

0.0779

0.2298

22

23

0.017823

0.8387

0.0240

0.8626

23.136

45.308

68.444

0.0813

0.2426

23

24

0.018965

0.8415

0.0256

0.8671

24.142

48.246

72.388

0.0847

0.2560

24

25

0.020173

0.8443

0.0273

0.8716

25.148

51.355

76.504

0.0881

0.2698

25

26

0.021451

0.8472

0.0291

0.8763

26.155

54.647

80.801

0.0915

0.2842

26

27

0.022802

0.8500

0.0311

0.8811

27.161

58.129

85.290

0.0948

0.2992

27

28

0.024229

0.8529

0.0331

0.8860

28.167

61.813

89.980

0.0982

0.3148

28

29

0.025738

0.8557

0.0353

0.8910

29.174

65.709

94.883

0.1015

0.3311

29

30

0.027333

0.8585

0.0376

0.8961

30.180

69.829

100.010

0.1048

0.3481

30

31

0.029018

0.8614

0.0400

0.9014

31.187

74.186

105.373

0.1081

0.3658

31

32

0.030797

0.8642

0.0426

0.9069

32.193

78.792

110.986

0.1115

0.3843

32

33

0.032677

0.8671

0.0454

0.9124

33.200

83.661

116.861

0.1147

0.4035

33

34

0.034663

0.8699

0.0483

0.9182

34.207

88.807

123.014

0.1180

0.4236

34

35

0.036760

0.8727

0.0514

0.9241

35.213

94.247

129.460

0.1213

0.4447

35

36

0.038975

0.8756

0.0546

0.9302

36.220

99.995

136.215

0.1246

0.4666

36

37

0.041313

0.8784

0.0581

0.9365

37.227

106.069

143.296

0.1278

0.4895

37

38

0.043783

0.8813

0.0618

0.9430

38.233

112.488

150.722

0.1311

0.5135

38

39

0.046391

0.8841

0.0657

0.9498

39.240

119.272

158.512

0.1343

0.5386

39

40

0.049145

0.8869

0.0698

0.9567

40.247

126.440

166.687

0.1375

0.5649

40

41

0.052053

0.8898

0.0741

0.9639

41.254

134.016

175.270

0.1407

0.5923

41

42

0.055124

0.8926

0.0788

0.9714

42.261

142.023

184.284

0.1439

0.6211

42

43

0.058368

0.8955

0.0837

0.9791

43.268

150.486

193.754

0.1471

0.6512

43

44

0.061795

0.8983

0.0888

0.9871

44.275

159.432

203.707

0.1503

0.6828

44

45

0.065416

0.9011

0.0943

0.9955

45.282

168.890

214.172

0.1535

0.7159

45

46

0.069242

0.9040

0.1002

1.0041

46.289

178.892

225.181

0.1566

0.7507

46

47

0.073286

0.9068

0.1063

1.0131

47.297

189.470

236.766

0.1598

0.7871

47

48

0.077561

0.9096

0.1129

1.0225

48.304

200.660

248.964

0.1629

0.8254

48

49

0.082081

0.9125

0.1198

1.0323

49.311

212.501

261.812

0.1660

0.8655

49

50

0.086863

0.9153

0.1272

1.0425

50.319

225.034

275.353

0.1692

0.9078

50

51

0.091922

0.9182

0.1350

1.0531

51.326

238.305

289.631

0.1723

0.9522

51

52

0.097278

0.9210

0.1433

1.0643

52.334

252.362

304.695

0.1754

0.9989

52

53

0.102949

0.9238

0.1521

1.0759

53.341

267.256

320.598

0.1785

1.0481

53

54

0.108958

0.9267

0.1614

1.0881

54.349

283.047

337.395

0.1816

1.0999

54

55

0.115326

0.9295

0.1714

1.1009

55.356

299.794

355.151

0.1846

1.1545

55

56

0.122080

0.9324

0.1819

1.1143

56.364

317.567

373.931

0.1877

1.2121

56

57

0.129248

0.9352

0.1932

1.1284

57.372

336.439

393.811

0.1908

1.2729

57

58

0.136858

0.9380

0.2051

1.1432

58.380

356.490

414.869

0.1938

1.3371

58

59

0.144945

0.9409

0.2179

1.1587

59.388

377.809

437.197

0.1968

1.4050

59

60

0.153545

0.9437

0.2315

1.1752

60.396

400.493

460.889

0.1999

1.4769

60

61

0.162697

0.9465

0.2460

1.1925

61.404

424.650

486.054

0.2029

1.5530

61

62

0.172446

0.9494

0.2615

1.2108

62.412

450.398

512.810

0.2059

1.6338

62

63

0.182842

0.9522

0.2780

1.2302

63.420

477.868

541.287

0.2089

1.7195

63

64

0.193937

0.9551

0.2957

1.2508

64.428

507.204

571.632

0.2119

1.8105

64

65

0.205794

0.9579

0.3147

1.2726

65.436

538.570

604.006

0.2149

1.9075

65

66

0.218478

0.9607

0.3350

1.2957

66.445

572.145

638.590

0.2179

2.0107

66

67

0.232067

0.9636

0.3568

1.3204

67.453

608.133

675.587

0.2208

2.1209

67

68

0.246645

0.9664

0.3803

1.3467

68.462

646.762

715.224

0.2238

2.2386

68

69

0.262309

0.9692

0.4056

1.3748

69.470

688.288

757.759

0.2268

2.3647

69

70

0.279167

0.9721

0.4328

1.4049

70.479

733.004

803.483

0.2297

2.4998

70

71

0.297343

0.9749

0.4622

1.4372

71.488

781.240

852.728

0.2326

2.6449

71

72

0.316979

0.9778

0.4941

1.4719

72.496

833.375

905.872

0.2356

2.8012

72

73

0.338237

0.9806

0.5287

1.5093

73.505

889.844

963.350

0.2385

2.9697

73

74

0.361304

0.9834

0.5663

1.5497

74.514

951.149

1025.663

0.2414

3.1520

74

75

0.386399

0.9863

0.6072

1.5935

75.523

1017.871

1093.394

0.2443

3.3497

75

76

0.413774

0.9891

0.6520

1.6411

76.532

1090.688

1167.220

0.2472

3.5645

76

77

0.443727

0.9919

0.7010

1.6930

77.542

1170.398

1247.939

0.2501

3.7989

77

78

0.476610

0.9948

0.7550

1.7497

78.551

1257.941

1336.492

0.2529

4.0554

78

79

0.512842

0.9976

0.8145

1.8121

79.560

1354.439

1433.999

0.2558

4.3371

79

80

0.552926

1.0005

0.8805

1.8809

80.570

1461.236

1541.806

0.2587

4.6478

80

81

0.597470

1.0033

0.9539

1.9572

81.579

1579.961

1661.540

0.2615

4.9921

81

82

0.647218

1.0061

1.0360

2.0421

82.589

1712.604

1795.193

0.2644

5.3755

82

83

0.703089

1.0090

1.1283

2.1373

83.598

1861.625

1945.223

0.2672

5.8048

83

84

0.766233

1.0118

1.2328

2.2446

84.608

2030.099

2114.707

0.2701

6.2886

84

85

0.838105

1.0146

1.3519

2.3665

85.618

2221.922

2307.539

0.2729

6.8377

85

86

0.920580

1.0175

1.4887

2.5062

86.628

2442.105

2528.732

0.2757

7.4661

86

87

1.016105

1.0203

1.6473

2.6676

87.638

2697.204

2784.842

0.2785

8.1920

87

88

1.127952

1.0232

1.8332

2.8564

88.648

2995.967

3084.614

0.2813

9.0397

88

89

1.260579

1.0260

2.0539

3.0799

89.658

3350.325

3439.983

0.2841

10.0422

89

90

1.420235

1.0288

2.3198

3.3487

90.668

3776.998

3867.666

0.2869

11.2459

90


4. THERMODYNAMIC PROPERTIES OF WATER AT SATURATION

Table 3 shows thermodynamic properties of water at saturation for temperatures from −60 to 160°C, calculated by the formulations described by IAPWS (2007, 2009, 2011, 2014). Symbols in the table follow standard steam table nomenclature. These properties are based on ITS-90. The internal energy and entropy of saturated liquid water are both assigned the value zero at the triple point, 0.01°C. Between the triple-point and critical-point temperatures of water, both saturated liquid and saturated vapor may coexist in equilibrium; below the triple-point temperature, both saturated ice and saturated vapor may coexist in equilibrium.

Table 3 Thermodynamic Properties of Water at Saturation

Temp., °C t

Absolute Pressure pws, kPa

Specific Volume, m3/kgw

Specific Enthalpy, kJ/kgw

Specific Entropy, kJ/(kgw·K)

Temp., °C t

Sat. Solid vi/vf

Evap. vig/vfg

Sat. Vapor vg

Sat. Solid hi/hf

Evap. hig/hfg

Sat. Vapor hg

Sat. Solid si/sf

Evap. sig/sfg

Sat. Vapor sg

−60

0.00108

0.001081

90971.58

90971.58

−446.12

2836.27

2390.14

−1.6842

13.3064

11.6222

−60

−59

0.00124

0.001082

79885.31

79885.31

−444.46

2836.45

2391.99

−1.6764

13.2452

11.5687

−59

−58

0.00141

0.001082

70235.77

70235.78

−442.79

2836.63

2393.85

−1.6687

13.1845

11.5158

−58

−57

0.00161

0.001082

61826.23

61826.24

−441.11

2836.81

2395.70

−1.6609

13.1243

11.4634

−57

−56

0.00184

0.001082

54488.28

54488.28

−439.42

2836.97

2397.55

−1.6531

13.0646

11.4115

−56

−55

0.00209

0.001082

48077.54

48077.54

−437.73

2837.13

2399.40

−1.6453

13.0054

11.3601

−55

−54

0.00238

0.001082

42470.11

42470.11

−436.03

2837.28

2401.25

−1.6375

12.9468

11.3092

−54

−53

0.00271

0.001082

37559.49

37559.50

−434.32

2837.42

2403.10

−1.6298

12.8886

11.2589

−53

−52

0.00307

0.001083

33254.07

33254.07

−432.61

2837.56

2404.95

−1.6220

12.8310

11.2090

−52

−51

0.00348

0.001083

29474.87

29474.87

−430.88

2837.69

2406.81

−1.6142

12.7738

11.1596

−51

−50

0.00394

0.001083

26153.80

26153.80

−429.16

2837.81

2408.66

−1.6065

12.7171

11.1106

−50

−49

0.00445

0.001083

23232.03

23232.04

−427.42

2837.93

2410.51

−1.5987

12.6609

11.0622

−49

−48

0.00503

0.001083

20658.70

20658.70

−425.68

2838.04

2412.36

−1.5909

12.6051

11.0142

−48

−47

0.00568

0.001083

18389.75

18389.75

−423.93

2838.14

2414.21

−1.5832

12.5498

10.9666

−47

−46

0.00640

0.001083

16387.03

16387.03

−422.17

2838.23

2416.06

−1.5754

12.4950

10.9196

−46

−45

0.00720

0.001084

14617.39

14617.39

−420.40

2838.32

2417.91

−1.5677

12.4406

10.8729

−45

−44

0.00810

0.001084

13052.07

13052.07

−418.63

2838.39

2419.76

−1.5599

12.3867

10.8267

−44

−43

0.00910

0.001084

11666.02

11666.02

−416.85

2838.47

2421.62

−1.5522

12.3331

10.7810

−43

−42

0.01022

0.001084

10437.46

10437.46

−415.06

2838.53

2423.47

−1.5444

12.2801

10.7356

−42

−41

0.01146

0.001084

9347.38

9347.38

−413.27

2838.59

2425.32

−1.5367

12.2274

10.6907

−41

−40

0.01284

0.001084

8379.20

8379.20

−411.47

2838.64

2427.17

−1.5289

12.1752

10.6462

−40

−39

0.01437

0.001085

7518.44

7518.44

−409.66

2838.68

2429.02

−1.5212

12.1234

10.6022

−39

−38

0.01607

0.001085

6752.43

6752.43

−407.85

2838.72

2430.87

−1.5135

12.0720

10.5585

−38

−37

0.01795

0.001085

6070.08

6070.08

−406.02

2838.74

2432.72

−1.5057

12.0210

10.5152

−37

−36

0.02004

0.001085

5461.68

5461.68

−404.19

2838.76

2434.57

−1.4980

11.9704

10.4724

−36

−35

0.02234

0.001085

4918.69

4918.69

−402.36

2838.78

2436.42

−1.4903

11.9202

10.4299

−35

−34

0.02489

0.001085

4433.64

4433.64

−400.51

2838.78

2438.27

−1.4825

11.8703

10.3878

−34

−33

0.02771

0.001085

3999.95

3999.95

−398.66

2838.78

2440.12

−1.4748

11.8209

10.3461

−33

−32

0.03081

0.001086

3611.82

3611.82

−396.80

2838.77

2441.97

−1.4671

11.7718

10.3047

−32

−31

0.03423

0.001086

3264.15

3264.16

−394.94

2838.75

2443.82

−1.4594

11.7231

10.2638

−31

−30

0.03801

0.001086

2952.46

2952.46

−393.06

2838.73

2445.67

−1.4516

11.6748

10.2232

−30

−29

0.04215

0.001086

2672.77

2672.77

−391.18

2838.70

2447.51

−1.4439

11.6269

10.1830

−29

−28

0.04672

0.001086

2421.58

2421.58

−389.29

2838.66

2449.36

−1.4362

11.5793

10.1431

−28

−27

0.05173

0.001086

2195.80

2195.80

−387.40

2838.61

2451.21

−1.4285

11.5321

10.1036

−27

−26

0.05724

0.001087

1992.68

1992.68

−385.50

2838.56

2453.06

−1.4208

11.4852

10.0644

−26

−25

0.06327

0.001087

1809.79

1809.79

−383.59

2838.49

2454.91

−1.4131

11.4386

10.0256

−25

−24

0.06989

0.001087

1644.99

1644.99

−381.67

2838.42

2456.75

−1.4054

11.3925

9.9871

−24

−23

0.07714

0.001087

1496.36

1496.36

−379.75

2838.35

2458.60

−1.3977

11.3466

9.9489

−23

−22

0.08508

0.001087

1362.21

1362.21

−377.81

2838.26

2460.45

−1.3899

11.3011

9.9111

−22

−21

0.09376

0.001087

1241.03

1241.03

−375.88

2838.17

2462.29

−1.3822

11.2559

9.8736

−21

−20

0.10324

0.001087

1131.49

1131.49

−373.93

2838.07

2464.14

−1.3745

11.2110

9.8365

−20

−19

0.11360

0.001088

1032.38

1032.38

−371.98

2837.96

2465.98

−1.3668

11.1665

9.7996

−19

−18

0.12490

0.001088

942.64

942.65

−370.01

2837.84

2467.83

−1.3591

11.1223

9.7631

−18

−17

0.13722

0.001088

861.34

861.34

−368.05

2837.72

2469.67

−1.3514

11.0784

9.7269

−17

−16

0.15065

0.001088

787.61

787.61

−366.07

2837.59

2471.51

−1.3437

11.0348

9.6910

−16

−15

0.16527

0.001088

720.70

720.70

−364.09

2837.45

2473.36

−1.3360

10.9915

9.6554

−15

−14

0.18119

0.001088

659.94

659.94

−362.10

2837.30

2475.20

−1.3284

10.9485

9.6201

−14

−13

0.19849

0.001089

604.72

604.73

−360.10

2837.14

2477.04

−1.3207

10.9058

9.5851

−13

−12

0.21729

0.001089

554.51

554.51

−358.10

2836.98

2478.88

−1.3130

10.8634

9.5504

−12

−11

0.23771

0.001089

508.81

508.81

−356.08

2836.80

2480.72

−1.3053

10.8213

9.5160

−11

−10

0.25987

0.001089

467.19

467.19

−354.06

2836.62

2482.56

−1.2976

10.7795

9.4819

−10

−9

0.28391

0.001089

429.25

429.26

−352.04

2836.44

2484.40

−1.2899

10.7380

9.4481

−9

−8

0.30995

0.001089

394.66

394.66

−350.00

2836.24

2486.23

−1.2822

10.6967

9.4145

−8

−7

0.33817

0.001090

363.09

363.09

−347.96

2836.03

2488.07

−1.2745

10.6558

9.3812

−7

−6

0.36871

0.001090

334.26

334.26

−345.91

2835.82

2489.91

−1.2668

10.6151

9.3482

−6

−5

0.40174

0.001090

307.92

307.92

−343.86

2835.60

2491.74

−1.2592

10.5747

9.3155

−5

−4

0.43745

0.001090

283.82

283.83

−341.79

2835.37

2493.57

−1.2515

10.5345

9.2830

−4

−3

0.47604

0.001090

261.78

261.78

−339.72

2835.13

2495.41

−1.2438

10.4946

9.2508

−3

−2

0.51770

0.001091

241.60

241.60

−337.64

2834.88

2497.24

−1.2361

10.4550

9.2189

−2

−1

0.56266

0.001091

223.10

223.11

−335.56

2834.63

2499.07

−1.2284

10.4157

9.1872

−1

0

0.61115

0.001091

206.15

206.15

−333.47

2834.36

2500.90

−1.2208

10.3766

9.1558

0

Transition from saturated solid to saturated liquid

0

0.6112

0.001000

206.139

206.140

−0.04

2500.93

2500.89

−0.0002

9.1559

9.1558

0

1

0.6571

0.001000

192.444

192.445

4.18

2498.55

2502.73

0.0153

9.1138

9.1291

1

2

0.7060

0.001000

179.763

179.764

8.39

2496.17

2504.57

0.0306

9.0721

9.1027

2

3

0.7581

0.001000

168.013

168.014

12.60

2493.80

2506.40

0.0459

9.0306

9.0765

3

4

0.8135

0.001000

157.120

157.121

16.81

2491.42

2508.24

0.0611

8.9895

9.0506

4

5

0.8726

0.001000

147.016

147.017

21.02

2489.05

2510.07

0.0763

8.9486

9.0249

5

6

0.9354

0.001000

137.637

137.638

25.22

2486.68

2511.91

0.0913

8.9081

8.9994

6

7

1.0021

0.001000

128.927

128.928

29.43

2484.31

2513.74

0.1064

8.8678

8.9742

7

8

1.0730

0.001000

120.833

120.834

33.63

2481.94

2515.57

0.1213

8.8278

8.9492

8

9

1.1483

0.001000

113.308

113.309

37.82

2479.58

2517.40

0.1362

8.7882

8.9244

9

10

1.2282

0.001000

106.308

106.309

42.02

2477.21

2519.23

0.1511

8.7488

8.8998

10

11

1.3129

0.001000

99.792

99.793

46.22

2474.84

2521.06

0.1659

8.7096

8.8755

11

12

1.4028

0.001001

93.723

93.724

50.41

2472.48

2522.89

0.1806

8.6708

8.8514

12

13

1.4981

0.001001

88.069

88.070

54.60

2470.11

2524.71

0.1953

8.6322

8.8275

13

14

1.5989

0.001001

82.797

82.798

58.79

2467.75

2526.54

0.2099

8.5939

8.8038

14

15

1.7057

0.001001

77.880

77.881

62.98

2465.38

2528.36

0.2245

8.5559

8.7804

15

16

1.8188

0.001001

73.290

73.291

67.17

2463.01

2530.19

0.2390

8.5181

8.7571

16

17

1.9383

0.001001

69.005

69.006

71.36

2460.65

2532.01

0.2534

8.4806

8.7341

17

18

2.0647

0.001001

65.002

65.003

75.55

2458.28

2533.83

0.2678

8.4434

8.7112

18

19

2.1982

0.001002

61.260

61.261

79.73

2455.92

2535.65

0.2822

8.4064

8.6886

19

20

2.3392

0.001002

57.760

57.761

83.92

2453.55

2537.47

0.2965

8.3696

8.6661

20

21

2.4881

0.001002

54.486

54.487

88.10

2451.18

2539.29

0.3108

8.3331

8.6439

21

22

2.6452

0.001002

51.421

51.422

92.29

2448.81

2541.10

0.3250

8.2969

8.6218

22

23

2.8109

0.001003

48.551

48.552

96.47

2446.45

2542.92

0.3391

8.2609

8.6000

23

24

2.9856

0.001003

45.862

45.863

100.66

2444.08

2544.73

0.3532

8.2251

8.5783

24

25

3.1697

0.001003

43.340

43.341

104.84

2441.71

2546.54

0.3673

8.1895

8.5568

25

26

3.3637

0.001003

40.976

40.977

109.02

2439.33

2548.35

0.3813

8.1542

8.5355

26

27

3.5679

0.001004

38.757

38.758

113.20

2436.96

2550.16

0.3952

8.1192

8.5144

27

28

3.7828

0.001004

36.674

36.675

117.38

2434.59

2551.97

0.4091

8.0843

8.4934

28

29

4.0089

0.001004

34.718

34.719

121.56

2432.21

2553.78

0.4230

8.0497

8.4727

29

30

4.2467

0.001004

32.881

32.882

125.75

2429.84

2555.58

0.4368

8.0153

8.4521

30

31

4.4966

0.001005

31.153

31.154

129.93

2427.46

2557.39

0.4506

7.9812

8.4317

31

32

4.7592

0.001005

29.528

29.529

134.11

2425.08

2559.19

0.4643

7.9472

8.4115

32

33

5.0351

0.001005

28.000

28.001

138.29

2422.70

2560.99

0.4780

7.9135

8.3914

33

34

5.3247

0.001006

26.561

26.562

142.47

2420.32

2562.79

0.4916

7.8800

8.3715

34

35

5.6286

0.001006

25.207

25.208

146.64

2417.94

2564.58

0.5052

7.8467

8.3518

35

36

5.9475

0.001006

23.931

23.932

150.82

2415.56

2566.38

0.5187

7.8136

8.3323

36

37

6.2818

0.001007

22.728

22.729

155.00

2413.17

2568.17

0.5322

7.7807

8.3129

37

38

6.6324

0.001007

21.594

21.595

159.18

2410.78

2569.96

0.5457

7.7480

8.2936

38

39

6.9997

0.001007

20.525

20.526

163.36

2408.39

2571.75

0.5591

7.7155

8.2746

39

40

7.3844

0.001008

19.516

19.517

167.54

2406.00

2573.54

0.5724

7.6832

8.2557

40

41

7.7873

0.001008

18.564

18.565

171.72

2403.61

2575.33

0.5858

7.6512

8.2369

41

42

8.2090

0.001009

17.664

17.665

175.90

2401.21

2577.11

0.5990

7.6193

8.2183

42

43

8.6503

0.001009

16.815

16.816

180.08

2398.82

2578.89

0.6123

7.5876

8.1999

43

44

9.1118

0.001009

16.012

16.013

184.26

2396.42

2580.67

0.6255

7.5561

8.1816

44

45

9.5944

0.001010

15.252

15.253

188.44

2394.02

2582.45

0.6386

7.5248

8.1634

45

46

10.0988

0.001010

14.534

14.535

192.62

2391.61

2584.23

0.6517

7.4937

8.1454

46

47

10.6259

0.001011

13.855

13.856

196.80

2389.21

2586.00

0.6648

7.4628

8.1276

47

48

11.1764

0.001011

13.212

13.213

200.98

2386.80

2587.77

0.6778

7.4320

8.1099

48

49

11.7512

0.001012

12.603

12.604

205.16

2384.39

2589.54

0.6908

7.4015

8.0923

49

50

12.3513

0.001012

12.027

12.028

209.34

2381.97

2591.31

0.7038

7.3711

8.0749

50

51

12.9774

0.001013

11.481

11.482

213.52

2379.56

2593.08

0.7167

7.3409

8.0576

51

52

13.6305

0.001013

10.963

10.964

217.70

2377.14

2594.84

0.7296

7.3109

8.0405

52

53

14.3116

0.001014

10.472

10.473

221.88

2374.72

2596.60

0.7424

7.2811

8.0235

53

54

15.0215

0.001014

10.006

10.007

226.06

2372.30

2598.35

0.7552

7.2514

8.0066

54

55

15.7614

0.001015

9.5639

9.5649

230.24

2369.87

2600.11

0.7680

7.2219

7.9899

55

56

16.5322

0.001015

9.1444

9.1454

234.42

2367.44

2601.86

0.7807

7.1926

7.9733

56

57

17.3350

0.001016

8.7461

8.7471

238.61

2365.01

2603.61

0.7934

7.1634

7.9568

57

58

18.1708

0.001016

8.3678

8.3688

242.79

2362.57

2605.36

0.8060

7.1344

7.9405

58

59

19.0407

0.001017

8.0083

8.0093

246.97

2360.13

2607.10

0.8186

7.1056

7.9243

59

60

19.9458

0.001017

7.6666

7.6677

251.15

2357.69

2608.85

0.8312

7.0770

7.9082

60

61

20.8873

0.001018

7.3418

7.3428

255.34

2355.25

2610.58

0.8438

7.0485

7.8922

61

62

21.8664

0.001018

7.0328

7.0338

259.52

2352.80

2612.32

0.8563

7.0201

7.8764

62

63

22.8842

0.001019

6.7389

6.7399

263.71

2350.35

2614.05

0.8687

6.9919

7.8607

63

64

23.9421

0.001019

6.4591

6.4601

267.89

2347.89

2615.78

0.8811

6.9639

7.8451

64

65

25.0411

0.001020

6.1928

6.1938

272.08

2345.43

2617.51

0.8935

6.9361

7.8296

65

66

26.1827

0.001020

5.9392

5.9402

276.27

2342.97

2619.23

0.9059

6.9083

7.8142

66

67

27.3680

0.001021

5.6976

5.6986

280.45

2340.50

2620.96

0.9182

6.8808

7.7990

67

68

28.5986

0.001022

5.4674

5.4684

284.64

2338.03

2622.67

0.9305

6.8534

7.7839

68

69

29.8756

0.001022

5.2479

5.2490

288.83

2335.56

2624.39

0.9428

6.8261

7.7689

69

70

31.2006

0.001023

5.0387

5.0397

293.02

2333.08

2626.10

0.9550

6.7990

7.7540

70

71

32.5750

0.001023

4.8392

4.8402

297.21

2330.60

2627.81

0.9672

6.7720

7.7392

71

72

34.0001

0.001024

4.6488

4.6498

301.40

2328.11

2629.51

0.9793

6.7452

7.7245

72

73

35.4775

0.001025

4.4671

4.4681

305.59

2325.62

2631.21

0.9915

6.7185

7.7100

73

74

37.0088

0.001025

4.2937

4.2947

309.78

2323.13

2632.91

1.0035

6.6920

7.6955

74

75

38.5954

0.001026

4.1281

4.1291

313.97

2320.63

2634.60

1.0156

6.6656

7.6812

75

76

40.2389

0.001026

3.9699

3.9709

318.17

2318.13

2636.29

1.0276

6.6393

7.6669

76

77

41.9409

0.001027

3.8188

3.8198

322.36

2315.62

2637.98

1.0396

6.6132

7.6528

77

78

43.7031

0.001028

3.6743

3.6754

326.56

2313.11

2639.66

1.0516

6.5872

7.6388

78

79

45.5271

0.001028

3.5363

3.5373

330.75

2310.59

2641.34

1.0635

6.5613

7.6248

79

80

47.4147

0.001029

3.4042

3.4053

334.95

2308.07

2643.01

1.0754

6.5356

7.6110

80

81

49.3676

0.001030

3.2780

3.2790

339.15

2305.54

2644.68

1.0873

6.5100

7.5973

81

82

51.3875

0.001030

3.1572

3.1582

343.34

2303.01

2646.35

1.0991

6.4846

7.5837

82

83

53.4762

0.001031

3.0415

3.0426

347.54

2300.47

2648.01

1.1109

6.4592

7.5701

83

84

55.6355

0.001032

2.9309

2.9319

351.74

2297.93

2649.67

1.1227

6.4340

7.5567

84

85

57.8675

0.001032

2.8249

2.8259

355.95

2295.38

2651.33

1.1344

6.4090

7.5434

85

86

60.1738

0.001033

2.7234

2.7244

360.15

2292.83

2652.98

1.1461

6.3840

7.5301

86

87

62.5565

0.001034

2.6262

2.6272

364.35

2290.27

2654.62

1.1578

6.3592

7.5170

87

88

65.0174

0.001035

2.5330

2.5341

368.56

2287.70

2656.26

1.1694

6.3345

7.5039

88

89

67.5587

0.001035

2.4437

2.4448

372.76

2285.14

2657.90

1.1811

6.3099

7.4909

89

90

70.1824

0.001036

2.3581

2.3591

376.97

2282.56

2659.53

1.1927

6.2854

7.4781

90

91

72.8904

0.001037

2.2760

2.2771

381.18

2279.98

2661.16

1.2042

6.2611

7.4653

91

92

75.6849

0.001037

2.1973

2.1983

385.38

2277.39

2662.78

1.2158

6.2368

7.4526

92

93

78.5681

0.001038

2.1217

2.1228

389.59

2274.80

2664.39

1.2273

6.2127

7.4400

93

94

81.5420

0.001039

2.0492

2.0502

393.81

2272.20

2666.01

1.2387

6.1887

7.4275

94

95

84.6089

0.001040

1.9796

1.9806

398.02

2269.60

2667.61

1.2502

6.1648

7.4150

95

96

87.7711

0.001040

1.9128

1.9138

402.23

2266.98

2669.22

1.2616

6.1411

7.4027

96

97

91.0308

0.001041

1.8486

1.8497

406.45

2264.37

2670.81

1.2730

6.1174

7.3904

97

98

94.3902

0.001042

1.7870

1.7880

410.66

2261.74

2672.40

1.2844

6.0938

7.3782

98

99

97.8518

0.001043

1.7277

1.7288

414.88

2259.11

2673.99

1.2957

6.0704

7.3661

99

100

101.4180

0.001043

1.6708

1.6719

419.10

2256.47

2675.57

1.3070

6.0471

7.3541

100

101

105.0910

0.001044

1.6161

1.6171

423.32

2253.83

2677.15

1.3183

6.0238

7.3421

101

102

108.8735

0.001045

1.5635

1.5645

427.54

2251.18

2678.72

1.3296

6.0007

7.3303

102

103

112.7678

0.001046

1.5129

1.5140

431.76

2248.52

2680.28

1.3408

5.9777

7.3185

103

104

116.7765

0.001047

1.4642

1.4653

435.99

2245.85

2681.84

1.3520

5.9548

7.3068

104

105

120.9021

0.001047

1.4174

1.4185

440.21

2243.18

2683.39

1.3632

5.9320

7.2951

105

106

125.1472

0.001048

1.3724

1.3734

444.44

2240.50

2684.94

1.3743

5.9092

7.2836

106

107

129.5145

0.001049

1.3290

1.3301

448.67

2237.81

2686.48

1.3854

5.8866

7.2721

107

108

134.0065

0.001050

1.2873

1.2883

452.90

2235.12

2688.02

1.3965

5.8641

7.2607

108

109

138.6261

0.001051

1.2471

1.2481

457.13

2232.41

2689.55

1.4076

5.8417

7.2493

109

110

143.3760

0.001052

1.2083

1.2094

461.36

2229.70

2691.07

1.4187

5.8194

7.2380

110

111

148.2588

0.001052

1.1710

1.1721

465.60

2226.99

2692.58

1.4297

5.7972

7.2268

111

112

153.2775

0.001053

1.1351

1.1362

469.83

2224.26

2694.09

1.4407

5.7750

7.2157

112

113

158.4348

0.001054

1.1005

1.1015

474.07

2221.53

2695.60

1.4517

5.7530

7.2047

113

114

163.7337

0.001055

1.0671

1.0681

478.31

2218.78

2697.09

1.4626

5.7310

7.1937

114

115

169.1770

0.001056

1.0349

1.0359

482.55

2216.03

2698.58

1.4735

5.7092

7.1827

115

116

174.7678

0.001057

1.0038

1.0049

486.80

2213.27

2700.07

1.4844

5.6874

7.1719

116

117

180.5090

0.001058

0.9739

0.9750

491.04

2210.51

2701.55

1.4953

5.6658

7.1611

117

118

186.4036

0.001059

0.9450

0.9461

495.29

2207.73

2703.02

1.5062

5.6442

7.1504

118

119

192.4547

0.001059

0.9171

0.9182

499.53

2204.94

2704.48

1.5170

5.6227

7.1397

119

120

198.6654

0.001060

0.8902

0.8913

503.78

2202.15

2705.93

1.5278

5.6013

7.1291

120

122

211.5782

0.001062

0.8392

0.8403

512.29

2196.53

2708.82

1.5494

5.5587

7.1081

122

124

225.1676

0.001064

0.7916

0.7927

520.80

2190.88

2711.69

1.5708

5.5165

7.0873

124

126

239.4597

0.001066

0.7472

0.7483

529.32

2185.19

2714.52

1.5922

5.4746

7.0668

126

128

254.4813

0.001068

0.7058

0.7068

537.85

2179.47

2717.32

1.6134

5.4330

7.0465

128

130

270.2596

0.001070

0.6670

0.6681

546.39

2173.70

2720.09

1.6346

5.3918

7.0264

130

132

286.8226

0.001072

0.6308

0.6318

554.93

2167.89

2722.83

1.6557

5.3508

7.0066

132

134

304.1989

0.001074

0.5969

0.5979

563.49

2162.04

2725.53

1.6767

5.3102

6.9869

134

136

322.4175

0.001076

0.5651

0.5662

572.05

2156.15

2728.20

1.6977

5.2698

6.9675

136

138

341.5081

0.001078

0.5353

0.5364

580.62

2150.22

2730.84

1.7185

5.2298

6.9483

138

140

361.5010

0.001080

0.5074

0.5085

589.20

2144.24

2733.44

1.7393

5.1900

6.9293

140

142

382.4271

0.001082

0.4813

0.4823

597.79

2138.22

2736.01

1.7600

5.1505

6.9105

142

144

404.3178

0.001084

0.4567

0.4577

606.39

2132.15

2738.54

1.7806

5.1112

6.8918

144

146

427.2053

0.001086

0.4336

0.4346

615.00

2126.04

2741.04

1.8011

5.0723

6.8734

146

148

451.1220

0.001088

0.4118

0.4129

623.62

2119.88

2743.50

1.8216

5.0335

6.8551

148

150

476.1014

0.001091

0.3914

0.3925

632.25

2113.67

2745.92

1.8420

4.9951

6.8370

150

152

502.1771

0.001093

0.3722

0.3733

640.89

2107.41

2748.30

1.8623

4.9569

6.8191

152

154

529.3834

0.001095

0.3541

0.3552

649.55

2101.10

2750.64

1.8825

4.9189

6.8014

154

156

557.7555

0.001097

0.3370

0.3381

658.21

2094.74

2752.95

1.9027

4.8811

6.7838

156

158

587.3287

0.001100

0.3209

0.3220

666.89

2088.32

2755.21

1.9228

4.8436

6.7664

158

160

618.1392

0.001102

0.3057

0.3068

675.57

2081.86

2757.43

1.9428

4.8063

6.7491

160

The water vapor saturation pressure is required to determine a number of moist air properties, principally the saturation humidity ratio. Values may be obtained from Table 3 or calculated from the following formulas (Hyland and Wexler 1983b). The 1983 formulas are within 300 ppm of the latest IAPWS formulations. For higher accuracy, developers of software and others are referred to IAPWS (2007, 2011).

The saturation (sublimation) pressure over ice for the temperature range of −100 to 0°C is given by

(5)

where

C1 = −5.674 535 9 E+03
C2 = 6.392 524 7 E+00
C3 = −9.677 843 0 E−03
C4 = 6.221 570 1 E−07
C5= 2.074 782 5 E−09
C6 = −9.484 024 0 E−13
C7 = 4.163 501 9 E+00

The saturation pressure over liquid water for the temperature range of 0 to 200°C is given by

(6)

where

C8 = −5.800 220 6 E+03
C9 = 1.391 499 3 E+00
C10 = −4.864 023 9 E−02
C11 = 4.176 476 8 E−05
C12 = −1.445 209 3 E−08
C13 = 6.545 967 3 E+00

In both Equations (5) and (6),

pws= saturation pressure, Pa
T= absolute temperature, K = °C + 273.15

The coefficients of Equations (5) and (6) were derived from the Hyland-Wexler equations. Because of rounding errors in the derivations and in some computers’ calculating precision, results from Equations (5) and (6) may not agree precisely with Table 3 values.

The vapor pressure ps of water in saturated moist air differs negligibly from the saturation vapor pressure pws of pure water at the same temperature. Consequently, ps can be used in equations in place of pws with very little error:

where xws is the mole fraction of water vapor in saturated moist air at temperature t and pressure p, and p is the total barometric pressure of moist air.

5. HUMIDITY PARAMETERS

 Basic Parameters

Humidity ratio W (or mixing ratio) of a given moist air sample is defined as the ratio of the mass of water vapor to the mass of dry air in the sample:

(7)

W equals the mole fraction ratio xw/xda multiplied by the ratio of molecular masses (18.015 268/28.966 = 0.621 945):

(8)

Specific humidity γ is the ratio of the mass of water vapor to total mass of the moist air sample:

(9a)

In terms of the humidity ratio,

(9b)

Absolute humidity (alternatively, water vapor density) dv is the ratio of the mass of water vapor to total volume of the sample:

(10)

Density ρ of a moist air mixture is the ratio of total mass to total volume:

(11)

where v is the moist air specific volume, m3/kgda, as defined by Equation (24).

 Humidity Parameters Involving Saturation

The following definitions of humidity parameters involve the concept of moist air saturation:

 

Saturation humidity ratio Ws(t, p) is the humidity ratio of moist air saturated with respect to water (or ice) at the same temperature t and pressure p.

Relative humidity ϕ is the ratio of the actual water vapor partial pressure in moist air at the dew-point pressure and temperature to the reference saturation water vapor partial pressure at the dry-bulb pressure and temperature:

(12)

Note that Equations (12) and (22) have been revised so that they cover both the normal range of relative humidity where e(tdb) < p and the extended range (e.g., atmospheric pressure drying kilns) where e(tdb) ≥ p. The definitions in earlier editions applied only to the normal range.

Dew-point temperature td is the temperature of moist air saturated at pressure p, with the same humidity ratio W as that of the given sample of moist air. It is defined as the solution td(p, W) of the following equation:

(13)

Thermodynamic wet-bulb temperature t* is the temperature at which water (liquid or solid), by evaporating into moist air at dry-bulb temperature t and humidity ratio W, can bring air to saturation adiabatically at the same temperature t* while total pressure p is constant. This parameter is considered separately in the section on Thermodynamic Wet-Bulb and Dew-Point Temperature.

6. PERFECT GAS RELATIONSHIPS FOR DRY AND MOIST AIR

When moist air is considered a mixture of independent perfect gases (i.e., dry air and water vapor), each is assumed to obey the perfect gas equation of state as follows:

(14)

(15)

where

pda= partial pressure of dry air
pw= partial pressure of water vapor
V= total mixture volume
nda= number of moles of dry air
nw = number of moles of water vapor
R = universal gas constant, 8314.472 J/(kmol · K)
T = absolute temperature, K

The mixture also obeys the perfect gas equation:

(16)

or

(17)

where p = pda + pw is the total mixture pressure and n = nda + nw is the total number of moles in the mixture. From Equations (14) to (17), the mole fractions of dry air and water vapor are, respectively,

(18)

and

(19)

From Equations (8), (18), and (19), the humidity ratio W is

(20)

The saturation humidity ratio Ws is

(21)

The term pws represents the saturation pressure of water vapor in the absence of air at the given temperature t. This pressure pws is a function only of temperature and differs slightly from the vapor pressure of water in saturated moist air.

The relative humidity ϕ is defined in Equation (12). Using the second equality and eliminating the enhancement factors, which are not applicable using the perfect gas assumption, gives

(22)

Substituting Equation (21) for Ws into Equation (13),

(23)

Both ϕ and μ are zero for dry air and unity for saturated moist air. At intermediate states, their values differ, substantially at higher temperatures.

The specific volume v of a moist air mixture is expressed in terms of a unit mass of dry air:

(24)

where V is the total volume of the mixture, Mda is the total mass of dry air, and nda is the number of moles of dry air. By Equations (14) and (24), with the relation p = pda + pw,

(25)

Using Equation (18),

(26)

In Equations (25) and (26), v is specific volume, T is absolute temperature, p is total pressure, pw is partial pressure of water vapor, and W is humidity ratio.

In specific units, Equation (26) may be expressed as

where

v = specific volume, m3/kgda
t = dry-bulb temperature, °C
W = humidity ratio, kgw/kgda
p = total pressure, kPa

The enthalpy of a mixture of perfect gases equals the sum of the individual partial enthalpies of the components. Therefore, the specific enthalpy of moist air can be written as follows:

(27)

where hda is the specific enthalpy for dry air in kJ/kgda and hg is the specific enthalpy for saturated water vapor in kJ/kgw at the mixture’s temperature. As an approximation,

(28)

(29)

where t is the dry-bulb temperature in °C. The moist air specific enthalpy in kJ/kgda then becomes

(30)

7. THERMODYNAMIC WET-BULB AND DEW-POINT TEMPERATURE

For any state of moist air, a temperature t* exists at which liquid (or solid) water evaporates into the air to bring it to saturation at exactly this same temperature and total pressure (Harrison 1965). During adiabatic saturation, saturated air is expelled at a temperature equal to that of the injected water. In this constant-pressure process,

  • Humidity ratio increases from initial value W to Ws*, corresponding to saturation at temperature t*

  • Enthalpy increases from initial value h to hs*, corresponding to saturation at temperature t*

  • Mass of water added per unit mass of dry air is (Ws* − W), which adds energy to the moist air of amount (Ws* − W)hw*, where hw* denotes specific enthalpy in kJ/kgw of water added at temperature t*

Therefore, if the process is strictly adiabatic, conservation of enthalpy at constant total pressure requires that

(31)

Ws*, hw*, and hs* are functions only of temperature t* for a fixed value of pressure. The value of t* that satisfies Equation (31) for given values of h, W, and p is the thermodynamic wet-bulb temperature.

A psychrometer consists of two thermometers; one thermometer’s bulb is covered by a wick that has been thoroughly wetted with water. When the wet bulb is placed in an airstream, water evaporates from the wick, eventually reaching an equilibrium temperature called the wet-bulb temperature. This process is not one of adiabatic saturation, which defines the thermodynamic wet-bulb temperature, but one of simultaneous heat and mass transfer from the wet bulb. The fundamental mechanism of this process is described by the Lewis relation [Equation (40) in Chapter 6]. Fortunately, only small corrections must be applied to wet-bulb thermometer readings to obtain the thermodynamic wet-bulb temperature.

As defined, thermodynamic wet-bulb temperature is a unique property of a given moist air sample independent of measurement techniques.

Equation (31) is exact because it defines the thermodynamic wet-bulb temperature t*. Substituting the approximate perfect gas relation [Equation (30)] for h, the corresponding expression for hs*, and the approximate relation for saturated liquid water

(32)

into Equation (31), and solving for the humidity ratio,

(33)

where t and t* are in °C. Below freezing, the corresponding equations are

(34)

(35)

A wet/ice-bulb thermometer is imprecise when determining moisture content at 0°C.

The dew-point temperature td of moist air with humidity ratio W and pressure p was defined as the solution td(p, W) of Ws(p, td). For perfect gases, this reduces to

(36)

where pw is the water vapor partial pressure for the moist air sample and pws(td) is the saturation vapor pressure at temperature td. The saturation vapor pressure is obtained from Table 3 or by using Equation (5) or (6). Alternatively, the dew-point temperature can be calculated directly by one of the following equations (Peppers 1988):

Between dew points of 0 and 93°C,

(37)

Below 0°C,

(38)

where

td = dew-point temperature, °C
α = ln pw
pw = water vapor partial pressure, kPa
C14 = 6.54
C15 = 14.526
C16 = 0.7389
C17 = 0.09486
C18 = 0.4569

8. NUMERICAL CALCULATION OF MOIST AIR PROPERTIES

The following are outlines, citing equations and tables already presented, for calculating moist air properties using perfect gas relations. These relations are accurate enough for most engineering calculations in air-conditioning practice, and are readily adapted to either hand or computer calculating methods. For more details, refer to Tables 15 through 18 in Chapter 1 of Olivieri (1996). Graphical procedures are discussed in the section on Psychrometric Charts.


SITUATION 1.


Given: Dry-bulb temperature t, Wet-bulb temperature t*, Pressure p

To Obtain

Use

Comments

pws(t*)

Table 3 or Equation (5) or (6)

Sat. press. for temp. t*

Ws*

Equation (21)

Using pws(t*)

W

Equation (33) or (35)

 

pws(t)

Table 3 or Equation (5) or (6)

Sat. press. for temp. t

Ws

Equation (21)

Using pws(t)

ϕ

Equation (23)

Using pws(t)

v

Equation (26)

 

h

Equation (30)

 

pw

Equation (36)

 

td

Table 3 with Equation (36), (37), or (38)



SITUATION 2.


Given: Dry-bulb temperature t, Dew-point temperature td, Pressure p

To Obtain

Use

Comments

pw = pws(td)

Table 3 or Equation (5) or (6)

Sat. press. for temp. td

W

Equation (20)

 

pws(t)

Table 3 or Equation (5) or (6)

Sat. press. for temp. t

Ws

Equation (21)

Using pws(t)

ϕ

Equation (23)

Using pws(t)

v

Equation (26)

 

h

Equation (30)

 

t*

Equation (21) and (33) or (35) with Table 3 or with Equation (5) or (6)

Requires trial-and-error or numerical solution method


SITUATION 3.


Given: Dry-bulb temperature t, Relative humidity ϕ, Pressure p

To Obtain

Use

Comments

pws(t)

Table 3 or Equation (5) or (6)

Sat. press. for temp. t

pw

Equation (22)

 

W

Equation (20)

 

Ws

Equation (21)

Using pws(t)

v

Equation (26)

 

h

Equation (30)

 

td

Table 3 with Equation (36), (37), or (38)

 

t*

Equation (21) and (33) or (35) with Table 3 or with Equation (5) or (6)

Requires trial-and-error or numerical solution method


 Moist Air Property Tables for Standard Pressure

Table 2 shows thermodynamic properties for standard atmospheric pressure at temperatures from −60 to 90°C calculated using the ASHRAE RP-1485 (Herrmann et al. 2009) research project numerical model. Properties of intermediate moist air states can be calculated using the degree of saturation μ:

(39)

(40)

These equations are accurate to about 350°C. At higher temperatures, errors can be significant.

9. PSYCHROMETRIC CHARTS

A psychrometric chart graphically represents the thermodynamic properties of moist air.

The choice of coordinates for a psychrometric chart is arbitrary. A chart with coordinates of enthalpy and humidity ratio provides convenient graphical solutions of many moist air problems with a minimum of thermodynamic approximations. ASHRAE developed five such psychrometric charts. Chart 1 is shown as Figure 1; the others may be obtained through ASHRAE.

ASHRAE Psychrometric Chart No. 1

Figure 1. ASHRAE Psychrometric Chart No. 1


Charts 1, 2, 3 and 4 are for sea-level pressure (101.325 kPa). Chart 5 is for 750 m altitude (92.634 kPa), Chart 6 is for 1500 m altitude (84.54 kPa), and Chart 7 is for 2250 m altitude (77.058 kPa). All charts use oblique-angle coordinates of enthalpy and humidity ratio, and are consistent with the data of Table 2 and the properties computation methods of Hyland and Wexler (1983a) and ASHRAE research project RP-1485. Palmatier (1963) describes the geometry of chart construction applying specifically to Charts 1 and 4.

The dry-bulb temperature ranges covered by the charts are

Charts 1, 5, 6, 7

Normal temperature

0 to 50°C

Chart 2

Low temperature

−40 to 10°C

Chart 3

High temperature

10 to 120°C

Chart 4

Very high temperature

100 to 200°C

Charts 8 to 16 are for 200 to 320°C and cover the same pressures as 1, 5, 6, and 7 plus the additional pressures of 0.2, 0.5,1.0, 2.0, and 5.0 MPa. They were produced by Nelson and Sauer (2002) and are available as a download with Gatley (2013).

Psychrometric properties or charts for other barometric pressures can be derived by interpolation. Sufficiently exact values for most purposes can be derived by methods described in the section on Perfect Gas Relationships for Dry and Moist Air. Constructing charts for altitude conditions has been discussed by Haines (1961), Karig (1946), and Rohsenow (1946).

Comparison of charts 1 and 6 by overlay reveals the following:

  • The dry-bulb lines coincide.

  • Wet-bulb lines for a given temperature originate at the intersections of the corresponding dry-bulb line and the two saturation curves, and they have the same slope.

  • Humidity ratio and enthalpy for a given dry- and wet-bulb temperature increase with altitude, but there is little change in relative humidity.

  • Volume changes rapidly; for a given dry-bulb and humidity ratio, it is practically inversely proportional to barometric pressure.

The following table compares properties at sea level (chart 1) and 1500 m (chart 6):

Chart No.

db

wb

h

W

rh

v

1

40

30

99.5

23.0

49

0.920

6

40

30

114.1

28.6

50

1.111

Figure 1 shows humidity ratio lines (horizontal) for the range from 0 (dry air) to 30 grams moisture per kilogram dry air. Enthalpy lines are oblique lines across the chart precisely parallel to each other.

Dry-bulb temperature lines are straight, not precisely parallel to each other, and inclined slightly from the vertical position. Thermodynamic wet-bulb temperature lines are oblique and in a slightly different direction from enthalpy lines. They are straight but are not precisely parallel to each other.

Relative humidity lines are shown in intervals of 10%. The saturation curve is the line of 100% rh, whereas the horizontal line for W = 0 (dry air) is the line for 0% rh.

Specific volume lines are straight but are not precisely parallel to each other.

A narrow region above the saturation curve has been developed for fog conditions of moist air. This two-phase region represents a mechanical mixture of saturated moist air and liquid water, with the two components in thermal equilibrium. Isothermal lines in the fog region coincide with extensions of thermodynamic wet-bulb temperature lines. If required, the fog region can be further expanded by extending humidity ratio, enthalpy, and thermodynamic wet-bulb temperature lines.

The protractor to the left of the chart shows two scales: one for sensible/total heat ratio, and one for the ratio of enthalpy difference to humidity ratio difference. The protractor is used to establish the direction of a condition line on the psychrometric chart.

Example 1 shows use of the ASHRAE psychrometric chart to determine moist air properties.

Example 1.

Moist air exists at 40°C dry-bulb temperature, 20°C thermodynamic wet-bulb temperature, and 101.325 kPa pressure. Determine the humidity ratio, enthalpy, dew-point temperature, relative humidity, and specific volume.

Solution: Locate state point on chart 1 (Figure 1) at the intersection of 40°C dry-bulb temperature and 20°C thermodynamic wet-bulb temperature lines. Read humidity ratio W = 6.5 gw/kgda.

The enthalpy can be found by using two triangles to draw a line parallel to the nearest enthalpy line (60 kJ/kgda) through the state point to the nearest edge scale. Read h = 56.7 kJ/kgda.

Dew-point temperature can be read at the intersection of W = 6.5 gw/kgda with the saturation curve. Thus, td