Thermodynamics and refrigeration

The subject of thermodynamics was dealt with in part, in chapter 2, where it referred to the physics of air-water vapour mixtures. It is necessary to reconsider the topic here, as it refers to the behaviour of refrigerants in vapour compression cycles of refrigeration, in order to deal with such cycles quantitatively. As a preamble to this, some principles and definitions must be reviewed.

(a) Thermodynamics. This is simply the study of changes involving energy but it is also defined by ASHRAE (1997) as the study of energy, its transformations, and its relation to states of matter.

(b) Thermodynamic system. This is defined by ASHRAE (1997) as ‘… a region of space or quantity of matter, bounded by a closed surface’. There are two sorts of systems to be considered: closed systems, where there is no interchange of matter with the surroundings, and open systems where there is such an interchange. With a closed system the mass within the boundary of the system is constant as, for example, in a hermetic refrigeration plant. With an open system there is a mass flow through the system boundaries, for example with a pumping process that introduces a fluid to the system from the surroundings.

(c) The first law of thermodynamics. Otherwise interpreted as the conservation of energy, this law states that energy can neither be created nor destroyed.

For an open system, under steady-state conditions and with unit mass flow rate of a pure substance, the first law is expressed by the steady flow energy equation:

TOC o "1-5" h z ^ + (g — W) = 0 (9.1)

Where h = enthalpy J kg-1

V = velocity m s’1

G = local acceleration due to gravity m s-2

Z = elevation above a reference level m

Q — rate of heat transfer to the system W

W — rate of work done by the system W

Note that equation (2.19) offers an alternative expression of enthalpy.

(d) The second law of thermodynamics. In simple terms, this states that heat only flows from a higher temperature to a lower temperature. More formally, Spalding and Cole (1961) state: it is impossible for a system working in a cycle to have, as its sole effect, the transfer of heat from a system at a low temperature to a system at a high temperature.

(e) Heat. Energy has been described by ASHRAE (1997) as a capacity for producing an effect and it can be in a stored form or in a transient form. Stored energy is exemplified by such concepts as potential energy and kinetic energy, whereas heat is a form of transient energy. Heat can be defined as an interaction between two systems of differing temperatures and the flow is always from the higher to the lower temperature.

(/) Work. This is an aspect of energy. Work is the application of a force through a distance, transferring energy across the boundary between two systems.

(g) Entropy. This is a concept that is of value when analysing the behaviour of a thermodynamic system. It is expressed in terms of change in entropy, defined as the quantity of heat crossing the boundary of a reversible system, divided by the absolute temperature of the system, and is given by

Thermodynamics and refrigeration

(9.2)

Where s = specific entropy in kJ kg-1 K-1 q = heat energy in kJ kg-1 T = absolute temperature in K

Entropy is a property of the system and it depends on the state of the substance. For a pure substance, its value can be established since it depends on two other independent properties, heat and absolute temperature. Since it is defined as a difference, in equation (9.2), an arbitrary zero must be adopted if it is to be tabulated. This is usually at a temperature of zero degrees absolute.

Entropy can also be considered in terms of the disorder of the molecules in a system: if they are disordered the entropy is greater than if they are in some sort of order. Alternatively, it can be regarded as the availability of a given amount of heat: in equation (9.2) it is seen that if the entropy change is small, the absolute temperature must be large, for the given change of heat. Hence, it is possible to construct an absolute temperature-entropy diagram (see Figures 9.4 and 9.5), in which areas represent heat.

A process which occurs at constant entropy is termed isentropic.

(h) Reversibility. A reversible process is one which, after completion, has returned both the system and its surroundings to their original states. This is not true for an irreversible process, an example of which is any process involving friction.

If there were no heat exchange with the surroundings and no internal frictional losses, a reciprocating machine could either act as a compressor or as an expansion engine. When acting as a compressor the supply of power to the machine would be used to compress the gas handled. When acting as an expansion machine the pressure difference across the inlet and outlet ports would allow the gas handled to expand, driving the machine. The machine would liberate to the surroundings the same power that was taken from them when the machine acted as a compressor. The processes of compression and expansion would then be reversible.

It is possible to prove that the efficiency of a reversible engine is always greater than that of an irreversible engine, operating between the same two heat reservoirs. Hence it is desirable that refrigeration compressors should execute reversible compression, as far as possible.

(0 Adiabatic processes. If a system is isolated from its surroundings as regards heat transfer, the processes performed are termed adiabatic. Thus, an adiabatic process is one in which no heat is supplied or rejected.

All reversible, adiabatic processes are isentropic. The converse may not be true: all isentropic processes are not necessarily reversible and adiabatic.

The line joining the points 1 and 2 in Figure 9.2 depicts a reversible, adiabatic, isentropic process of compression from an evaporating pressure, pe, to a condensing pressure, pc.

(j) Saturated liquid. This is a substance existing at its saturated temperature and pressure. If the pressure falls, the substance can no longer exist as a saturated liquid and some of it flashes to vapour, with a corresponding fall in the temperature of the parent liquid, until it is again a saturated liquid, existing at a lower saturated temperature and pressure.

(k) Throttling expansion. This is an irreversible, adiabatic process of expansion that occurs at constant enthalpy, no heat being supplied or rejected and no work being done. It is the process occurring when liquid refrigerant flows through an expansion valve: the loss of pressure resulting from the frictional resistance to fluid flow causes some of the saturated liquid to flash to vapour, with a corresponding fall in temperature. The broken line joining the points 3 and 4 in Figure 9.2 represents a process of throttling expansion from the condensing pressure, pc, to the evaporating pressure, pc. It is customary to show the process by a broken line because it is irreversible.

(/) Sub-cooled liquid. This is liquid existing at a temperature less than the saturation temperature for the prevailing pressure. Figure 9.2 shows the region of sub-cooled liquid.

(m) Wet vapour. This is a mixture of saturated liquid and saturated vapour. The quality of the mixture is expressed in terms of its dryness fraction, defined as the mass of saturated vapour divided by the total mass of saturated vapour and saturated liquid. The point 4 in Figure 9.2 represents wet vapour: it is a mixture of saturated liquid at state 4′ and dry saturated vapour at state 1. The state of the wet vapour entering the evaporator can be defined in terms of the relevant enthalpies and its dryness fraction,/, at state 4, is given by

H4 — hr _ h3 — h4.

T hx- hr hx — hA. K ’

(n) Dry saturated vapour. This is the fluid existing as a vapour, without the presence of any saturated liquid, at its saturation vapour pressure. The points 1 and 2′ in Figure 9.2 represent states of dry saturated vapour, at saturated vapour pressures of pe and pc, respectively.

(o) Superheated vapour. This is the fluid existing as a vapour at a temperature greater than the saturated temperature for the pressure prevailing. The point 2 in Figure 9.2 is a state of superheated vapour.

In the following examples (9.1-9.6) R134a is used as the refrigerant but any other, single substance refrigerant would be dealt with using similar principles. Example 9.9 repeats these examples using ammonia as a refrigerant which, because of the format of Table 9.1, is an easier calculation. The treatment is likely to be different when mixtures of refrigerants are used.

EXAMPLE 9.1

An air conditioning plant using Refrigerant 134a has evaporating and condensing temperatures of 0°C and 35°C, respectively. Determine the dryness fraction of the vapour entering the evaporator.

Answer

Using the notation of Figure 9.2, refer to Table 9.1 and interpolate as necessary to determine the saturated liquid leaving the condenser at state 3:

Tc = 35°C pc = 887.11 kPa h3 = 248.94 kJ kg-1

Table 9.1 Saturated properties of R134a

Temper­

Ature

°C

Absolute

Pressure

KPa

Specific heats Liquid

KJ kg“1 K-

Vapour

-l

Vapour volume m3 kg-1

Liquid

Enthalpy

KJkg-1

Vapour enthalpy kJ kg-1

Vapour entropy kJ kg’1 K“1

— 10

200.52

1.306

0.842

0.099 63

186.78

392.75

1.7337

— 8

216.84

1.312

0.850

0.092 46

189.40

393.95

1.7323

-6

234.18

1.317

0.858

0.085 91

192.03

395.15

1.7310

-4

252.57

1.323

0.866

0.079 91

194.68

396.33

1.7297

-2

272.06

1.329

0.875

0.074 40

197.33

397.51

1.7285

0

292.69

1.335

0.883

0.069 35

200.00

398.68

1.7274

2

314.50

1.341

0.892

0.064 70

202.68

399.84

1.7263

4

337.55

1.347

0.901

0.060 42

205.37

401.00

1.7252

6

361.86

1.353

0.910

0.056 48

208.08

402.14

1.7242

8

387.49

1.360

0.920

0.052 84

210.80

403.27

1.7233

10

414.49

1.367

0.930

0.049 48

213.53

404.40

1.7224

12

442.89

1.374

0.939

0.046 36

216.27

405.51

1.7215

14

472.76

1.381

0.950

0.043 48

219.03

406.61

1.7207

16

504.13

1.388

0.960

0.040 81

221.80

407.70

1.7199

18

537.06

1.396

0.971

0.038 33

224.59

408.78

1.7191

20

571.59

1.404

0.982

0.036 03

227.40

409.84

1.7183

22

607.77

1.412

0.994

0.033 88

230.21

410.89

1.7176

24

645.66

1.420

1.006

0.031 89

233.05

411.93

1.7169

26

685.31

1.429

1.018

0.030 03

235.90

412.95

1.7162

28

726.76

1.438

1.031

0.028 29

238.77

413.95

1.7155

30

770.08

1.447

1.044

0.026 67

241.65

414.94

1.7149

32

815.30

1.457

1.058

0.025 16

244.55

415.90

1.7142

34

862.50

1.467

1.073

0.023 74

247.47

416.85

1.7135

36

911.72

1.478

1.088

0.022 41

250.41

417.78

1.7129

38

963.01

1.489

1.104

0.021 16

253.37

418.69

1.7122

40

1016.5

1.500

1.120

0.019 99

256.35

419.58

1.7115

42

1072.1

1.513

1.138

0.018 90

259.35

420.44

1.7108

44

1130.0

1.525

1.156

0.017 86

262.38

421.28

1.7101

46

1190.1

1.539

1.175

0.016 89

265.42

422.09

1.7094

48

1252.7

1.553

1.196

0.015 98

268.49

422.88

1.7086

50

1317.7

1.569

1.218

0.015 11

271.59

423.63

1.7078

52

1385.2

1.585

1.241

0.014 30

274.71

424.35

1.7070

54

1455.3

1.602

1.266

0.013 53

277.86

425.03

1.7061

56

1528.0

1.621

1.293

0.012 80

281.04

425.68

1.7051

58

1603.3

1.641

1.322

0.012 12

284.25

426.29

1.7041

60

1681.5

1.663

1.354

0.011 46

287.49

426.86

1.7031

Data reproduced with permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers from the (1997) ASHRAE Handbook.

For the mixture of saturated liquid and saturated vapour leaving the expansion valve at state 4:

Te = 0°C

Pe = 292.69 kPa

H4 = h3 = 248.94 kJ kg“1

Temperature

°C

Absolute

Pressure

KPa

Vapour volume m3 kg“’

Liquid enthalpy kJ kg’1

Vapour enthalpy kJ kg’1

Vapour entropy kJ kg“1 K“1

Saturated — 10.07

200

0.099 90

186.69

392.71

1.7337

Superheated — 10

200

0.099 90

392.77

1.7339

-5

200

0.102 36

396.99

1.7496

0

200

0.104 82

401.21

1.7654

5

200

0.107 12

405.47

1.7808

10

200

0.109 53

409.73

1.7961

Saturated

8.94

400

0.051 23

212.08

403.80

1.7229

Superheated

10

400

0.051 52

404.78

1.7263

15

400

0.052 86

409.39

1.7423

20

400

0.054 20

414.00

1.7583

25

400

0.055 50

418.60

1.7738

30

400

0.056 79

423.21

1.7892

Saturated

21.58

600

0.034 33

229.62

410.67

1.7178

Superheated

25

600

0.035 00

414.04

1.7290

30

600

0.035 98

418.97

1.7455

35

600

0.036 92

423.84

1.7614

40

600

0.037 86

428.72

1.7772

45

600

0.038 74

433.58

1.7924

50

600

0.039 67

438.44

1.8077

Saturated

31.33

800

0.025 65

243.58

415.58

1.7144

Superheated

35

800

0.026 24

419.40

1.7268

40

800

0.027 04

424.61

1.7437

45

800

0.027 80

429.73

1.7598

50

800

0.028 55

434.85

1.7758

Saturated

39.39

1000

0.020 34

255.44

419.31

1.7117

Superheated

40

1000

0.020 43

419.99

1.7139

45

1000

0.022 12

415.45

1.7310

50

1000

0.021 81

430.91

1.7482

Saturated

46.32

1200

0.016 74

265.91

422.22

1.7092

Superheated

50

1200

0.017 21

426.51

1.7226

55

1200

0.017 81

432.17

1.7398

60

1200

0.018 41

437.83

1.7571

Data reproduced with permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers from the ASHRAE Handbook (1997).

Temperature

°C

Absolute

Pressure

KPa

Liquid volume m3 kg“1

Vapour volume m3 kg’1

Liquid

Enthalpy

KJkg-‘

Vapour enthalpy kJ kg“1

Liquid entropy kJ kg“1 K“1

Vapour entropy kJ kg’1 K

-5

3.549

0.001550

0.3468

158.0

1437.6

0.6297

5.4023

-4

3.689

0.001553

0.3343

162.6

1438.7

0.6467

5.3888

-3

3.834

0.001556

0.3224

167.2

1439.8

0.6637

5.3753

-2

3.983

0.001559

0.3109

171.8

1440.9

0.6806

5.3620

— 1

4.136

0.001563

0.3000

176.4

1442.0

0.6975

5.3487

0

4.294

0.001566

0.2895

181.1

1443.1

0.7143

5.3356

1

4.457

0.001569

0.2795

185.7

1444.2

0.7312

5.3225

2

4.625

0.001573

0.2698

190.3

1445.2

0.7479

5.3096

3

4.797

0.001576

0.2606

194.9

1446.3

0.7646

5.2967

4

4.975

0.001580

0.2517

199.6

1447.3

0.7813

5.2839

5

5.157

0.001583

0.2433

204.2

1448.3

0.7980

5.2712

6

5.345

0.001587

0.2351

208.9

1449.2

0.8146

5.2587

7

5.538

0.001590

0.2273

213.6

1450.2

0.8311

5.2461

8

5.736

0.001594

0.2198

218.2

1451.1

0.8477

5.2337

9

5.940

0.001597

0.2126

222.9

1452.1

0.8641

5.2214

10

6.149

0.001601

0.2056

227.6

1453.0

0.8806

5.2091

11

6.364

0.001604

0.1990

232.3

1453.9

0.8970

5.1949

12

6.585

0.001608

0.1926

237.0

1454.8

0.9134

5.1849

13

6.812

0.001612

0.1864

241.7

1455.6

0.9297

5.1728

14

7.044

0.001616

0.1805

246.4

1456.5

0.9460

5.1609

15

7.283

0.001619

0.1748

251.1

1457.3

0.9623

5.1490

16

7.528

0.001623

0.1693

255.8

1458.1

0.9785

5.1373

17

7.779

0.001627

0.1641

260.6

1458.9

0.9947

5.1255

18

8.037

0.001631

0.1590

265.3

1459.7

1.0109

5.1139

19

8.301

0.001635

0.1541

270.0

1460.4

1.0270

5.1023

20

8.571

0.001639

0.1494

274.8

1461.2

1.0432

5.0908

21

8.849

0.001643

0.1448

279.6

1461.9

1.0592

5.0794

22

9.133

0.001647

0.1405

284.3

1462.6

1.0753

5.0680

23

9.424

0.001651

0.1363

289.1

1463.3

1.0913

5.0567

24

9.722

0.001655

0.1322

293.9

1464.0

1.1073

5.0455

25

10.03

0.001659

0.1283

298.7

1464.6

1.1232

5.0343

26

10.34

0.001663

0.1245

303.5

1465.2

1.1391

5.0232

27

10.66

0.001667

0.1208

308.3

1465.9

1.1550

5.0121

28

10.99

0.001671

0.1173

313.1

1466.4

1.1708

5.0011

29

11.32

0.001676

0.1139

318.0

1467.0

1.1867

4.9902

30

11.66

0.001680

0.1106

322.8

1467.6

1.2025

4.9793

31

12.02

0.001684

0.1075

327.7

1468.1

1.2182

4.9685

32

12.37

0.001689

0.1044

332.5

1468.6

1.2340

4.9577

33

12.74

0.001693

0.1014

337.4

1469.1

1.2497

4.9469

34

13.12

0.001698

0.0986

342.2

1469.6

1.2653

4.9362

35

13.50

0.001702

0.0958

347.1

1470.0

1.2810

4.9256

36

13.89

0.001707

0.0931

352.0

1470.4

1.2966

4.9149

37

14.29

0.001711

0.0905

356.9

1470.8

1.3122

4.9044

38

14.70

0.001716

0.0880

361.8

1471.2

1.3277

4.8938

39

15.12

0.001721

0.0856

366.7

1471.5

1.3433

4.8833

40

15.54

0.001726

0.0833

371.6

1471.9

1.3588

4.8728

41

15.98

0.001731

0.0810

376.6

1472.2

1.3742

4.8623

Temperature

°C

Absolute

Pressure

KPa

Liquid volume m3 kg"1

Vapour

Volume

3 -1

M mg

Liquid enthalpy kJ kg“1

Vapour enthalpy kJ kg’1

Liquid entropy kJ kg“1 K_1

Vapour entropy kJ kg“1 K’1

42

16.42

0.001735

0.0788

381.5

1472.4

1.3897

4.8519

43

16.88

0.001740

0.0767

386.5

1472.7

1.4052

4.8414

44

17.34

0.001745

0.0746

391.4

1472.9

1.4206

4.8310

45

17.81

0.001750

0.0726

396.4

1473.0

1.4360

4.8206

46

18.30

0.001756

0.0707

401.4

1473.2

1.4514

4.8102

47

18.79

0.001761

0.0688

406.4

1473.3

1.4668

4.7998

48

19.29

0.001766

0.0669

411.4

1473.3

1.4822

4.7893

49

19.80

0.001771

0.0652

416.5

1473.4

1.4977

4.7789

50

20.33

0.001777

0.0635

421.6

1473.4

1.5131

4.7684

Reproduced from Thermodynamic Properties of Ammonia by W. B. Gosney and O. Fabris, with the kind permission of the authors.

For saturated liquid at a temperature of 0°C and a pressure of 292.69 kPa, h4> =

200.0 kJ kg"1.

For dry saturated vapour at 0°C and 292.69 kPa, h = 398.68 kJ kg-1.

Hence, by equation (9.3)

/= (248.94 — 200.00)/(398.68 — 200.00) = 0.25

Thus 25 per cent, by weight, of the liquid refrigerant entering the expansion valve flashes to vapour as the pressure drop through the valve occurs. Since the volume of the vapour is much greater than that of the liquid, the space occupied by the vapour is significantly large. Consequently, the mixture of liquid and vapour leaving the expansion valve must be distributed uniformly into the evaporator before the vapour and liquid get a chance to separate. This is because it is the liquid in the mixture that has the ability to provide refrigeration, by absorbing heat through the surfaces of the evaporator and boiling to a saturated vapour at the evaporating pressure.

Posted in Air Conditioning Engineering


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