# 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

(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.

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.

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