# The refrigerating effect

In the basic vapour compression cycle of refrigeration shown in Figure 9.2 a mixture of relatively cold, saturated liquid and saturated vapour enters the evaporator. The liquid part of the mixture is boiled to a saturated vapour and leaves the evaporator at state 1 (in Figure 9.2). The refrigerating effect (q{) is the enthalpy change across the evaporator. Using the notation of Figure 9.2, this is expressed by

Qx = (hx — h4) (9.4)

EXAMPLE 9.2

(a) Calculate the refrigerating effect for the plant used in example 9.1.

(,b) If the duty is 352 kW of refrigeration, determine the mass flow rate of refrigerant,

(c) What is the volumetric flow rate under suction conditions?

Table 9.4 Superheated properties of R717, ammonia (NH3)

 T-t, II 1 O O U O
 T-ts Fs = 29 °C II O O N Ts = 31°C K P= 1132.2 kPa P= 1166.5 kPa P= 1201.6 kPa V H S V H S V H S 0 0.1139 1467.0 4.9902 0.1106 1467.6 4.9793 0.1075 1468.1 4.9685 5 0.1170 1482.9 5.0423 0.1137 1483.6 5.0316 0.1104 1484.2 5.0210 10 0.1201 1498.2 5.0916 0.1166 1498.9 5.0811 0.1133 1499.6 5.0706 15 0.1230 1512.9 5.1386 0.1195 1513.8 5.1281 0.1161 1514.6 5.1177 20 0.1259 1527.3 5.1834 0.1223 1528.2 5.1731 0.1189 1529.1 5.1628 25 0.1287 1541.2 5.2265 0.1250 1542.2 5.2163 0.1215 1543.2 5.2060 30 0.1314 1554.9 5.2681 0.1277 1556.0 5.2579 0.1241 1557.0 5.2477 35 0.1341 1568.4 5.3083 0.1303 1569.5 5.2982 0.1267 1570.6 5.2881 T~h Ts = 32°C Fs = 33°C II O N K P = 1237.4 kPa P = 1274.1 kPa P= 1311.6 kPa V H S V H S V H S 0 0.1044 1468.6 4.9577 0.1014 1469.1 4.9469 0.0986 1469.6 4.9362 5 0.1073 1484.8 5.0103 0.1043 1485.4 4.9998 0.1014 1486.0 4.9893 10 0.1101 1500.4 5.0601 0.1070 1501.1 5.0497 0.1041 1501.7 5.0393 15 0.1129 1515.4 5.1074 0.1097 1516.2 5.0971 0.1067 1516.9 5.0869 20 0.1155 1529.9 5.1525 0.1123 1530.8 5.1424 0.1092 1531.7 5.1323 25 0.1181 1544.1 5.1959 0.1148 1545.1 5.1858 0.1117 1546.0 5.1758 30 0.1207 1558.0 5.2377 0.1173 1559.0 5.2277 0.1141 1560.0 5.2177 35 0.1232 1571.7 5.2781 0.1198 1572.7 5.2681 0.1165 1573.8 5.2582 T-ts Fs = 35 °C Ts = 36°C Fs = 37°C K P = 1349.9 kPa P = 1389.0 kPa P = 1429.0 kPa V H S V H S V H S 0 0.0958 1470.0 4.9256 0.0931 1470.4 4.9149 0.0905 1470.8 4.9044 5 0.0985 1486.5 4.9788 0.0958 1487.1 0.9684 0.0931 1487.6 4.9580 10 0.1012 1502.4 5.0290 0.0984 1503.0 5.0188 0.0957 1503.7 5.0086 15 0.1037 1517.7 5.0767 0.1009 1518.4 5.0666 0.0981 1519.1 5.0565 20 0.1062 1532.5 5.1222 0.1033 1533.3 5.1122 0.1005 1534.1 5.0923 25 0.1086 1546.9 5.1658 0.1056 1547.8 5.1559 0.1028 1548.7 5.1461 30 0.1110 1561.0 5.2078 0.1079 1562.0 5.1980 0.1050 1562.9 5.1883 35 0.1133 1574.8 5.2484 0.1102 1575.9 5.2387 0.1072 1576.9 5.2290 40 0.1155 1588.4 5.2878 0.1124 1589.5 5.2781 0.1094 1590.6 5.2685 45 0.1178 1601.8 5.3260 0.1146 1603.0 5.3163 0.1115 1604.1 5.3068 50 0.1200 1615.1 5.3632 0.1167 1616.3 5.3536 0.1136 1617.4 5.3441 55 0.1222 1628.2 5.3995 0.1189 1629.4 5.3900 0.1157 1630.6 5.3805 60 0.1243 1641.1 5.4350 0.1210 1642.4 5.4255 0.1177 1643.7 5.4160 T-h Fs = 38°C Fs = 39°C Rs = 40°C K P = 1469.9 kPa P= 1511.7 kPa P = 1554.3 kPa V H S V H S V H S 0 0.0880 1471.2 4.8938 0.0856 1471.5 4.8833 0.0833 1471.9 4.8728 5 0.0906 1488.1 4.9477 0.0881 1488.6 4.9374 0.0857 1489.0 4.9371 10 0.0931 1504.3 4.9984 0.0905 1504.8 4.9883 0.0881 1505.4 4.9783 15 0.0954 1519.8 5.0465 0.0929 1520.5 5.0366 0.0904 1521.2 5.0267 20 0.0977 1534.9 5.0924 0.0951 1535.7 5.0826 0.0926 1536.4 5.0728

Table 9.4 (Contd)

 T-k Ts = 38°C Ts = 39°C WT* II O O N K P = 1469.9 kPa P= 1511.7 kPa P = 1554.3 kPa V H S V H S V H S 25 0.1000 1549.6 5.1363 0.0973 1550.4 5.1266 0.0947 1551.2 5.1169 30 0.1022 1563.9 5.1786 0.0995 1564.8 5.1690 0.0968 1565.7 5.1594 35 0.1043 1577.9 5.2194 0.1016 1578.9 5.2098 0.0989 1579.8 5.2003 40 0.1065 1591.6 5.2589 0.1036 1592.7 5.2494 0.1009 1593.7 5.2400 45 0.1085 1605.2 5.2973 0.1057 1606.3 5.2878 0.1029 1607.4 5.2784 50 0.1106 1618.6 5.3346 0.1076 1619.8 5.3252 0.1048 1620.9 5.3159 60 0.1126 1631.8 5.3710 0.1096 1633.1 5.3617 0.1067 1634.3 5.3524 T-ts /s = 41 °C U O CM II Rs = 43°C K P = 1597.9 kPa P = 1642.4 kPa P = 1687.8 kPa V H S V H S V H S 0 0.0810 1472.2 4.8623 0.0788 1472.4 4.8519 0.0767 1472.7 4.8414 5 0.0834 1489.4 4.9169 0.0812 1489.8 0.9067 0.0790 1490.2 4.8965 10 0.0857 1505.9 4.9682 0.0834 1506.5 4.9583 0.0812 1507.0 4.9483 15 0.0879 1521.8 5.0168 0.0856 1522.4 5.0070 0.0833 1523.0 4.9972 20 0.0901 1537.1 5.0631 0.0877 1537.9 5.0534 0.0854 1538.6 5.0438 25 0.0922 1552.0 5.1073 0.0898 1552.8 5.0978 0.0874 1553.6 5.0883 30 0.0943 1566.6 5.1499 0.0918 1567.4 5.1404 0.0894 1568.3 5.1310 35 0.0963 1580.8 5.1909 0.0937 1581.7 5.1815 0.0913 1582.7 5.1722 40 0.0982 1594.7 5.2306 0.0957 1595.8 5.2213 0.0932 1596.8 5.2120 45 0.1002 1608.5 5.2691 0.0976 1609.6 5.2599 0.0950 1610.6 5.2507 50 0.1021 1622.0 5.3066 0.0994 1623.2 5.2974 0.0968 1624.3 5.2882 60 0.1058 1648.7 5.3788 0.1031 1649.9 5.3697 0.1004 1651.1 5.3606

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

(a) From Table 9.1, hx, leaving the evaporator, is 398.68 kJ kg-1. Since the value of h4, entering the evaporator, is the same as that of hj, leaving the condenser as a saturated liquid at a temperature of 35°C, the value of h4 is found from Table 9.1 to be 248.94 kJ kg-1. Hence by equation (9.4) the refrigerating effect is

Qt = (398.68 — 248.94) = 149.74 kJ kg’1

(b) The mass flow rate of refrigerant, m, is given by

M = QMt (9-5)

Where QT is the refrigeration duty in kW.

Hence the mass flow rate of refrigerant handled is

M = 352/149.74 = 2.351kg s“1

(c) Assuming that there is no pressure drop in the suction line and that there are no heat exchanges between the suction line and its surroundings, the state entering the compressor is the same as that leaving the evaporator, namely, 0°C saturated. From Table 9.1 the

Specific volume at this state is 0.06935 m3 kg Hence the volumetric flow rate at the suction state is

Vj = 2.351 X 0.06935 = 0.16304 m3 s’1

Posted in Engineering Fifth Edition