r LIBRARY Connecticut Agricultural College A-OJLil^ K J" libl.stx TJ 270.M4 Tables and diagrams of the ttiermal 3 T1S3 DDSMSMbS T ►-3 TKi«^ "Boole may be kept out STEAM TABLES AND DIAGRAMS MARKS AND DAVIS TABLES AND DIAGRAMS OF THE THERMAL PROPERTIES OF SATURATED AND SUPERHEATED STEAM BY LIONEL S. MARKS, M.M.E. PROFESSOR OF MECHANICAL ENGINEERING, HARVARD UNIVERSITY AND MASSACHUSETTS INSTITUTE OF TECHNOLOGY AND HARVEY N. DAVIS, Ph.D. PROFESSOR OF MECHANICAL KNGINEERING, HARVARD UNIVERSITY Fourteenth Impression L O N G ]M A N S , GREEN AND CO 55 FIFTH AVENUE, NEW YORK 39 PATERNOSTER ROW, LONDON, E.G. 4 TORONTO, BOMBAY, CALCUTTA, AND MADRAS 1927 COPYRIGHT, 1909, BY LONGMANS, GREEN & CO. ALL RIGHTS RESERVED 2.0 5T 6" FIKST EDITION JUNE I9OQ HEl'RINTED JINE TQTO Vnil COKKECTIONS, FEBRUARY iglZ REPRINTED MARCH I9I3 ".EPRINTED WITH CORRECTIONS, NOVEMUEK ic: WITH CORRECTIONS, OCTOBER IQ16 REPRINTED MARCH iqiS REPRINTED JANUARY I9I9 REPRINTED DECEMBER I9I9 REPRINTED SEPTEMBER I92O REPRINTED FEBRUARY 1<)22 REPRINTED SEPTEMBER 1923 REPRINTED JUNE 192$ REPRINTED JUNE I927 rjADE i:j united state; PREFACE The tables of the properties of saturated steam which have appeared up to the present time have all been based upon the classic investigations of Regnault, carried out more than sixty years ago. It has been apparent for some time that the total heatf of dry and saturated steam, as determined by those admirable researches, are belo^\ the correct values. The great difficulty in obtaining steam which is exactly dry and saturated has not been appreciated until very recently; and it is undoubtedly true that Regnault was investigating steam containing a small amount of moisture when he tliought that he was dealing with dry steam. Fortunately, the recent investiga- tions of Dieterici, Smith Griffiths, Henning and Joly give a trustworthy body of new values of the total heat of dry steam at pressures below atmospheric pressure ; while the method recently elaborated by Davis, when applied to the throttling experiments of Grindley, of Peake, and of Griessmann, gives remarkably accordant determinations at pressures above atmospheric pressure. The table which we have prepared is based entirely upon these new values, and is probably correct to one tenth of one per cent within the range of steam pressures usual in engineering practice. Regnault's formula gives results which are too high by i8 B. t. u. at 32° F. ; too low by 6 B. t. u. at 275° F. ; and again too high at 380° F.; the error increasing rapidly at higher temperatures. The investigations of Knoblauch, of Thomas and of Henning are the necessary basis for any determinations of the properties of superheated steam. These investi- gations have been subjected to a careful analysis, both as to the probable errors resulting from the methods of experimentation, and also as to the relation of the experimental results to the values deduced from thermodynamic theory, so far as this latter throws any light on the matter. Where the results of the separate investiga- tions are not closely accordant, a critical estimate has been made of the relative values to be given to each, in the region under consideration. The properties of super- heated steam are tabulated for every pound pressure, and for every ten degrees of superheat, within a range which exceeds present practice. All the information relating to superheated steam of any pressure is given on one double-page; an arrangement which permits the immediate finding of any desired quantity. Supplementary tables extend the superheated steam table to very high temperatures and give the properties of water, metric conversion factors, Naperian logarithms and other quantities. Beside the tables, we have prepared two large diagrams showing the properties of saturated and superheated steam, These diagrams can be used, instead of the tables, for finding the total heat, entropy and specific volume of steam of any known quality or superheat (within an extended range); but their chief purpose is to facilitate certain calculations. In consequence of the variation of the specific heat of super- (3> PREFACE heated steam with both pressure and temperature, the solution of commonly occurring problems involving superheated steam is either laborious or approximate. If the tables are arranged in such a manner as to aid the solution of problems of one class, they become inconvenient for other purposes. The total heat-entropy diagram, de- vised by Mollier, makes it possible to solve immediately many of the problems which arise in connection with either saturated or superheated steam. A total heat-pressure diagram, showing specific volumes, permits the solution of problems involving vol- umes. By the use of the two diagrams, either separately or together, a large number of the steam problems occurring in the design of engines and turbines, or in con- nection with the flow of steam, or its throttling, can be solved without any calculation. These two diagrams have been plotted with great care from the data given in the tables, and should prove useful to all engineers or students engaged in making calcu- lations which involve saturated or superheated steam. The authors desire to express their indebtedness to Professor E. V. Huntington for the use of the plates of his four-place tables of logarithms, and to Mr. M. R. Wolfard, S. B., for his patient and skilful assistance in the arduous work of computation and in drawing the diagrams. L. S. M. H. N. D Cambridge, Mass., December, 1908. Note to the 1916 Reprint. The experimental information which has become avail- able since these tables were computed does not justify any appreciable change in them except in one respect. The work of Holborn and Baumann * on the pressure-temperature relations of saturated steam at high pressures should apparently be accepted in preference to all previous work. The pressures involved are from 400 lb. per sq. in. to the critical pressure and are consequently outside the range of usual engineering experience. The last few entries in Tables 1,2, 3, and 6 have been changed to bring them into agreement with this new information. A new Mollier chart has been prepared which will be found to be more convenien'. than the earlier Diagram I. L. S. M. H. N. D. CAMBRroGE, Mass., August, 1916. * Marks, Trans. Am. Soc. Mech. Eng., vol. i^;} (1911). t4) CONTENTS Part I. Tables and Diagrams Description of tables ,-,.,,.... 6 Description of diagrams , 7 Tables 1. Saturated steam: temperature table 8 2. Saturated steam: pressure table 16 3. Saturated and superheated steam 22 4. Superheated steam at high superheats . . .... 66 5. Boiling points, for thermometer calibrations . . , . . 67 6. TaERMAL properties of water 68 7. Conversion tables , . . 70 8. Logarithms to the base 10 ............ 72 9. Logarithms to the base e .,.„.,....... 76 Diagrams (at end of book) I. Total heat-entropy diagram II. Total heat-pressure diagram Part II, The Use of the Diagrams General discussion , 78 Solutions of illustrative problems = , . . 80 Part III. Discussion of Sources 1. Absolute temperature 87 2. The specific heat of water 88 3. The mechanical equivalent of heat 92 4. The pressure-temperature relation 93 5. The specific heat of superheated steam 95 6. The specific volume of superheated steam 98 7. The total heat of saturated steam 98 8. The specific volume of saturated steam 102 9. The volume of saturated steam at high temperatures . 103 10. The computation of the tables 106 Ci THE TABLES Of the three main steam tables, the first and second are for water and saturated steam only, and give explicitly all of the properties that are ordinarily needed. Table 3 is primarily for superheated steam, but includes saturated steam as the special case of zero superheat. In Table i, the argument is the temperature. This table is useful for hygrometric and other purposes as well as for steam engineering. To facilitate the handling of con- denser vacuums, all pressures below one atmosphere are given in inches of mercury as well as in lbs. per sq. in. The use of this table in accurate calorimetry is made possible by giving the heat of the liquid to hundredths of a mean B. t. u. between 32° and 212°. The data upon which steam tables must be based are well known only to about 400°. It is, however, often convenient to be able to work roughly at much higher tem- peratures. Table i has, therefore, been extended to the critical point itself, but the values above 400° should not be used with too much confidence (see the discussion cf sources in Part III of this book). In Tables 2 and 3, the argument is the pressure. These tables extend to 600 lbs., the values above 250 lbs. being less certain than those below. Table 3 can be extended to very high superheats by means of Table 4. There is also a table of boiling points for use in calibrating thermometers, a table of the thermal properties of water, a full set of conversion tables, particularly for energy units, and tables of four-place logarithms, both common and Naperian. The unit of heat and of energy in these tables is a " mean B. t. u.," that is, 1/180 of the heat needed to raise one pound of water from the freezing to the boiling point. The use of such a unit instead of the B. t. u. at 60° F. corresponds to the rapidly increas- ing use of the Bunsen or mean calorie in the metric system, and has many advantages, among which is the ease with which tables based on the two mean units can be com- pared. The most important reason for such a choice in these tables is that, at the present time, the value of the mean unit is better known than that of the 60° unit, be- cause of the rapidity with which the specific heat of water changes with the tempera- ture near 60°. The mean B. t. u. is larger than the 60° B. t. u. by between three and ten hundredths of one per cent, a difference that is negligible for engineering purposes <6) THE DIAGRAMS I.v order to facilitate the solution of many problems of common occurrence, twc large diagrams have been prepared to accompany this book. The Total Heat-Entropy Diagram (Diagram I) has two families of curves: {a) curvesof constant pressure, and {b) curves of constant quality and constant superheat. The ordinates are total heat {i. e. heat of formation measured above water at 32° F.) ; the abscissae are entropies. Vertical lines are lines of constant entropy and show the change in the condition of steam during adiabatic expansion. Measurements aloiig vertical lines give the change in the total heat of steam during adiabatic expansion (which is equal to the work done in the Rankine ideal cycle) ; the same measurements transferred to the velocity scale give the theoretical velocity of escape of steam through a properly shaped orifice or nozzle. Horizontal lines are lines of constant total heat; they show the change in the condition of steam which results from throttling. The Total Heat-Pressure Diagram (Diagram II) has two families of curves: (a) curves of constant specific volume, and (b) curves of constant quality and constant superheat. The ordinates are total heats; the abscissae, pressures. Vertical lines are lines of constant pressure; measurements along vertical lines give the heat supply accompanying changes of volume or quality at constant pressure. Horizontal lines are lines of constant total heat ; they show the change of volume and condition of the steam resulting from throttling. The scale of abscissae is a uniform scale of tem- peratures of saturated steam, which gives a varying scale of steam pressures. This varying scale has the advantage of spreading out the specific volume curves at low pressures. The use of total heats as ordinates has certain special advantages. The energy given up by steam that is passing through any appliance is equal to the difference between the total heat of the entering and of the leaving steam. This difference is represented by vertical measurements on the diagram. The method of using these diagrams for the solution of problems is explained in detail in Part II. (7) Table 1. Saturated Steam: Temperature Table Temp. Pressure Sp. Vol. Density Heat Latent Total lolernal Energy Entropy lbs. per sq. in. inches of Hg. cu. ft. per lb. lbs per cu. ft, of the heat of heat of liquid evap. stfi^m h or q L or r \H) Evap. Steam Temp. Fahr. Fahr. Water Evap, Steam t P — \_v or s i/v lorp (T) ^re L/Torr/T Nor* t 32° 0.0886 0.1804 3294. 0.000304 0.00 1073.4 1073.4 1019.3 1019.3 0.0000 2.1832 2.1832 32° 33 0.0922 0.1878 3170. 0.000316 1.01 1072.8 1073.8 1018.6 1019.6 0.0020 2.1777 2.1797 33 34 0.0960 0.1955 3052. 0.000328 2.01 1072.2 1074.2 1018.0 1020.0 0.0041 2.1721 2.1762 34 36° 0.0999 0.2034 2938. 0.000340 3.02 1071.7 1074,7 1017.3 1020.3 0.0062 2.1666 2.1728 35^ 36 0.1040 0.2117 2829. 0.000353 4.03 1071.1 1075.1 1016.6 1020.7 0.0082 2.1611 2.1693 36 37 0.1081 0.2202 2725. 0.000367 5.04 1070.6 1075.6 1016.0 1021.0 0.0102 2.1557 2.1659 37 38 0.1125 0.2290 2626. 0.000381 6.04 1070.0 1076.0 1015.3 1021.3 0,0122 2.1503 2.1625 38 39 0.1170 0.2382 2530. 0.000395 7.05 1069.4 1076.5 1014.6 1021.7 0.0142 2.1449 2.1591 39 40° 0.1217 0.2477 2438. 0.000410 8.05 1068.9 1076.9 1014.0 1022.0 0.0162 2.1394 2.1556 40° 41 0.1265 0.2575 2350. 0.000425 9.05 1068.3 1077.4 1013.3 1022.3 0.0182 2.1341 2.1523 41 42 0.1315 0.2677 2266. 0.000441 10.06 1067.8 1077.8 1012.6 1022.7 0.0202 2.1287 2.1489 42 43 0.1366 0.2782 2185. 0.000458 11.06 1067.2 1078.3 1012.0 1023.0 0.0222 2.1234 2,1456 43 44 0.1420 0.2890 2107. 0.000475 12.06 1066.7 1078.7 1011.3 1023.4 0.0242 2.1181 2.1423 44 45° 0.1475 0.3002 2033. 0.000492 13.07 1066.1 1079.2 1010.6 1023.7 0,0262 2,1127 2.1389 45° 46 0.1532 0.3118 1961. 0.000510 14.07 1065.6 1079.6 1010.0 1024.0 0,0282 2.1074 2.1356 46 47 0.1591 0.3238 1892. 0.000529 15.07 1065.0 1080.1 1009.3 1024.4 0.0301 2.1022 2.1323 47 48 0.1651 0.3363 1826. 0.000548 16.07 1064.5 1080.5 1008.6 1024.7 0,0321 2.0970 2.1291 48 49 0.1715 0.3492 1763. 0.000567 17.08 1063.9 1081.0 1007.9 1025.0 0.0341 2.0917 2.1258 49 50° 0.1780 0.3625 1702. 0.000587 18.08 1063.3 1081.4 1007.3 1025.4 0.0361 2.0865 2.1226 60° 61 0.1848 0.3762 1643. 0.000608 19.08 1062.8 1081.9 1006.6 1025.7 0.0381 2.0814 2.1195 51 62 0.1917 0.3903 1586. 0.000630 20.08 1062.2 1082.3 1006.0 1026.1 0.0401 2.0763 2.1164 62 53 0.1989 0.4049 1532. 0.000653 21.08 1061.7 1082.7 1005.3 1026.4 0.0420 2.0712 2.1132 63 54 0.2063 0.4201 1480. 0.000676 22.08 1061.1 1083.2 1004.6 1026.7 0.0440 2.0660 2.1100 54 56° 0.2140 0.4357 1430. 0.000700 23.08 1060.6 1083.6 1004,0 1027.1 0.0459 2.0609 2.1068 65'* 66 0.2219 0.4518 1381. 0.000724 24.08 1060.0 1084.1 1003.3 1027.4 0.0478 2.0559 2.1037 66 57 0.2301 0.4684 1335. 0.000749 25.08 1059.5 1084.5 1002.7 1027.7 0.0498 2.0508 2.1006 57 58 0.2385 0.4856 1291. 0.000775 26.08 1058.9 1085.0 1002.0 1028.1 0.0517 2.0458 2.0975 58 59 0.2472 0.5034 1249. 0.000801 27.08 1058.3 1085.4 1001.3 1028.4 0.0536 2.0408 2.0944 69 60° 0.2562 0.522 1208. 0.000828 28.08 1057.8 1085.9 1000.7 1028.7 0.0555 2.0358 2.0913 60° 61 0.2654 0.541 1168. 0.000856 29.08 1057.2 1086.3 1000.0 1029.1 0.0574 2.0308 2.0882 61 62 0.2749 0.560 1130. 0.000885 30.08 1056.7 1086.8 999.3 1029.4 0.0593 2.0258 2.0851 62 63 0.2847 0.580 1093. 0.000915 31.07 1056.1 1087.2 998.7 1029.8 0.0612 2.0209 2.0821 63 64 0.2949 0.601 1058. 0.000946 32.07 1055.6 1087.6 998.0 1030.1 0.0631 2.0160 2.0791 64 65° 0.3054 0.622 1024. 0.000977 33.07 1055.0 1088.1 997.4 1030.4 0.0650 2.0110 2.0760 65' 66 0.3161 0.644 991. 0.001009 34.07 1054.5 1088.5 996.7 1030.8 0.0669 2,0062 2.0731 66 67 0.3272 0.667 959. 0.001043 35.07 1053.9 1089.0 996.0 1031.1 0.0688 2.0013 2.0701 67 68 0.3386 0.690 928. 0.001077 36.07 1053.4 1089.4 995.4 1031.4 0.0707 1.9965 2,0672 68 69 0.3504 0.714 899. 0.001112 37.06 1052.8 1089.9 994.7 1031.8 0.0726 1.9916 2.0642 69 70° 0.3626 0.739 871. 0.001148 38.06 1052.3 1090.3 994.0 1032.1 0.0745 1.9868 2.0613 70' 71 0.3751 0.764 843. 0.001186 39.06 1051.7 1090.8 993.4 1032.4 0.0764 1.9821 2.0585 71 72 0.3880 0.790 817. 0.001224 40.05 1051.2 1091.2 992.7 1032.8 0.0783 1.9773 2.0556 72 73 0.4012 0.817 792. 0.001263 41.05 1050.6 1091.6 992.0 1033.1 0.0802 1.9726 2.0528 73 74 0.4148 0.845 767. 0.001304 42.05 1050.0 1092.1 991.4 1033.4 0.0821 1.9678 2.0499 74 75° 0.4288 0.873 743. 0.001346 43.05 1049.5 1092.5 990.7 1033.8 0.0840 1.9631 2.0471 75' 76 0.4432 0.903 720. 0.001389 44.04 1048.9 1093.0 990.1 1034.1 0.0858 1.9585 2.0443 76 77 0.4581 0.933 698. 0.001433 45.04 1048.4 1093.4 989.4 1034.4 0.0876 1.9538 2.0414 77 78 0.4735 0.964 677. 0.001477 46.04 1047.8 1093.9 988.7 1034.8 0.0895 1.9491 2.0386 78 79 0.4893 0.996 657. 0.001523 47.04 1047.3 1094.3 988.1 1035.1 0.0913 1.9445 2.0358 79 T°=t° + 459,6! J=777.5ft.lbs.perB.t,n. [log = 2.89 07111 A= Vj = 1.286 XIQ-^*! 144 A=: 0.1852 [log= 1.26 764 j. For water, at 45^ (0.15 lbs.), sp. vol., v' or a = 0.01602 cu. ft. per lb, ; i/v' = 62.4 lbs, per cu. ft. ; 144 Apv' = 0.0004 B.t.u, | at 70^ (0.36 lbs,), v' or <^= 0,01605 " j Vv' = 62.3 " ; 144 Apv' = 0,001 " . (8) Table 1 : Temperatures Temp, Fahr. Pressure lbs. per inches sq. in. of Hg. So. Vol. cu ft. per lb, Density lbs. per cu. a Heat Latent of the heat of liquid evap. Total heat of steam t P - V or s l/y h or q L or r H 80° 0.505 1.029 636.8 0.001570 48.03 1046.7 1094.8 81 0.522 1.063 617.5 0.001619 49.03 1046.2 1095.2 82 0.539 1.098 598.7 0.001670 50.03 1045.6 1095.6 83 0.557 1.134 580.5 0.001723 51.02 1045.1 1096.1 84 0.575 1.171 562.9 0.001777 52.02 1044.5 1096.5 86° 0.594 1.209 545.9 0.001832 53.02 1044.0 1097.0 86 0.613 1.248 529.5 0.001889 54.01 1043.4 1097.4 87 0.633 1.289 513.7 0.001947 55.01 1042.8 1097.9 88 0.654 1.331 498.4 0.002007 56.01 1042.2 1098.3 89 0.675 1.373 483.6 0.002068 57.00 1041.7 1098.7 90° 0.696 1.417 469.3 0.002131 58.00 1041.2 1099.2 91 0.718 1.462 455.5 0.002195 59.00 1040.6 1099.6 92 0.741 1.508 442.2 0.002261 60.00 1040.0 1100.1 93 0.765 1.556 429.4 0.002329 60.99 1039.5 1100.5 94 0.789 1.605 417.0 0.002398 61.99 1039.0 1101.0 95° 0.813 1.655 405.0 0.002469 62.99 1038.4 1101.4 96 0.838 1.706 393.4 0.002542 63.98 1037.8 1101.8 97 0.864 1.759 382.2 0.002617 64.98 1037.3 1102.3 98 0.891 1.813 371.4 0.002693 65.98 1036.7 1102.8 99 0.918 1.869 360.9 0.002771 66.97 1036.2 1103.2 100° 0.946 1.926 350.8 0.002851 67.97 1035.6 1103.6 101 0.975 1.985 341.0 0.002933 68.97 1035.1 1104.0 102 1.005 2.045 331.5 0.003017 69.96 1034.5 1104.5 103 1.035 2.107 322.2 0.003104 70.96 1034.0 1104.9 104 1.066 2.171 313.3 0.003192 71.96 1033.4 1105.3 105° 1.098 2.236 304.7 0.003282 72.95 1032.8 1105.8 106 1.131 2.303 296.4 0.003374 73.95 1032.3 1106.2 107 1.165 2.372 288.3 0.003469 74.95 1031.7 1106.7 108 1.199 2.443 280.5 0.003565 75.95 1031.2 1107.1 109 1.235 2.515 272.9 0.003664 76.94 1030.6 1107.5 110° 1.271 2.589 265.5 0.003766 HI 1.308 2.665 258.3 0.003871 112 1.346 2.740 251.4 0.003978 113 1.386 2.822 244.7 0.004087 114 1.426 2.904 238.2 0.004198 115° U6 117 118 119 120° 121 122 123 124 125° 126 127 128 129 1.467 1.509 1.553 1.597 1.642 1.689 1.736 1.785 1.835 1.886 1.938 1.992 2.047 2.103 2.160 2.987 3.073 3.161 3.252 3.344 3.438 3.535 3.635 3.737 3.841 3.948 4.057 4.168 4.282 4.399 231.9 0.004312 225.8 0.004429 0.004548 0.004671 0.004796 219.9 214.1 208.5 203.1 197.9 192.8 187.9 183.1 178.4 173.9 169.6 165.3 161.1 0.004924 0.005054 0.005187 0.005323 0.005462 0.005605 0.005751 0.005900 0.006052 0.006207 77.94 1030.0 1108.0 78.94 1029.5 1108.4 79.93 1028.9 1108.8 80.93 1028.4 1109.3 81.93 1027.8 1109.7 82.92 1027.2 1110.2 83.92 1026.7 1110.6 84.92 1026.1 1111.0 85.92 1025.5 1111.5 86.91 1025.0 1111.9 87.91 1024.4 1112.3 88.91 1023.9 1112.8 89.91 1023.3 1113.2 90.90 1022.7 1113.6 91.90 1022.2 1114.1 92.90 1021.6 1114.5 93.90 1021.1 1115.0 94.89 1020.5 1115.4 95.89 1019.9 1115.8 96.89 1019.4 1116.2 Internal Energy Evap. Steam I or p E 987.4 1035.4 986.7 1035.8 986.1 1036.1 985.4 1036.4 984.8 1036.8 984.1 1037.1 983.4 1037.4 982.8 1037.8 982.1 1038.1 981.4 1038.4 980.8 1038.8 980.1 1039.1 979.4 1039.4 978.8 1039.8 978.1 1040.1 977.4 1040.4 976.8 1040.8 976.1 1041.1 975.5 1041.4 974.8 1041.8 974.1 1042.1 973.5 1042.4 972.8 1042.8 972.1 1043.1 971.5 1043.4 970.8 1043.8 970.1 1044.1 969.5 1044.4 968.8 1044.8 968.2 1045.1 967.5 1045.4 966.8 1045.8 966.2 1046.1 965.5 1046.4 964.8 1046.8 964.2 1047.1 963.5 1047.4 962.8 1047.8 962.2 1048.1 961.5 1048.4 960.8 1048.7 960.2 1049.1 959.5 1049.4 958.8 1049.7 958.2 1050.0 957.5 1050.4 956.8 1050.7 956.1 1051.0 955.5 1051.3 954.8 1051.7 Entropy _ Temp. Water Evap. Steam Fahr. nore L/Torr/T Nor<^ t 0.0932 1.9398 2.0330 80° 0.0950 1.9352 2.0302 81 0.0969 1.9306 2.0275 82 0.0987 1.9260 2.0247 83 0.1005 1.9215 2.0220 84 0.1023 1.9169 2.0192 85° 0.1041 1.9124 2.0165 86 0.1060 1.9079 2.0139 87 0.1078 1.9034 2.0112 88 0.1096 X.8989 2.0085 89 0.1114 1.8944 2.0058 90° 0.1133 1.8900 2.0033 91 0.1151 1.8856 2.0007 92 0.1169 1.8812 1.9981 93 0.1187 1.8767 1.9954 94 0.1205 1.8723 1.9928 95° 0.1223 1.8680 1.9903 96 0.1241 1.8636 1.9877 97 0.1259 1.8592 1.9851 98 0.1277 1.8549 1.9826 99 0.1295 1.8505 1.9800 100° 0.1313 1.8463 1.9776 101 0.1330 1.8420 1.9750 102 0.1347 1.8377 1.9724 103 0.1365 1.8335 1.9700 104 0.1383 1.8292 1.9675 105" 0.1401 1.8250 1.9651 106 0.1418 1.8208 1.9626 107 0.1436 1.8166 1.9602 108 0.1454 1.8124 1.9578 109 0.1471 1.8082 1.9553 110° 0.1489 1.8041 1.9530 111 0.1506 1.8000 1.9506 112 0.1524 1.7959 1.9483 113 0.1541 1.7917 1.9458 114 0.1559 1.7876 1.9435 115^" 0.1576 1.7836 1.9412 116 0.1594 1.7795 1.9389 117 0.1611 1.7755 1.9366 118 0.1628 1.7715 1.9343 119 0.1645 1.7674 1.9319 120° 0.1662 1.7634 1.92% 121 0.1679 1.7594 1.9273 122 0.1696 1.7555 1.9251 123 0.1713 1.7515 1.9228 124 0.1730 1.7475 1.9205 125° 0.1747 1.7436 1.9183 126 0.1764 1.7397 1.9161 127 0.1781 1.7358 1.9139 128 0.1799 1.7318 1.9117 129 T''-t^4-459.6; J=777,5 ft. lbs. per B,t,i3. llog=2.89 0711; A = i/J=1.286X10-''; 144A-0,1852 [log=1.26 764]. For water, at 95 (0.81 Ibs.^sp, vol., v'or is.),sp, vol, V or t- 0.0163 en, ft, per lb,; Vv'- 61,3 lbs. per cu, ft,; 144 Apv'- 0.01 B.t.Tii^ atl70 15,99 lbs,), v'or 46.2 0.69 1.45 484. 727. 1211. &+3. 1125. 0.686 0.757 1.443 500° ^510 743. 50.5 0.63 1.59 4%. 715. 1211. 632. 1125. 0.698 0.737 1.435 510 520 810. 55.1 0.57 1.74 507. 703. 1210. 620. 1125. 0.709 0.718 1.427 520 530 883. 60.1 0.52 1.91 519. 690. 1209. 608. 1124. 0.720 0.698 1.418 530 540 960. 65.3 0.48 2.08 531. 677. 1208. 596. 1123. 0.732 0.678 1.409 540 - 550° 1043. 70.9 0.44 2.28 542. 6M. 1206. 583. 1121. 0.743 0.657 1.400 550° 560 1130. 76.9 0.40 2.49 554. 650. 1204. 570. 1119. 0.754 0.637 1.391 560 570 1224. 83.3 0.37 2.71 566. 635. 1201. 556. 1117. 0.765 0.616 1381 570 580 1323. 90.0 0.34 2.96 578. 619. 1197. 542. 1115. 0.776 0.595 1371 580 590 1428. 97.2 0.31 3.23 591. 602. 1193. 527. 1112. 0.787 0.574 1.361 590 600° 1540. 104.8 0.28 3.53 604. 585. 1189. 511. 1108. 0.799 0.552 1.351 600° 610 1658. 112.8 0.26 3.9 566. 494. 0.530 610 620 1783. 1213 0.24 4.2 546. 476. 0.506 620 630 1916. 130.4 0.22 4.6 525. 457. 0.482 630 640 2056. 139.9 0.20 5.1 501. 436. 0.456 640 650° 2204. 150.0 0.18 5.6 475. 4B. 0.428 650° 660 2361. 160.6 0.16 6.2 446. 387. 0.398 660 670 2526. 171.9 0.14 6.9 411. 357. 0.3M 670 690 2883. 196.2 0.11 9.0 316. 274. 0.275 690 706.13200. 217.8 0.05 20.1 000. 000. 0.000 706 J T°=t-^+459.6|J=777.5 ft. lbs. per B.t,u.[log=2.89 071]; A=i'J= 1.286 xio--; 144 A=0.1852[loe=i.26764]. For water, at 40^ (247 lbs,), sp. vol., v' or Press. lbs. Deg. F. Atmoe* per lb. cu. ft. liquid evap. steam Evap. Steam Water Evap. Steam lbs. p t — V or c Vv horq Lorr H I or p E nore L/Torr/T Nor<^ p 100 327.8 6.80 4.429 0.2258 298.3 888.0 1186.3 806.6 1104.6 0.4743 1.1277 1.6020 100 101 328.6 6.87 4.388 0.2279 299.1 887.4 1186.5 806.0 1104.8 0.4752 1.1260 1.6012 101 102 329.3 6.94 4.347 0.2300 299.8 886.9 1186.7 805.4 1104.9 0.4762 1.1242 1.6004 102 103 330.0 7.01 4.307 0.2322 300.6 886.3 1186.9 804.8 1105.0 0.4771 1.1225 1.5996 103 104 330.7 7.08 4.268 0.2343 301.3 885.8 1187.0 804.2 1105.1 0.4780 1.1208 1.5988 104 105 331.4 7.14 4.230 0.2365 302.0 885.2 1187.2 803.6 1105.3 0.4789 1.1191 1.5980 106 106 332.0 7.21 4.192 0.2386 302.7 884.7 1187.4 803.0 1105.4 0.4798 1.1174 1.5972 106 107 332.7 7.28 4.155 0.2408 303.4 884.1 1187.5 802.5 1105.5 0.4807 1.1158 1.5965 107 108 333.4 7.35 4.118 0.2429 304.1 883.6 1187.7 801.9 1105.7 0.4816 1.1141 1.5957 108 109 334.1 7.42 4.082 0.2450 304.8 883.0 1187.9 801.3 1105.8 0.4825 1.1125 1.5950 109 110 334.8 7.49 4.047 0.2472 305.5 882.5 1188.0 800.7 1105.9 0.4834 1.1108 1.5942 110 HI 335.4 7.55 4.012 0.2493 306.2 881.9 1188.2 800.2 1106.0 0.4843 1.1092 1.5935 111 112 336.1 7.62 3.978 0.2514 306.9 881.4 1188.4 799.6 1106.2 0.4852 1.1076 1.5928 112 113 336.8 7.69 3.945 0.2535 307.6 880.9 1188.5 799.0 1106.3 0.4860 1.1061 1.5921 113 114 337.4 7.76 3.912 0.2556 308.3 880.4 1188.7 798.5 1106.4 0.4869 1.1045 1.5914 114 U5 338.1 7.83 3.880 0.2577 309.0 879.8 1188.8 797.9 1106.5 0.4877 1.1030 1.5907 115 116 338.7 7.89 3.848 0.2599 309.6 879.3 1189.0 797.4 1106.6 0.4886 1.1014 1.5900 116 117 339.4 7.96 3.817 0.2620 310.3 878.8 1189.1 796.8 1106.8 0.4894 1.0999 1.5893 117 118 340 8.03 3.786 0.2641 311.0 878.3 1189.3 796.3 1106.9 0.4903 1.0984 1.5887 118 119 340.6 8.10 3.756 0.2662 311.6 877.8 1189.4 795.7 1107.0 0.4911 1.0969 1.5880 119 120 341 3 8.17 3.726 0.2683 312.3 877.2 1189.6 795.2 1107.1 0.4919 1.0954 1.5873 120 121 341.9 8.23 3.697 0.2705 313.0 876.7 1189.7 794.7 1107.2 0.4927 1.0939 1.5866 121 122 342.5 8.30 3.668 0.2726 313.6 876.2 1189.8 794.2 1107.3 0.4935 1.0924 1.5859 122 123 343 2 8.37 3.639 0.2748 314.3 875.7 1190.0 793.6 1107.4 0.4943 1.0910 1.5853 123 124 343.8 8.44 3.611 0.2769 314.9 875.2 1190.1 793.1 1107.6 0.4951 1.0895 1.5846 124 125 344.4 8.50 3.583 0.2791 315.5 874.7 1190.3 792.6 1107.7 0.4959 1.0880 1.5839 125 126 345 8.57 3.556 0.2812 316.2 874.2 1190.4 792.0 1107.8 0.4967 1.0865 1.5832 126 127 3^5.6 8.64 3.530 0.2833 316.8 873.8 1190.5 791.5 1107.9 0.4974 1.0851 1.5825 127 128 346 2 8.71 3.504 0.2854 317.4 873.3 1190.7 791.0 1108.0 0.4982 1.0837 1.5819 128 129 346.8 8.78 3.478 0.2875 318.0 872.8 1190.8 790.5 1108.1 0.4990 1.0823 1.5813 129 130 347 4 8.85 3.452 0.2897 318.6 872.3 1191.0 790.0 1108.2 0.4998 1.0809 1.5807 130 131 348 8 91 3.427 0.2918 319.3 871.8 1191.1 789.5 1108.3 0.5005 1.0796 1.5801 131 132 348 5 8.98 3.402 0.2939 319.9 871.3 1191.2 789.0 1108.4 0.5013 1.0782 1.5795 132 133 349 1 9 05 3.378 0.2960 320.5 870.9 1191.3 788.5 1108.5 0.5020 1.0769 1.5789 133 134 349.7 9.12 3.354 0.2981 321.1 870.4 1191.5 788.0 1108.6 0.5028 1.0755 1.5783 134 135 350 3 9.19 3.331 0.3002 321.7 869.9 1191.6 787.5 1108.7 0.5035 1.0742 1.5777 135 136 350.8 9.25 3.308 0.3023 322.3 869.4 1191.7 787.0 1108.8 0.5043 1.0728 1.5771 136 137 351.4 9.32 3.285 0.3044 322.8 869.0 1191.8 786.5 1108.9 0.5050 1.0715 1.5765 137 138 352.0 9.39 3.263 0.3065 323.4 868.5 1192.0 786.0 1109.0 0.5057 1.0702 1.5759 138 139 352.5 9.46 3.241 0.3086 324.0 868.1 1192.1 785.5 1109.1 0.5064 1.0689 1.5753 139 140 353.1 9.53 3.219 0.3107 324.6 867.6 1192.2 785.0 1109.2 0.5072 1.0675 1.5747 140 141 353.6 9.59 3.197 0.3129 325.2 867.2 1192.3 784.6 1109.3 0.5079 1.0662 1.5741 141 142 354 2 9.66 3.175 0.3150 325.8 866.7 1192.5 784.1 1109.4 0.5086 1.0649 1.5735 142 143 354 7 9.73 3.154 0.3171 326.3 866.3 1192.6 783.6 1109.5 0.5093 1.0637 1.5730 143 144 355.3 9.80 3.133 0.3192 326.9 865.8 1192.7 783.2 1109.6 0.5100 1.0624 1.5724 144 145 355 8 9 87 3.112 0.3213 327.4 865.4 1192.8 782.7 1109.6 0.5107 1.0612 1.5719 145 146 356 3 9.93 3.092 0.3234 328.0 864.9 1192.9 782.2 1109.7 0.5114 1.0599 1.5713 146 147 356 9 10 00 3.072 0.3255 328.6 864.5 1193.0 781.7 1109.8 0.5121 1.0587 1.5708 147 148 357 4 10 07 3.052 0.3276 329.1 864.0 1193.2 781.3 1109.9 0.5128 1.0574 1.5702 148 149 357.9 10.14 3.033 0.3297 329.7 863.6 1193.3 780.8 1110.0 0.5135 1.0562 1.5697 149 • 1 atmo (standard atmosphere) =760 mms. of Hg. by definition = 29.921 ins, of Hg. = 14.696 lbs. per sq. in. For water, at 115 lbs., sp, vol., v' or p 0.5142 1.0550 1.5692 150 0.5148 1.0538 1.5686 151 0.5155 1.0525 1.5680 152 0.5162 1.0513 1.5675 153 0.5169 1.0501 1.5670 154 0.5175 1.0489 1.5664 155 0.5182 1.0477 1.5659 156 0.5188 1.0466 1.5654 157 0.5195 1.0454 1.5649 158 0.5201 1.0443 1.5644 159 0.5208 1.0431 1.5639 160 0.5214 1.0420 1.5634 161 0.5220 1.0409 1.5629 162 0.5226 1.0398 1.5624 163 0.5233 1.0387 1.5620 164 0.5239 1.0376 1.5615 165 0.5245 1.0365 1.5610 166 0.5251 1.0354 1.5605 167 0.5257 1.0343 1.5600 168 0.5263 1.0332 1.5595 169 0.5269 1.0321 1.5590 170 0.5275 1.0311 1.5586 171 0.5281 1.0300 1.5581 172 0.5287 1.0289 1.5576 173 0.5293 1.0278 1.5571 174 0.5299 1.0268 1.5567 175 0.5305 1.0257 1.5562 176 0.5311 1.0246 1.5557 177 0.5317 1.0235 1.5552 178 0.5322 1.0225 1.5547 179 0.5328 1.0215 1.5543 180 0.5334 1.0205 1.5539 181 0.5339 1.0195 1.5534 182 0.5345 1.0185 1.5530 183 0.5351 1.0174 1.5525 184 0.5356 1.0164 1.5520 185 0.5362 1.0154 1.5516 186 0.5367 1.0144 1.5511 187 0.5373 1.0134 1.5507 188 0.5378 1.0124 1.5502 189 0.5384 1.0114 1.5498 190 0.5389 1.0105 1.5494 191 0.5395 1.0095 1.5490 192 0.5400 1.0085 1.5485 193 0.5405 1.0076 1.5481 194 0.5410 1.0066 1.5476 195 0.5416 1.0056 1.5472 196 0.5421 1.0047 1.5468 197 0.5426 1.0038 1.5464 198 0.5431 1.0029 1.5460 199 T''=t°+459,6; J=777.5ft.lbs.perB.t.n. [log=2.89 071]! A=i/j=1.286X10-'il44A=0,1852[log=1.26 664]. For water, at 165 lbs., sp, vol., v' or <7 = 0.0182 en, ft. per lb. ; i/V= 54.9 lbs. per en, ft, ; 144 Apv'= 0,56 B.t.u.) at 190 lbs., v'ora=:0,0184 " ii/v'r=54,5 " ; 144 Apv' = 0.65 " • (19) Table 2 : Pressures -„,„ T„ n.-„- Sp. Vol. Density Heat Latent Total Internal Energy Entropy . Press. Temp. Press, cu. ft. lbs. per of the heat of heat of B.tu. . '^ , Press. lbs. Deg. F. Atmos* per lb. cu. ft. liquid evap. steam Evap. Steam Water Evap. Steam lbs. p t — V or s i/v horq Lorr H I or p E nore l/Torr/l N or* p 200 381.9 13.61 2.290 0.437 354.9 843.2 1198.1 759.5 1113.7 0.5437 1.0019 1.5456 200 201 382.3 13.68 2.279 0.439 355.3 842.8 1198.2 759.2 1113.8 0.5442 1.0010 1.5452 201 202 382.7 13.74 2.269 0.441 355.8 842.4 1198.2 758.8 1113.9 0.5447 1.0001 1.5448 202 203 383.1 13.81 2.258 0.443 356.2 842.1 1198.3 758.4 1113.9 0.5452 0.9992 1.5444 203 204 383.5 13.88 2.247 0.445 356.7 841.7 1198.4 758.0 1114.0 0.5458 0.9982 1.5440 204 205 384.0 13.95 2.237 0.447 357.1 841.4 1198.5 757.6 1114.0 0.5463 0.9973 1.5436 205 206 384.4 14.02 2.227 0.449 357.5 841.0 1198.5 757.3 1114.1 0.5468 0.9964 1.5432 206 207 384.8 14.08 2.217 0.451 358.0 840.6 1198.6 756.9 1114.2 0.5473 0.9955 1.5428 207 208 385.2 14.15 2.207 0.453 358.4 840.3 1198.7 756.5 1114.2 0.5478 0.9946 1.5424 208 209 385.6 14.22 2.197 0.455 358.8 839.9 1198.8 756.2 1114.3 0.5483 0.9937 1.5420 209 210 386.0 14.29 2.187 0.457 359.2 839.6 1198.8 755.8 1114.4 0.5488 0.9928 1.5416 210 211 386.4 14.36 2.177 0.459 359.6 839.3 1198.9 755.5 1114.4 0.5493 0.9920 1.5413 211 212 386.8 14.43 2.167 0.461 360.1 838.9 1199.0 755.1 1114.5 0.5498 0.9911 1.5409 212 213 387.2 14.49 2.158 0.463 360.5 838.6 1199.1 754.7 1114.5 0.5503 0.9902 1.5405 213 214 387.6 14.56 2.148 0.466 360.9 838.2 1199.1 754.4 1114.6 0.5508 0.9893 1.5401 214 215 388.0 14.63 2.138 0.468 361.4 837.9 1199.2 754.0 1114.6 0.5513 0.9885 1.5398 215 216 388.4 14.70 2.128 0.470 361.8 837.5 1199.3 753.7 1114.7 0.5518 0.9876 1.5394 216 217 388.8 14.77 2.118 0.472 362.2 837.2 1199.4 753.3 1114.7 0.5523 0.9867 1.5390 217 218 389.1 14.83 2.109 0.474 362.6 836.8 1199.4 753.0 1114.8 0.5528 0.9858 1.5386 218 219 389.5 14.90 2.100 0.476 363.0 836.5 1199.5 752.6 1114.8 0.5533 0.9850 1.5383 219 220 389.9 14.97 2.091 0.478 363.4 836.2 1199.6 752.3 1114.9 0.5538 0.9841 1.5379 220 221 390.3 15.04 2.082 0.480 363.8 835.8 1199.6 751.9 1115.0 0.5543 0.9833 1.5376 221 222 390.7 15.11 2.073 0.482 364.2 835.5 1199.7 751.6 1115.0 0.5548 0.9824 1.5372 222 223 391.1 15.17 2.064 0.485 364.6 835.1 1199.8 751.2 1115.1 0.5553 0.9816 1.5369 223 224 391.5 15.24 2.055 0.487 365.0 834.8 1199.8 750.8 1115.1 0.5557 0.9808 1.5365 224 225 391.9 15.31 2.046 0.489 365.5 834.4 1199.9 750.5 1115.2 0.5562 0.9799 1.5361 225 226 392.2 15.38 2.038 0.491 365.9 834.1 1200.0 750.1 1115.2 0.5567 0.9791 1.5358 226 227 392.6 15.45 2.030 0.493 366.3 833.8 1200.0 749.8 1115.3 0.5572 0.9783 1.5355 227 228 393.0 15.51 2.021 0.495 366.7 833.4 1200.1 749.4 1115.3 0.5577 0.9774 1.5351 228 229 393.4 15.58 2.013 0.497 367.1 833.1 1200.2 749.1 1115.4 0.5582 0.9766 1.5348 229 230 393.8 15.65 2.004 0.499 367.5 832.8 1200.2 748.8 1115.4 0.5586 0.9758 1.5344 230 231 394.1 15.72 1.996 0.501 367.9 832.4 1200.3 748.4 1115.5 0.5591 0.9750 1.5341 231 232 394.5 15.79 1.988 0.503 368.3 832.1 1200.4 748.1 1115.5 0.5596 0.9741 1.5337 232 233 394.9 15.86 1.980 0.505 368.7 831.8 1200.4 747.7 1115.6 0.5601 0.9733 1.5334 233 234 395.2 15.92 1.972 0.507 369.0 831.4 1200.5 747.4 1115.6 0.5605 0.9725 1.5330 234 235 395.6 15.99 1.964 0.509 369.4 831.1 1200.6 747.0 1115.7 0.5610 0.9717 1.5327 235 236 396.0 16.06 1.956 0.511 369.8 830.8 1200.6 746.7 1115.7 0.5615 0.9708 1.5323 236 237 396.4 16.13 1.948 0.513 370.2 830.4 1200.7 746.4 1115.8 0.5619 0.9700 1.5319 237 238 396.7 16.20 1.940 0.515 370.6 830.1 1200.7 746.0 1115.8 0.5624 0.9692 1.5316 238 239 397.1 16.26 1.932 0.518 371.0 829.8 1200.8 745.7 1115.9 0.5629 0.9684 1.5313 239 240 397.4 16.33 1.924 0.520 371.4 829.5 1200.9 745.4 1115.9 0.5633 0.9676 1.5309 240 241 397.8 16.40 1.917 0.522 371.8 829.2 1200.9 745.0 1116.0 0.5638 0.9668 1.5306 241 242 398.2 16.47 1.909 0.524 372.2 828.8 1201.0 744.7 1116.0 0.5642 0.9661 1.5303 242 243 398.5 16.53 1.902 0.526 372.6 828.5 1201.1 744.4 1116.1 0.5647 0.9653 1.5300 243 244 398.9 16.60 1.894 0.528 372.9 828.2 1201.1 744.0 1116.1 0.5651 0.9646 1.5297 244 245 399.3 16.67 1.887 0.530 373.3 827.9 1201.2 743.7 1116.2 0.5655 0.9638 1.5293 245 246 399.6 16.74 1.879 0.532 373.7 827.5 1201.2 743.4 1116.2 0.5659 0.9630 1.5289 246 247 400.0 16.81 1.872 0.534 374.1 827.2 1201.3 743.0 1116.3 0.5663 0.9623 1.5286 247 248 400.3 16.88 1.864 0.536 374.5 826.9 1201.4 742.7 1116.3 0.5668 0.9615 1.5283 248 249 400.7 16.94 1.857 0.538 374.8 826.6 1201.4 742.4 1116.4 0.5672 0.9607 1.5279 249 1 atmo (standard atmosphere) = 760 mms. of Hg. by def. = 29.921 ins. of Hg. = 14.698 lbs. per sq. io. per lb. (20) For water, at 215 lb p 250 401.1 17.01 1.850 0.541 375.2 826.3 1201.5 742.0 1116.4 0.5676 0.9600 1.5276 250 252 401.8 17.15 1.836 0.545 376.0 825.6 1201.6 741.4 1116.5 0.5685 0.9584 1.5269 252 254 402.4 17.28 1.822 0.549 376.7 825.0 1201.7 740.8 1116.6 0.5694 0.9569 1.5263 254 256 403.1 17.42 1.809 0.553 377.5 824.4 1201.8 740.1 1116.7 0.5702 0.9554 1.5256 256 258 403.8 17.56 1.795 0.557 378.2 823.7 1201.9 739.5 1116.8 0.5711 0.9539 1.5250 258 260 404.5 17.69 1.782 0.561 378.9 823.1 1202.1 738.9 1116.9 0.5719 0.9525 1.5244 260 262 405.2 17.83 1.769 0.565 379.6 822.5 1202.2 738.2 1117.0 0.5727 0.9511 1.5238 262 264 405.9 17.96 1.756 0.569 380.4 821.9 1202.3 737.6 1117.1 0.5735 0.9497 1.5232 264 266 406.6 18.10 1.743 0.574 381.1 821.3 1202.4 737.0 1117.2 0.5744 0.9482 1.5226 266 268 407.2 18.24 1.731 0.578 381.8 820.7 1202.5 736.4 1117.2 0.5752 0.9468 1.5220 268 270 407.9 18.37 1.718 0.582 382.5 820.1 1202.6 735.8 1117.3 0.5760 0.9454 1.5214 270 272 408.6 18.51 1.705 0.587 383.2 819.5 1202.7 735.1 1117.4 0.5768 0.9440 1.5208 272 274 409.2 18.64 1.693 0.591 383.9 818.9 1202.8 734.5 1117.5 0.5776 0.9426 1.5202 274 276 409.9 18.78 1.681 0.595 384.6 818.3 1202.9 733.9 1117.6 0.5784 0.9412 1.5196 276 278 410.5 18.92 1.669 0.599 385.3 817.7 1203.0 733.3 1117.6 0.5792 0.9398 1.5190 278 280 411.2 19.05 1.658 0.603 386.0 817.1 1203.1 732.7 1117.7 0.5800 0.9385 1.5185 280 282 411.8 19.19 1.646 0.608 386.7 816.5 1203.2 732.1 1117.8 0.5808 0.9371 1.5179 282 284 412.4 19.32 1.635 612 387.4 815.9 1203.3 731.5 1117.9 0.5816 0.9357 1.5173 284 286 413.1 19.46 1.624 0.616 388.1 815.4 1203.4 730.9 1118.0 0.5824 0.9344 1.5168 286 288 413.7 19.60 1.613 0.620 388.7 814.8 1203.5 730.3 1118.1 0.5832 0.9330 1.5162 288 290 414.4 19.73 1.602 0.624 389.4 814.2 1203.6 729.7 1118.1 0.5840 0.9316 1.5156 290 292 415.0 19.87 1.591 0.629 390.1 813.6 1203.7 729.2 1118.2 0.5848 0.9302 1.5150 292 294 415.6 20.01 1.581 0.633 390.8 813.0 1203.8 728.6 1118.3 0.5856 0.9289 1.5145 294 296 416.2 20.14 1.571 0.637 391.4 812.5 1203.9 728.0 1118.4 0.5863 0.9276 1 5139 296 298 416.8 20.28 1.561 0.641 392.1 811.9 1204.0 727.4 1118.4 0.5871 0.9263 1.5134 298 300 417.5 20.41 1.551 0.645 392.7 811.3 1204.1 726.8 1118.5 0.5878 0.9251 1.5129 300 310 420.5 21.09 1.502 0.666 395.9 80S.S 1204.5 724.0 1118.9 0.5915 0.9187 1.5102 310 320 423.4 21.78 1.456 0.687 399.1 805.8 1204.9 721.2 1119.2 0.5951 0.9125 1.5076 320 330 426.3 22.46 1.413 0.708 402.2 803.1 1205.3 718.5 1119.6 0.5986 0.9065 1 5051 330 340 429.1 23.14 1.372 0.729 405.3 800.4 120i).7 715.9 1119.9 0.6020 0.9006 1.5026 340 350 431.9 23.82 1.334 0.750 408.2 797.8 1206.1 713.3 1120.2 0.6053 8949 1 5002 350 360 434.6 24.50 1.298 0.770 411.2 795.3 1206.4 710.7 1120.5 0.6085 0.8894 1.4979 360 370 437.2 25.18 1.264 0.791 414.0 792.8 1206.8 708.2 1120.8 0.6116 0.8840 1 4956 370 380 439.8 25.86 1.231 0.812 416.8 790.3 1207.1 705.7 1121.1 0.6147 0.8788 1 4935 380 390 442.3 26.54 1.200 0.833 419.5 787.9 1207.4 703.3 1121.4 0.6178 0.8737 1.4915 390 400 444.7 27.22 1.17 0.86 422. 786. 1208. 701. 1122. 0.621 0.868 1489 400 410 447.2 27.90 1.14 0.88 425. 783. 1208. 699. 1122. 0.624 0.863 1487 410 420 449.6 28.58 1.11 0.90 427. 780. 1208. 696. 1122. 0.627 0.858 1485 420 430 451.9 29.26 1.09 0.92 430. 778. 1208. 694. 1122. 0.629 0.854 1483 430 440 454.2 29.94 1.06 0.94 433. 776. 1208. 692. 1122. 0.632 0.849 1.481 440 450 456.5 30.62 1.04 0.96 435. 774. 1209. 690. 1123. 0.635 0.844 1 479 450 460 45P.7 31.30 1.01 0.99 438. 771. 1209. 687. 1123. 0.637 0.840 1.477 460 470 460.9 31.98 0.99 1.01 440. 769. 1209. 685. 1123. 0.640 0.835 1.475 470 480 463.0 32.66 0.97 1.03 443. 767. 1209. 683. 1123. 0.643 0.831 1.474 480 490 465.1 33.34 0.95 1.05 445. 764. 1210. 680. 1124. 0.645 0.827 1.472 490 500 467.2 34.02 0.93 1.08 448. 762. 1210. 678. 1124. 0.W8 0.823 1.471 500 525 472.3 35.72 0.89 1.12 453. 757. 1210. 673. 1124. 0.654 0.813 1.467 525 560 477.2 37.42 0.85 1.18 458. 752. 1210. 668. 1125. 0.659 0.803 1.462 550 575 481.9 39.13 0.81 1.24 464. 747. 1211. 663. 1125. 0.664 0.794 1.458 575 600 486.4 40.83 0.781 .28 469. 742. 1211. 658. 1125. 0.670 0.784 1.454 600 T-=r + 459.6! J= 777.5 ft. lbs. per B.t.n, [log- 2, 89 0711iA = i/J = 1.286X 10-' j 144 A = 0,1852riog= 1,26 7641. For water, at 280 lbs., sp, vol.,v'or Table 3 : Superheated Steam Degrees of Superheat t Water sfeam 10° 20° 30° 40° 50° B0° 70° 80° 90° 100° 110° 120" 225 t 391.9 401.9 411.9 421.9 431.9 441.9 451.9 461.9 471.9 481.9 491.9 501.9 511.9 V 0.02 2.05 2.09 2.12 2.15 2.19 2.23 2.26 2.30 2.33 2.37 2.40 2.43 2.47 h 365.5 1199.9 1207.2 1214.1 1220.5 1226.8 1232.7 1238.5 1244.1 1249.5 1254.9 1260.2 1265.4 1270.5 n 0.5562 1.5361 1.5447 1.5525 1.5600 1.5671 1.5738 1.5800 1.5861 1.5920 1.5977 1.6033 1.6088 1.6141 226 t 392.2 402.2 412.2 422.2 432.2 442.2 452.2 462.2 472.2 482.2 492.2 502.2 512.2 V 0.02 2.04 2.08 2.11 2.14 2.18 2.22 2.25 2.29 2.32 2.36 2.39 2.42 2.46 h 365.9 1200.0 1207.3 1214.2 1220.6 1226.9 1232.8 1238.6 1244.2 1249.7 1255.0 1260.3 1265.6 127C 7 n 0.5567 1.5358 1.5443 1.5522 1.5596 1.5667 1.5734 1.5797 1.5858 1.5917 1.5974 1.6030 1.6085 1.613b 227 t 392.6 402.6 412.6 422.6 432.6 442.6 452.6 462.6 472.6 482.6 492.6 502.6 512.6 V 0.02 2.03 2.07 2.10 2.14 2.17 2.21 2.24 2.28 2.31 2.35 2.38 2.41 2.45 h 366.3 1200.0 1207.3 1214.2 1220.7 1227.0 1232.9 1238.7 1244.3 1249.8 1255.1 1260.4 1265.7 1270.8 n 0.5572 1.5355 1.5440 1.5519 1.5593 1.5664 1.5731 1.5794 1.5855 1.5914 1.5971 1.6027 1.6082 1.6135 228 t 393.0 403.0 413.0 423.0 433.0 443.0 453.0 463.0 473.0 483.0 493.0 503.0 513.0 V 0.02 2.02 2.06 2.09 2.13 2.16 2.20 2.23 2.27 2.30 2.34 2.37 2.40 2.44 h 366.7 1200.1 1207.4 1214.3 1220.8 1227.1 1233.0 1238.8 1244.4 1249.9 1255.2 1260.5 1265.8 1270.9 n 0.5577 1.5351 1.5436 1.5515 1.5590 1.5661 1.5728 1.5791 1.5852 1.5910 1.5967 1.6023 1.6078 1.6131 229 t 393.4 403.4 413.4 423.4 433.4 443.4 453.4 463.4 473.4 483.4 493.4 503.4 513.4 V 0.02 2.01 2.05 2.08 2.12 2.16 2.19 2.23 2.26 2.29 2.33 2.36 2.39 2.43 h 367.1 1200.2 1207.5 1214.4 1220.9 1227.2 1233.1 1238.9 1244.6 1250.0 1255.3 1260.6 1265.9 1271.1 n 0.5582 1.5348 1.5433 1.5512 1.5587 1.5658 1.5725 1.5788 1.5849 1.5908 1.5965 1.6020 1.6075 1.6128 230 t 393.8 403.8 413.8 423.8 433.8 443.8 453.8 463.8 473.8 483.8 493.8 503.8 513.8 V 0.02 2.00 2.04 2.07 2.11 2.15 2.18 2.22 2.25 2.28 2.32 2.35 2.38 2.42 h 367.5 1200.2 1207.6 1214.5 1221.0 1227.3 1233.2 1239.0 1244.7 1250.1 1255.4 1260.7 1266.0 1271.1 n 0.5586 1.5344 1.5430 1.5509 1.5584 1.5655 1.5721 1.5784 1.5845 1.5904 1.5961 1.6017 1.6072 1.6125 231 t 394.1 404.1 414.1 424.1 434.1 444.1 454.1 464.1 474.1 484.1 494.1 504.1 514.1 V 0.02 1.99 2.03 2.06 2.10 2.14 2.17 2.21 2.24 2.28 2.31 2.34 2.38 2.41 h 367.9 1200.3 1207.7 1214.6 1221.1 1227.4 1233.4 1239.2 1244.8 1250.3 1255.6 1260.9 1266.1 1271.2 n 0.5591 1.5341 1.5427 1.5506 1.5581 1.5652 1.5718 1.5781 1.5842 1.5901 1.5958 1.6014 1.6069 1.6122 232 t 394.5 404.5 414.5 424.5 434.5 444.5 454.5 464.5 474.5 484.5 494.5 504.5 514.5 V 0.02 1.99 2.03 2.06 2.09 2.13 2.16 2.20 2.23 2.27 2.30 2.33 2.37 2.40 h 368.3 1200.4 1207.8 1214.7 1221.2 1227.5 1233.5 1239.3 1244.9 1250.4 1255.7 1261.0 1286.3 1271.4 n 0.5596 1.5337 1.5423 1.5502 1.5577 1.5648 1.5715 1.5778 1.5839 1.5898 1.5955 1.6011 1.6065 1.6118 233 t 394.9 404.9 414.9 424.9 434.9 444.9 454.9 464.9 474.9 484.9 494.9 504.9 514.9 V 0.02 1.98 2.02 2.05 2.08 2.12 2.16 2.19 2.22 2.26 2.29 2.32 2.36 2.39 h 368.7 1200.4 1207.8 1214.8 1221.3 1227.6 1233.6 1239.4 1245.0 1250.5 1255.8 1261.1 1266.4 1271.5 n 0.5601 1.5334 1.5420 1.5499 1.5574 1.5645 1.5712 1.5775 1.5836 1.5895 1.5952 1.6008 1.6062 1.6115 234 t 395.2 405.2 415.2 425.2 435.2 445.2 455.2 465.2 475.2 485.2 495.2 505.2 515.2 V 0.02 1.97 2.01 2.04 2.07 2.11 2.15 2.18 2.22 2.25 2.28 2.31 2.35 2.38 h 369.0 1200.5 1207.9 1214.9 1221.4 1227.7 1233.7 1239.5 1245.1 1250.6 1255.9 1261.2 1266.5 1271.6 n 0.5605 1.5330 1.5416 1.5496 1.5571 1.5642 1.5709 1.5772 1.5833 1.5891 1.5948 1.6004 1.6059 1.6112 235 t 395.6 405.6 415.6 425.6 435.6 445.6 455.6 465.6 475.6 485.6 495.6 505.6 515.6 V 0.02 1.96 2.00 2.03 2.07 2.10 2.14 2.17 2.21 2.24 2.27 2.30 2.34 2.37 h 369.4- 1200.6 1208.0 1215.0 1221.5 1227.8 1233.8 1239.6 1245.2 1250.7 1256.1 1261.4 1266.6 1271.7 n 0.5610 1.5327 1.5413 1.5493 1.5568 1.5639 1.5706 1.5769 1.5830 1.5888 1.5945 1.6001 1.6056 1.6109 236 t 396.0 406.0 416.0 426.0 436.0 446.0 456.0 466.0 476.0 486.0 496.0 506.0 516.0 V 0.02 1.96 1.99 2.02 2.06 2.09 2.13 2.16 2.20 2.23 2.26 2.30 2.33 2.36 h 369.8 1200.6 1208.0 1215.0 1221.6 1227.9 1233.9 1239.7 1245.3 1250.8 1256.2 1261.5 1266.7 1271.8 n 0.5615 1.5323 1.5409 1.5489 1.5564 1.5635 1.5702 1.5765 1.5826 1.5885 1.5942 1.5998 1.6052 1.6105 237 t 396.4 406.4 416.4 426.4 436.4 446.4 456.4 466.4 476.4 486.4 496.4 506.4 516.4 V 0.02 1.95 1.98 2.01 2.05 2.09 2.12 2.16 2.19 2.22 2.25 2.29 2.32 2.35 h 370.2 1200.7 1208.1 1215.1 1221.7 1228.0 1234.0 12.-?9.8 1245.4 1250.9 1256.3 1261.6 1266.8 1271.9 n 0.5619 1.5319 1.5405 1.5^85 1.5561 1.5632 1.5699 1.5762 1.5823 1.5882 1.5939 1.5994 1.6049 1.6102 (58) 130° 140° 150° 160° 170° 180° 190° 200° 250° 300° 350^ Degrees of Superheat 400° 500° 600° Press, lbs. 521.9 531.9 541.9 551.9 561.9 571.9 581.9 2.50 2.53 2.57 2.60 2.63 2.66 2.69 1275.7 1280.8 1285.9 1290.9 1296.0 1301.0 1305.9 1.6194 1.6245 1.6296 1.6346 1.6396 1.6445 1.6493 522.2 532.2 542.2 552.2 562.2 572.2 582.2 2.49 2.52 2.56 2.59 2.62 2.65 2.68 1275.8 1280.9 1286.0 1291.0 1296.1 1301.1 1306.1 1.6190 1.6242 1.6293 1.6343 1.6392 1.6441 1.6489 522.6 532.6 542.6 552.6 562.6 572.6 582.6 2.48 2.51 2.55 2.58 2.61 2.64 2.67 1275.9 1281.0 1286.1 1291.1 1296.2 1301.2 1306.2 1.6187 1.6239 1.6290 1.6340 1.6389 1.6438 1.6486 523.0 533.0 543.0 553.0 563.0 573.0 583.0 2.47 2.50 2.54 2.57 2.60 2.63 2.66 1276.0 1281.1 1286.2 1291.2 1296.3 1301.3 1306.3 1.6184 1.6235 1.6286 1.6336 1.6386 1.6435 1.6483 523.4 533.4 543.4 553.4 563.4 573.4 583.4 2.46 2.49 2.52 2.56 2.59 2.62 2.65 1276.2 1281.3 1286.3 1291.3 1296.4 1301.4 1306.4 1.6181 1.6233 1.6283 1.6333 1.6383 1.6432 1.6480 523.8 533.8 543.8 553.8 563.8 573.8 583.8 2.45 2.48 2.51 2.55 2.58 2.61 2.64 1276.3 1281.4 1286.5 1291.5 1296.5 1301.5 1306.5 1.6177 1.6229 1.6280 1.6330 1.6379 1.6428 1.6476 524.1 534.1 544.1 554.1 564.1 574.1 584.1 2.44 2.47 2.50 2.54 2.57 2.60 2.63 1276.4 1281.5 1286.6 1291.6 1296.7 1301.7 1306.6 1.6174 1.6226 1.6277 1.6327 1.6376 1.6425 1.6473 524.5 534.5 544.5 554.5 564.5 574.5 584.5 2.43 2.46 2.49 2.52 2.56 2.59 2.62 1276.5 1281.6 1286.7 1291.7 1296.8 1301.8 1306.8 1.6170 1.6222 1.6273 1.6323 1.6372 1.6421 1.6469 524.9 534.9 544.9 554.9 564.9 574.9 584.9 2.42 2.45 2.48 2.51 2.55 2.58 2.61 1276.6 1281.7 1286.8 1291.9 1296.9 1301.9 1306.9 1.6167 1.6219 1.6270 1.6320 1.6369 1.6418 1.6466 525.2 535.2 545.2 555.2 565.2 575.2 585.2 2.41 2.44 2.47 2.50 2.54 2.57 2.60 1276.8 1281.9 1287.0 1292.0 1297.0 1302.0 1307.0 1.6164 1.6216 1.6267 1.6317 1.6366 1.6415 1.6463 525.6 535.6 545.6 555.6 565.6 575.6 585.6 2.40 2.43 2.46 2.50 2.53 2.56 2.59 1276.9 1282.0 1287.1 1292.1 1297.1 1302.1 1307.1 1.6161 1.6213 1.6264 1.6314 1.6363 1.6412 1.6460 526.0 536.0 546.0 556.0 566.0 576.0 586.0 2.39 2.42 2.45 2.49 2.52 2.55 2.58 1277.0 1282.1 1287.2 1292.2 1297.2 1302.2 1307.2 1.6157 1.6209 1.6260 1.6310 1.6359 1.6408 1.6456 526.4 536.4 546.4 556.4 566.4 576.4 586.4 2.38 2.41 2.44 2.48 2.51 2.54 2.57 1277.1 1282.2 1287.3 1292.3 1297.3 1302.4 1307.4 1.6154 1.6206 1.6256 1.6306 1.6355 1.6404 1.6452 591.9 641.9 691.9 741.9 2.72 2.88 3.03 3.18 1310.9 1335.7 1360.3 1384.9 1.6542 1.6771 1.6988 1.7197 592.2 642.2 692.2 742.2 2.71 2.87 3.02 3.17 1311.1 1335.8 1360.5 1385.0 1.6538 1.6767 1.6985 1.7193 592.6 642.6 692.6 742.6 2.70 2.86 3.01 3.15 1311.2 1336.0 1360.6 1385.2 1.6535 1.6764 1.6982 1.7190 593.0 643.0 693.0 743.0 2.69 2.84 2.99 3.14 1311.3 1336.1 1360.8 1385.3 1.6531 1.6760 1.6978 1.7186 593.4 643.4 693.4 743.4 2.68 2.83 2.98 3.13 1311.4 1336.2 1360.9 1385.4 1.6528 1.6757 1.6975 1.7183 593.8 643.8 693.8 743.8 2.67 2.82 2.97 3.12 1311.6 1336.3 1361.0 1385.6 1.6525 1.6753 1.6971 1.7179 594.1 644.1 694.1 744.1 2.66 2.81 2.96 3.10 1311.7 1336.4 1361.2 1385.7 1.6522 1.6750 1.6968 1.7176 594.5 644.5 694.5 744.5 2.65 2.80 2.95 3.09 1311.8 1336.6 1361.3 1385.8 1.6518 1.6747 1.6964 1.7172 594.9 644.9 694.9 744.9 2.64 2.79 2.93 3.08 1311.9 1336.7 1361.4 1386.0 1.6515 1.6744 1.6961 1.7169 595.2 645.2 695.2 745.2 2.63 2.78 2.92 3.07 1312.0 1336.8 1361.6 1386.1 1.6512 1.6740 1.6957 1.7165 595.6 645.6 695.6 745.6 2.62 2.77 2.91 3.06 1312.2 1337.0 1361.7 1386.2 1.6509 1.6737 1.6954 1.7162 596.0 646.0 696.0 746.0 2.61 2.76 2.90 3.04 1312.3 1337.1 1361.8 1386.4 1.6505 1.6733 1.6951 1.7158 596.4 646.4 696.4 746.4 2.60 2.75 2.89 3.03 1312.4 1337.2 1361.9 1386.5 1.6501 1.6729 1.6947 1.7154 '50) 791.9 891.9 991.9 t 225 3.33 3.62 3.89 v 1409.4 1458.4 1507.6 h 1.7398 1.7775 1.8127 n 792.2 892.2 992.2 t 226 3.31 3.60 3.88 v 1409.6 1458.6 1507.7 h 1.7394 1.7771 1.8123 n 792.6 892.6 992.6 t 227 3.30 3.59 3.86 V 1409.7 1458.7 1507.9 h 1.7391 1.7768 1 8119 n 793.0 893.0 993.0 t 228 3.29 3.57 3.84 v 1409.8 1458.8 1508.0 h 1.7387 1.7764 1.8115 n 793.4 893.4 993.4 t 229 3.28 3.56 3.83 v 1410.0 1459.0 1508.2 h 1.7383 1.7761 1.8112 n 793.8 893.8 993.8 t 230 3.26 3.54 3.82 v 1410.1 1459.1 1508.3 h 1.7379 1.7757 1.8108 n 794.1 894.1 994.1 t 231 3.25 3.53 3.80 V 1410.3 1459.3 1508.5 h 1.7376 1.7754 1.8105 n 794.5 894.5 994.5 t 232 3.23 3.51 3.78 v 1410.4 1459.4 1508.6 h 1.7372 1.7749 1.8101 n 794.9 894.9 994.9 t 233 3.22 3.50 3.77 v 1410.6 1459.6 1508.8 h 1.7369 1.7746 1.8098 n 795.2 895.2 995.2 t 234 3.21 3.49 3.76 v 1410.7 1459.7 1508.9 h 1.7365 1.7742 1.8094 n 795.6 895.6 995.6 t 235 3.20 3.47 3.74 v 1410.8 1459.8 1509.0 h 1.7362 1.7739 1.8091 n 796.0 896.0 996.0 t 236 3.18 3.46 3.73 v 1411.0 1460.G 1509.2 h 1.7358 1.7735 1.8087 n 796.4 896.4 996.4 t 237 3.17 3.44 3.71 v 1411.1 1460.1 1509.3 h 1.7354 1.7731 1.8082 n fable 3 : Superheated Steam Degrees of Superheat 10° 20° 30° 40° 50° 60° 70° 80° 90° 100° 110° 120° 406.7 416.7 426.7 436.7 446.7 456.7 466.7 476.7 486.7 496.7 506.7 516.7 1.98 2.01 2.04 2.08 2.11 2.15 2.18 2.21 2.24 2.28 2.31 2.34 1208.2 1215.2 1221.8 1228.1 1234.1 1239.9 1245.5 1251.0 1256.4 1261.7 1266.9 1272.1 1.5402 1.5482 1.5558 1.5629 1.5696 1.5759 1.5820 1.5879 1.5936 1.5991 1.6046 1.6099 407.1 417.1 427.1 437.1 447.1 457.1 467.1 477.1 487.1 497.1 507.1 517.1 197 2.00 2.03 2.07 2.10 2.14 2.17 2.20 2.24 2.27 2.30 2.33 1208 3 1215.3 1221.9 1228.2 1234.2 1240.0 1245.7 1251.2 1256.5 1261.8 1267.1 1272.3 1.5399 1.5479 1.5555 1.5626 1.5693 1.5756 1.5817 1.5876 1.5933 1.5988 1.6043 1.6096 407.4 417.4 427.4 437.4 447.4 457.4 467.4 477.4 487.4 497.4 507.4 517.4 196 1.99 2.02 2.06 2.09 2.13 2.16 2.20 2.23 2.26 2.29 2.32 1208.4 1215.4 1222.0 1228.3 1234.3 1240.1 1245.8 1251.3 1256.6 1261.9 1267.1 1272.3 1.5396 1.5476 1.5552 1.5623 1.5690 1.5753 1.5814 1.5873 1.5930 1.5985 1.6040 1.6093 407.8 417.8 427.8 437.8 447.8 457.8 467.8 477.8 487.8 497.8 507.8 517.8 195 1.98 2.02 2.05 2.09 2.12 2.16 2.19 2.22 2.25 2.28 2.31 1208 5 1215 5 1222.1 1228.4 1234.4 1240.2 1245.9 1251.4 1256.7 1262.0 1267.2 1272.4 1.5393 1.5473 1.5549 1.5620 1.5687 1.5750 1.5811 1.5870 1.5927 1.5982 1.6037 1.6090 408 2 418.2 428.2 438.2 448.2 458.2 468.2 478.2 488.2 498.2 508.2 518.2 194 1.97 2.01 2.04 2.08 2.11 2.15 2.18 2.21 2.24 2.27 2.30 1208 5 1215 6 1222.2 1228.5 1234.5 1240.4 1246.0 1251.5 1256.9 1262.2 1267.4 1272.5 1.5390 1.5470 1.5546 1.5617 1.5684 1.5747 1.5808 1.5867 1.5924 1.5979 1.6034 1.6087 408.5 418.5 428.5 438.5 448.5 458.5 468.5 478.5 488.5 498.5 508.5 518.5 193 196 2.00 2.04 2.07 2.10 2.14 2.17 2.20 2.23 2.26 2.30 1208 6 1215 7 1222.3 1228.6 1234.6 1240.5 1246.1 1251.6 1257.0 1262.3 1267.5 1272.6 1.5387 1.5467 1.5543 1.5614 1.5681 1.5744 1.5805 1.5864 1.5921 1.5976 1.6031 1.6084 408.9 418.9 428.9 438.9 448.9 458.9 468.9 478.9 488.9 498.9 508.9 518.9 193 196 1.99 2.03 2.06 2.10 2.13 2.16 2.19 2.22 2.26 2.29 1208 7 1215.8 1222.4 1228.7 1234.7 1240.6 1246.2 1251.7 1257.1 1262.4 1267.6 1272.7 1.5384 1.5464 1.5540 1.5611 1.5678 1.5741 1.5802 1.5861 1.5918 1.5973 1.6028 1.6081 409 3 419 3 429.3 439.3 449.3 459.3 469.3 479.3 489.3 499.3 509.3 519.3 192 195 1.99 2.02 2.05 2.09 2.12 2.15 2.18 2.22 2.25 2.28 1208 8 1215 9 1222.5 1228.8 1234.8 1240.7 1246.3 1251.8 1257.2 1262.5 1267.7 1272.8 1.5381 1.5461 1.5537 1.5608 1.5675 1.5738 1.5799 1.5858 1.5915 1.5970 1.6025 1.6078 409 6 419 6 429.6 439.6 449.6 459.6 469.6 479.6 489.6 499.6 509.6 519.6 191 1.94 1.98 2.01 2.05 2.08 2.11 2.14 2.18 2.21 2.24 2.27 1208 8 1215 9 1222 6 1228.9 1234.9 1240.8 1246.4 1251.9 1257.3 1262.6 1267.8 1272.9 1.5377 1.5458 1.5533 1.5605 1.5672 1.5735 1.5796 1.5855 1.5912 1.5967 1.6022 1.6075 410 420 430 440.0 450.0 460.0 470.0 480.0 490.0 500.0 510.0 520.0 190 193 197 2.00 2.04 2.07 2.10 2.14 2.17 2.20 2.23 2.26 1208.9 1216 1222.7 1229.0 1235.0 1240.9 1246.6 1252.0 1257.4 1262.7 1267.9 1273.0 1.5374 1.5455 1.5530 1.5602 1.5669 1.5732 1.5793 1.5852 1.5909 1.5964 1.6019 1.6072 410.3 420.3 430.3 440.3 450.3 460.3 470.3 480.3 490.3 500.3 510.3 520.3 190 193 1.96 2.00 2.03 2.06 2.10 2.13 2.16 2.19 2.22 2.25 1209 1216 1 1222.8 1229.1 1235.2 1241.0 1246.7 1252.1 1257.5 1262.8 1268.0 1273.2 1.5371 1.5452 1.5527 1.5599 1.5666 1.5729 1.5790 1.5849 1.5906 1.5961 1.6016 1.6069 410 7 420 7 430.7 440.7 450.7 460.7 470.7 480.7 490.7 500.7 510.7 520.7 189 192 196 1.99 2.03 2.06 2.09 2.12 2.15 2.18 2.21 2.24 1209 1 1216 2 1222 9 1229.2 1235.3 1241.1 1246.8 1252.2 1257.6 1262.9 1268.1 1273.3 1.5367 1.5448 1.5524 1.5596 1.5663 1.5726 1.5787 1.5846 1.5903 1.5958 1.6012 1.6065 t = temperature in P, degs. T Fahr. absolute = t° + 45 9, 6 '. Internal energy V=sp. vol. in cu. ft, per lb. J =777.5 ft. lbs, per B.t.u, [log = 2.89 071]. = total heat- 144 Apv, h = total heat in B.t.u. A = i/j = l,286X10-^ B,t.u, per ft, lb. [3.10 9291. Values for saturated steam n=entropy, 144 A= 0.1852 [log = 1,26 764], are given in Tables 1 and 2. (60) Press, lbs. Sat. Water Steam 238 t V h n 396.7 0.02 1.94 370.6 1200.7 0.5624 1.5316 239 t V h n 397.1 0.02 1.93 371.0 1200.8 0.5629 1.5313 240 t V h n 397.4 0.02 1.92 371.4 1200.9 0.5633 1.5309 241 t V h n 397.8 0.02 1.92 371.8 1200.9 0.5638 1.5306 242 t V h n 398.2 0.02 1.91 372.2 1201.0 0.5642 1.5303 243 t V h n 398.5 0.02 1.90 372.6 1201.1 0.5647 1.5300 244 t V h n 398.9 0.02 1.89 372.9 1201.1 0.5651 1.5297 245 t V h n 399.3 0.02 1.89 373.3 1201.2 0.5655 1.5293 246 t V h n 399.6 0.02 1.88 373.7 1201.2 0.5659 1.5289 247 t V h n 400.0 0.02 1.87 374.1 1201.3 0.5663 1.5286 248 t V h n 400.3 0.02 1.86 374.5 1201.4 0.5668 1.5283 249 t V h n 400.7 0.02 1.86 374.8 1201.4 0.5672 1.5279 uegrees qt iiuperheat 130° 140" 150° IBO^ 170° 180° 190° 200° 250° 300° 350° 400° 500° 600° *'!bT" 526.7 536.7 546.7 556.7 566.7 576.7 586 7 596.7 646.7 696.7 746.7 796.7 896.7 996 7 t 238 2.37 2.40 2.44 2.47 2.50 2.53 2 56 2.59 2.74 2.88 3.02 3.16 3.44 3 70 v 1277.2 1282.3 1287.4 1292.4 1297.5 1302.5 1307.5 1312.5 1337.3 1362.0 1386.6 1411.2 1460.2 1509 5 h 1.6151 1.6203 1.6253 1.6302 1.6352 1.6401 1.6449 1.6498 1.6726 1.6944 1.7151 1.7351 1.7728 1.8079 n 527.1 537.1 547.1 557.1 567.1 577.1 587.1 597.1 647.1 697.1 747.1 797.1 897.1 997 1 t 239 2.36 2.40 2.43 2.46 2.49 2.52 2.55 2.58 2.73 2.87 3.01 3.15 3.42 3 68 v 1277.4 1282.5 1287.5 1292.6 1297.6 1302.6 1307.6 1312.6 1337.5 1362.2 1386.8 1411.4 1460 4 1509 6 h 1.6148 1.6200 1.6250 1.6299 1.6349 1.6398 1.6446 1.6495 1.6723 1.6941 1.7148 1.7348 1.7725 1.8076 n 527.4 537.4 547.4 557.4 567.4 577.4 587.4 597.4 647.4 697.4 747.4 797.4 897.4 997.4 t 240 2.35 2.39 2.42 2.45 2.48 2.51 2.54 2.57 2.71 2.85 2.99 3.13 3.40 3.67 v 1277.5 1282.6 1287.6 1292.7 1297.7 1302.7 1307.7 1312.8 1337.6 1362.3 1386.9 1411.5 1460 5 1509.8 h 1.6145 1.6196 1.6246 1.6296 1.6346 1.6395 1.6443 1.6492 1.6720 1.6937 1.7144 1.7344 1.7721 1.8072 n 527.8 537.8 547.8 557.8 567.8 577.8 587.8 597.8 647.8 697.8 747.8 797.8 897.8 997.8 t 241 2.35 2.38 2.41 2.44 2.47 2.50 2.53 2.56 2.70 2.84 2.98 3.12 3.39 3.65 V 1277.6 1282.7 1287.8 1292.8 1297.8 1302.9 1307.9 1312.9 1337.7 1362.4 1387.0 1411.6 1460.7 1509.9 h 1.6142 1.6193 1.6243 1.6293 1.6343 1.6392 1.6440 1.6489 1.6717 1.6934 1.7141 1.7341 1.7718 1.8069 n 528.2 538.2 548.2 558.2 568.2 578.2 588.2 598.2 648.2 698.2 748.2 798.2 898.2 998.2 t 242 2.34 2.37 2.40 2.43 2.46 2.49 2.52 2.55 2.69 2.83 2.97 3.11 3.38 3.64 v 1277.7 1282.8 1287.9 1292.9 1297.9 1303.0 1308.0 1313.0 1337.8 1362.5 1387.1 1411.7 1460.8 1510.0 h 1.6139 1.6190 1.6240 1.6290 1.6340 1.6389 1.6437 1.6486 1.6714 1.6931 1.7138 1.7338 1.7715 1.8066 n 528.5 538.5 548.5 558.5 568.5 578.5 588.5 598.5 648.5 698.5 748.5 798.5 898.5 998.5 t 243 2.33 2.36 2.39 2.42 2.45 2.48 2.51 2.54 2.68 2.82 2.96 3.10 3.36 3.63 v 1277.8 1282.9 1288.0 1293.0 1298.1 1303.1 1308.1 1313.1 1337.9 1362.7 1387.3 1411.8 1460.9 1510.2 h 1.6136 1.6187 1.6237 1.6287 1.6337 1.6386 1.6434 1.6483 1.6711 1.6928 1.7135 1.7335 1.7712 1.8063 n 528.9 538.9 548.9 558.9 568.9 578.9 588.9 598.9 648.9 698.9 748.9 798.9 898.9 998.9 t 244 2.32 2.35 2.38 2.41 2.44 2.47 2.50 2.53 2.67 2.81 2.95 3.09 3.35 3.61 v 1277.9 1283.0 1288.1 1293.1 1298.2 1303.2 1308.2 1313.2 1338.1 1362.8 1387.4 1412.0 1461.0 1510.3 h 1.6133 1.6184 1.6234 1.6284 1.6334 1.6383 1.6431 1.6479 1.6707 1.6924 1.7132 1.7331 1.7708 1.8059 n 529.3 539.3 549.3 559.3 569.3 579.3 589.3 599.3 649.3 699.3 749.3 799.3 899.3 999.3 t 245 2.31 2.34 2.37 2.40 2.43 2.46 2.49 2.52 2.66 2.80 2.94 3.08 3.34 3.60 V 1278.0 1283.1 1288.2 1293.2 1298.3 1303.3 1308.3 1313.3 1338.2 1362.9 1387.5 1412.1 1461.2 1510.5 h 1.6130 1.6181 1.6231 1.6281 1.6331 1.6380 1.6428 1.6476 1.6704 1.6921 1.7129 1.7328 1.7705 1.8055 n 529.6 539.6 549.6 559.6 569.6 579.6 589.6 599.6 649.6 699.6 749.6 799.6 899.6 999.6 t 246 2.30 2.33 2.36 2.39 2.42 2.45 2.48 2.51 2.65 2.79 2.93 3.06 3.32 3.58 V 1278.1 1283.2 1288.3 1293.3 1298.4 1303.4 1308.4 1313.4 1338.3 1363.0 1387.6 1412.2 1461.3 1510.6 h 1.6127 1.6178 1.6228 1.6278 1.6327 1.6376 1.6424 1.6473 1.6701 1.6917 1.7125 1.7324 1.7701 1.8051 n 530.0 540.0 550.0 560.0 570.0 580.0 590.0 600.0 650.0 700.0 750.0 800.0 900.0 1000.0 t 247 2.29 2.32 2.35 2.38 2.41 2.44 2.47 2.50 2.64 2.78 2.92 3.05 3.31 3.57 V 1278.2 1283.3 1288.4 1293.4 1298.5 1303.6 1308.6 1313.6 1338.4 1363.2 1387.8 1412.3 1461.4 1510.7 h 1.6124 1.6175 1.6225 1.6275 1.6324 1.6373 1.6421 1.6470 1.6698 1.6914 1.7122 1.7321 1.7698 1.8048 n 530.3 540.3 550.3 560.3 570.3 580.3 590.3 600.3 650.3 700.3 750.3 800.3 900.3 1000.3 t 248 2.28 2.31 2.34 2.37 2.40 2.43 2.46 2.49 2.63 2.77 2.91 3.04 3.30 3.56 v 1278.4 1283.5 1288.6 1293.6 1298.6 1303.7 1308.7 1313.7 1338.6 1363.3 1387.9 1412.4 1461.6 1510.9 h 1.6121 1.6172 1.6222 1.6272 1.6321 i.6370 1.6418 1.6467 1.6695 1.6911 1.7119 1.7318 1.7695 1.8045 n 530.7 540.7 550.7 560.7 570.7 580.7 590.7 600.7 650.7 700.7 750.7 800.7 900.7 1000.7 t 249 2.27 2.30 2.33 2.36 2.39 2.42 2.45 2.48 2.62 2.76 2.90 3.03 3.29 3.54 v 1278.5 1283.6 1288.7 1293.7 1298.7 1303.8 1308.8 1313.8 1338.7 1363.4 1388.0 1412.6 1461.7 1511.0 h 1.6117 1.6168 1.6219 1.6269 1.6318 1.6367 1.6415 1.6463 1.6691 1.6908 1.7115 1.7314 1.7691 1.8041 n Conversion from Metric Units 1kg. per sq. cm, = 14.22 lbs. per sq. in, [log=1.15 300]. 1 cu. meter- 35.31 en. ft. riop;= 1.54 795]. To change degs. 0. to degs. F., multiply by ?, and add 32, To change mean kg. calories per kg. to mean B.t.u. per lb., multiply by s. Entropy same in both systems. ^61) Table 3 : Superheated Steam Degrees of Superheat t Water S?ea*m 10° 20° 30° 40° 50° 60° 70° 80° 90° 100° 110° 120" 250 t 401.0 411.0 421.0 431.0 441.0 451.0 461.0 471.0 481.0 491.0 501.0 511.0 521.0 V 0.02 1.85 1.88 1.91 1.95 1.98 2.02 2.05 2.08 2.11 2.14 2.17 2.21 2.24 h 375.2 1201.5 1209.2 1216.3 1223.0 1229.3 1235.4 1241.3 1246.9 1252.3 1257.7 1263.0 1268.2 1273.4 n 0.5676 1.5276 1.5364 1.5445 1.5521 1.5593 1.5660 1.5723 1.5784 1.5843 1.5900 1.5956 1.6010 1.6062 255 t 402.8 412.8 422.8 432.8 442.8 452.8 462.8 472.8 482.8 492.8 502.8 512.8 522.8 V 0.02 1.81 1.85 1.88 1.91 1.94 1.98 2.01 2.04 2.07 2.11 2.14 2.17 2.20 h 377.1 1201.8 1209.5 1216.7 1223.5 1229.8 1235.9 1241.8 1247.4 1252.9 1258.3 1263.6 1268.8 1273.9 n 0.5698 1.5260 1.5349 1.5431 1.5507 1.5579 1.5646 1.5709 1.5770 1.5829 1.5886 1.5942 1.5996 1.6048 260 t 404.5 414.5 424.5 434.5 444.5 454.5 464.5 474.5 484.5 494.5 504.5 514.5 524.5 V 0.02 1.78 1.81 1.84 1.87 1.91 1.94 1.97 2.00 2.04 2.07 2.10 2.13 2.16 h 378.9 1202.1 1209.9 1217.1 1223.9 1230.3 1236.4 1242.3 1247.9 1253.4 1258.8 1264.1 1269.3 1274.5 n 0.5719 1.5244 1.5334 1.5416 1.5492 1.5564 1.5631 1.5695 1.5756 1.5815 1.5871 1.5926 1.5980 1.6033 265 t 406.2 416.2 426.2 436.2 446.2 456.2 466.2 475.2 486.2 496.2 506.2 516.2 526.2 V 0.02 1.75 1.78 1.81 1.84 1.88 1.91 1.94 1.97 2.00 2.03 2.06 2.09 2.12 h 380.7 1202.3 1210.2 1217.5 1224.4 1230.8 1236.9 1242.8 1248.4 1253.9 1259.3 1264.6 1269.8 1275.0 n 0.5739 1.5229 1.5320 1.5402 1.5479 1.5551 1.5618 1.5682 1.5742 1.5801 1.5858 1.5914 1.5968 1.6020 270 t 407.9 417.9 427.9 437.9 447.9 457.9 467.9 477.9 487.9 497.9 507.9 517.9 527.9 V 0.02 1.72 1.75 1.78 1.81 1.84 1.87 1.90 1.93 1.96 1.99 2.02 2.05 2.08 h 382.5 1202.6 1210.6 1217.9 1224.8 1231.3 1237.4 1243.3 1248.9 1254.4 1259.8 1265,2 1270.4 1275.6 n 0.5760 1.5214 1.5305 1.5388 1.5466 1.5538 1.5605 1.5669 1.5729 1.5788 1.5844 1.5900 1.5954 1.6006 275 t 409.6 419.6 429.6 439.6 449.6 459.6 469.6 479.6 489.6 499.6 509.6 519.6 529.6 V 0.02 1.69 1.72 1.75 1.78 1.81 1.84 1.87 1.90 1.93 1.96 1.99 2.02 2.04 h 384.3 1202.9 1210.9 1218.3 1225.3 1231.8 1237.9 1243.8 1249.4 1254.9 1260.3 1265.7 1271.0 1276.1 n 0.5780 1.5199 1.5291 1.5375 1.5452 1.5524 1.5592 1.5656 1.5716 1.5775 1.5831 1.5886 1.5940 1.5993 280 t 411.2 421.2 431.2 441.2 451.2 461.2 471.2 481.2 491.2 501.2 511.2 521.2 531.2 V 0.02 1.66 1.69 1.72 1.75 1.78 1.81 1.84 1.87 1.90 1.93 1.95 1.98 2.01 h 386.0 1203.1 1211.3 1218.7 1225.7 1232.2 1238.4 1244.3 1250.0 1255.5 1260.9 1266.2 1271.4 1276.6 n 0.5800 1.5185 1.5278 1.5362 1.5440 1.5512 1.5580 1.5643 1.5704 1.5762 1.5819 1.5873 1.5927 1.5980 285 t 412.8 422.8 432.8 442.8 452.8 462.8 472.8 482.8 492.8 502.8 512.8 522.8 532.8 V 0.02 1.63 1.66 1.69 1.72 1.75 1.78 1.81 1.84 1.87 1.90 1.92 1.95 1.98 h 387.7 1203.4 1211.6 1219.1 1226.2 1232.7 1238.9 1244.8 1250.5 1256.0 1261.4 1266.7 1271.9 1277.1 n 0.5820 1.5171 1.5265 1.5349 1.5427 1.5500 1.5567 1.5631 1.5692 1.5750 1.5806 1.5861 1.5915 1.5968 290 t 414.4 424.4 434.4 444.4 454.4 464.4 474.4 484.4 494.4 504.4 514.4 524.4 534.4 V 0.02 1.60 1.63 1.66 1.69 1.72 1.75 1.78 1.81 1.83 1.86 1.89 1.92 1.94' h 389.4 1203.6 1211.9 1219.4 1226.6 1233.2 1239.3 1245.2 1250.9 1256.4 1261.8 1267.1 1272.4 1277.6 n 0.5840 1.5156 1.5251 1.5336 1.5414 1.5487 1.5554 1.5618 1.5679 1.5737 1.5793 1.5848 1.5902 1.5954 295 t 415.9 425.9 435.9 445.9 455.9 465.9 475.9 485.9 495.9 505.9 515.9 525.9 535.9 V 0.02 1.57 1.60 1.63 1.66 1.69 1.72 1.75 1.78 1.80 1.83 1.86 1.89 1.91 h 391.1 1203.8 1212.3 1219.8 1227.0 1233.6 1239.8 1245.7 1251.4 1256.9 1262.3 1267.7 1272.9 1278.^ n 0.5859 1.5142 1.5237 1.5323 1.5402 1.5475 1.5542 1.5606 1.5667 1.5725 1.5781 1.5835 1.5889 1.5942 300 t 417.5 427.5 437.5 447.5 457.5 467.5 477.5 487.5 497.5 507.5 517.5 527.5 537.5 "-""v 0.02 1.55 1.58 1.60 1.63 1.66 1.69 1.72 1.75 1.78 1.80 1.83 1.86 1.88 h 392.7 1204.1 1212.6 1220.2 1227.4 1234.1 1240.3 1246.2 1251.9 1257.4 1262.8 1268.2 1273.4 1278.6 n 0.5878 1.5129 1.5224 1.5310 1.5389 1.5462 1.5530 1.5594 1.5655 1.5713 1.5769 1,5824 1.5878 1.5930 429.0 439.0 449.0 459.0 469.0 479.0 489.0 499.0 509.0 519.0 529.0 539.0 1.56 1.58 1.61 1.64 1.67 1.69 1.72 1.75 1,78 1.80 1.83 1.85 1212.9 1220.6 1227.8 1234.5 1240.7 1246.6 1252.3 1257.9 1263.3 1268.6 1273.8 1279.0 1.5212 1.5299 1.5378 1.5451 1.5519 1.5583 1.5644 1.5702 1.5757 1.5812 1.5866 1.5918 430.5 440.5 450.5 460.5 470.5 480.5 490.5 500.5 510.5 520.5 530.5 540.S 1.53 1.55 1.58 1.61 1.64 1.67 1.69 1.72 1.75 1.78 1.81 1.83 1213.2 1221.0 1228.2 1234.9 1241.1 1247.0 1252.7 1258.3 1263.8 1269.1 1274.3 1279.5 1.5200 1.5987 1.5366 1.5440 1.5508 1.5572 1.5632 1.5690 1.5746 1.5801 1.5855 1.5907 (62) 305 t 419.0 V 0.02 1.53 n 394.4 1204.3 n 0.5897 1.5115 310 t 420.5 V 0.02 1.50 h 395.9 1204.5 D 0.5915 1.5102 Degrees of Superheat 130° 140° 150° 160° 170° 180° 190° 200° 250° 300° 350° 400° 500^ 600° ''ibT 531.0 541.0 551.0 561.0 571.0 581.0 591.0 601.0 651.0 701.0 751.0 801.0 901.0 1001.0 t 250 2.27 2.30 2.33 2.36 2.38 2.41 2.44 2.47 2.61 2.75 2.88 3.02 3.28 3.53 V 1278.6 1283.7 1288.8 1293.8 1298.9 1303.9 1308.9 1313.9 1338.8 1363.5 1388.1 1412.7 1461.8 1511.2 h 1.6114 1.6165 1.6216 1.6266 1.6315 1.6364 1.6412 1.6460 1.6688 1.6905 1.7112 1.7311 1.7688 1.8038 n 532.8 542.8 552.8 562.8 572.8 582.8 592.8 602.8 652.8 702.8 752.8 802.8 902.8 1002.8 t 255 2.23 2.26 2.28 2.31 2.34 2.37 2.40 2.43 2.56 2.70 2.83 2.96 3.22 3.47 V 1279.1 1284.2 1289.3 1294.4 1299.4 1304.5 1309.5 1314.5 1339.3 1364.1 1388.8 1413.4 1462.5 1511.8 h 1.6100 1.6151 1.6201 1.6251 1.6300 1.6349 1.6397 1.6445 1.6673 1.6890 1.7096 1.7296 1.7671 1.8021 n 534.5 544.5 554.5 564.5 574.5 584.5 594.5 604.5 654.5 704.5 754.5 804.5 904.5 1004.5 t 260 2.19 2.22 2.24 2.27 2.30 2.33 2.36 2.39 2.52 2.65 2.78 2.91 3.16 3.41 V 1279.6 1284.8 1289.9 1294.9 1300.0 1305.1 1310.1 1315.1 1340.0 1364.7 1389.4 1414.0 1463.2 1512.5 h 1.6085 1.6136 1.6186 1.6236 1.6285 1.6334 1.6382 1.6430 1.6658 1.6874 1.7081 1.7280 1.7655 1.8005 n 536.2 546.2 556.2 566.2 576.2 586.2 596.2 606.2 656.2 706.2 756.2 806.2 906.2 1006.2 t 265 2.15 2.18 2.20 2.23 2.26 2.29 2.32 2.35 2.48 2.61 2.74 2.86 3.11 3.35 V 1280.2 1285.3 1290.4 1295.5 1300.5 1305.6 1310.6 1315.6 1340.5 1365.3 1390.0 1414.6 1463.8 1513.2 h 1.6072 1.6123 1.6173 1.6222 1.6271 1.6320 1.6368 1.6416 1.6644 1.6860 1.7066 1.7265 1.7640 1.7990 n 537.9 547.9 557.9 567.9 577.9 587.9 597.9 607.9 657.9 707.9 757.9 807.9 907.9 1007.9 t 270 2.11 2.14 2.16 2.19 2.22 2.25 2.27 2.30 2.43 2.56 2.69 2.81 3.05 3.29 v 1280.7 1285.8 1290.9 1296.0 1301.0 1306.1 1311.1 1316.2 1341.1 1365.9 1390.6 1415.2 1464.5 1513.8 h 1.6058 1.6109 1.6159 1.6209 1.6258 1.6306 1.6354 1,6402 1.6630 1.6846 1.7052 1.7251 1.7625 1.7975 n 539.6 549.6 559.6 569.6 579.6 589.6 599.6 609.6 659.6 709.6 759.6 809.6 909.6 1009.6 t 275 2.07 2.10 2.13 2.16 2.18 2.21 2.24 2.26 2.39 2.52 2.64 2.77 3.00 3.24 v 1281.2 1286.3 1291.4 1296.5 1301.6 1306.7 1311.7 1316.7 1341.6 1366.5 1391.2 1415.8 1465.1 1514.5 h 1.6044 1.6095 1.6145 1.6195 1.6244 1.6292 1.6340 1.6388 1.6616 1.6831 1.7037 1.7236 1.7611 1.7959 n 541.2 551.2 561.2 571.2 581.2 591.2 601.2 611.2 661.2 711.2 761.2 811.2 911.2 1011.2 t 280 2.04 2.07 2.09 2.12 2.15 2.17 2.20 2.22 2.35 2.48 2.60 2.72 2.95 3.19 v 1281.7 1286.8 1291.9 1297.0 1302.1 1307.2 1312.2 1317.2 1342.2 1367.0 1391.7 1416.4 1465.7 1515.1 h 1.6032 1.6083 1.6133 1.6182 1.6231 1.6279 1.6327 1 6375 1.6603 1.6818 1.7024 1.7223 1.7597 1.7945 n 542.8 552.8 562.8 572.8 582.8 592.8 602.8 612.8 662.8 712.8 762.8 812.8 912.8 1012.8 t 285 2.00 2.03 2.06 2.09 2.11 2.14 2.16 2.19 2.31 2.44 2.56 2.68 2.90 3.13 V 1282.2 1287.4 1292.5 1297.6 1302.6 1307.7 1312.7 1317.8 1342.7 1367.5 1392.3 1417.0 1466.3 1515.8 h 1.6020 1.6071 1.6121 1.6170 1.6219 1.6267 1.6315 1.6363 1.6590 1.6805 1.7011 1.7209 1.7583 1.7931 n 544.4 554.4 564.4 574.4 584.4 594.4 604.4 614.4 664.4 714.4 764.4 814.4 914.4 1014.4 t 290 1.97 2.00 2.02 2.05 2.08 2.10 2.13 2.15 2.28 2.40 2.52 2.63 2.86 3.08 v 1282.7 1287.9 1293.0 1298.1 1303.1 1308.2 1313.2 1318.3 1343.2 1368.0 1392.8 1417.5 1466.9 1516.4 h 1.6006 1.6057 1.6107 1.6156 1.6205 1.6253 1.6301 1.6349 1.6576 1.6791 1.6996 1.7195 1.7568 1.7916 n 545.9 555.9 565.9 575.9 585.9 595.9 605.9 615.9 665.9 715.9 765.9 815.9 915.9 1015.9 t 295 ' 1.94 1.97 1.99 2.02 2.04 2.07 2.09 2.12 2.24 2.36 2.48 2.59 2.82 3.04 v 1283.2 1288.4 1293.5 1298.6 1303.6 1308.7 1313.7 1318.8 1343.8 1368.7 1393.4 1418.1 1467.5 1517.0 h 1.5994 1.6045 1.6095 1.6144 1.6192 1.6240 1.6288 1.6336 1.6563 1.6778 1.6983 1.7182 1.7554 1.7902 n 547.5 557.5 567.5 577.5 587.5 597.5 607.5 617.5 667.5 717.5 767.5 817.5 917.5 1017.5 t 300 1.91 1.94 1.96 1.99 2.01 2.04 .2.06 2.09 2.21 2.33 2.44 2.55 2.77 2.99 v 1283.7 1288.9 1294.0 1299.1 1304.1 1309.2 1314.2 1319.3 1344.3 1369.2 1393.9 1418.6 1468.0 1517.6 h 1.5981 1.6032 1.6082 1.6131 1.6180 1.6228 1.6275 1.6323 1.6550 1.6765 1.6970 1.7168 1.7541 1.7889 n 549.0 559.0 569.0 579.0 589.0 599.0 609.0 619.0 669.0 719.0 769.0 819.0 919.0 1019.0 t 305 1.88 1.91 1.93 1.96 1.98 2.01 2.03 2.05 2.17 2.29 2.41 2.52 2.73 2.95 v 1284.2 1289.3 1294.4 1299.5 1304.6 1309.7 1314.7 1319.8 1344.8 1369.7 1394.5 1419.2 1468.6 1518.2 h 1.5970 1.6021 1.6070 1.6119 1.6168 1.6216 1.6263 1.6311 1.6538 1.6753 1.6958 1.7156 1.7528 1.7876 n 550.5 560.5 570.5 580.5 590.5 600.5 610.5 620.5 670.5 720.5 770.5 820.5 920.5 1020.5 t 310 1.85 1.88 1,90 1.93 1.95 1.98 2.00 2,02 2.14 2.26 2.37 2.48 2.69 2.90 V 1284.7 1289,8 1294.9 1300.0 1305.1 1310.2 1315,2 1320.3 1345.3 1370.2 1395.0 1419.7 1469.2 1518.8 h 1.5958 1.6009 1.6059 1 6108 1 6156 1.6204 1.6252 1.6299 1.6526 1.6741 1.6946 1.7144 1.7516 1.7863 u '.S3) Table 3 : Superheated Steam Degrees of Superheat t Water sfeam 10° 20° 30° 40° 50° 60° 70° 80° 90° 100° 110° 120^ 320 t 423.4 433.4 443.4 453.4 463.4 473.4 483.4 493.4 503.4 513.4 523.4 533.4 543.4 V 0.02 1.46 1.49 1.51 1.53 1.56 1.59 1.62 1.64 1.67 1.70 1.72 1.75 1.77 h 399.1 1204.9 1213.8 1221.7 1229.0 1235.7 1242.0 1248.0 1253.7 1259.3 1264.7 1270.0 1275.2 1280.4 n 0.5951 1.5076 1.5176 1.5264 1.5344 1.5418 1.5486 1.5550 1.5610 1.5668 1.5723 1.5778 1.5832 1.5884 330 t 426.3 436.3 446.3 456.3 466.3 476.3 486.3 496.3 506.3 516.3 526.3 536.3 546.3 V 0.02 1.41 1.44 1.46 1.49 1.52 1.54 1.57 1.60 1.62 1.65 1.67 1.70 1.72 h 402.2 1205.3 1214.4 1222.5 1229.8 1236.6 1242.9 1248.9 1254.6 1260.2 1265.6 1270.9 1276.2 1281.4 n 0.5986 1.5051 1.5153 1.5242 1.5322 1.5396 1 5464 1.5528 1.5588 1.5647 1.5702 1.5756 1.5809 1.5861 340 t 429.1 439.1 449.1 459.1 469.1 479.1 489.1 499.1 509.1 519.1 529.1 539.1 549.1 V 0.02 1.37 1.40 1.42 1.44 1.47 1.50 1.53 1.55 1.57 1.60 1.63 1.65 1.67 h 405.3 1205.7 1215.0 1223.2 1230.6 1237.4 1243.8 1249.8 1255.5 1261.1 1266.5 1271.8 1277.1 1282.3 n 0.6020 1.5026 1.5130 1.5220 1.5301 1.5375 1.5443 1.5507 1.5568 1.5625 1.5681 1.5735 1.5789 1.5841 350 t 431.9 441.9 451.9 461.9 471.9 481.9 491.9 501.9 511.9 521.9 531.9 541,9 551.9 V 0.02 1.33 1.36 1.38 1.40 1.43 1.46 1.48 1.51 1.54 1.56 1.58 1.61 1.63 h 408.3 1206.1 1215.6 1223.9 1231.4 1238.2 1244.6 1250.6 1256.3 1261.9 1267.3 1272 7 1278.0 1283.2 n 0.6053 1.5002 1.5108 1.5199 1.5280 1.5355 1.5423 1.5487 1.5547 1.5605 1.5660 1.5715 1.5768 1.5820 360 t 434.6 444.6 454.6 464.6 474.6 484.6 494.6 504.6 514.6 524.6 534.6 544.6 554.6 V 0.02 1.30 1.32 1.34 1.37 1.40 1.42 1.44 1.46 1.48 1.52 1.54 1.56 1.59 h 411.2 1206.4 1216.1 1224.5 1232.2 1239.0 1245.4 1251.4 1257.2 1262.8 1268.2 1273.6 1278.9 1284.1 n 0.6085 1.4979 1.5087 1.5179 1.5261 1.5336 1.5404 1.5468 1.5528 1.5586 1.5641 1.5695 1.5749 1.5801 370 t 437.2 447.2 457.2 467.2 477.2 487.2 497.2 507.2 517.2 527.2 537.2 547.2 557.2 V 0.02 1.26 1.29 1.31 1.33 1.36 1.38 1.41 1.43 1.46 1.48 1.50 1.52 1.55 h 414.0 1206.8 1216.7 1225.2 1232.9 1239.8 1246.2 1252.3 1258.0 1263.6 1269.1 1274.4 1279.7 1284.9 n 0.6116 1.4956 1.5067 1.5160 1.5243 1.5318 1.5386 1.5450 1.5510 1.5568 1.5623 1.5677 1.5730 1.5782 380 t 439.8 449.8 459.8 469.8 479.8 489.8 499.8 509.8 519.8 529.8 539.8 549.8 559.8 V 0.02 1.23 1.25 1.27 1.30 1.32 1.35 1.37 1.40 1.42 1.44 1.47 1.49 1.51 h 416.8 1207.1 1217.2 1225.9 1233.6 1240.6 1247.0 1253.1 1258.9 1264.5 1269.9 1275.3 1280.6 1285.8 n 0.6147 1.4935 1.5048 1.5142 1.5226 1.5301 1.5370 1.5433 1.5493 1.5550 1.5605 1.5659 1.5713 1.5765 390 t 442.3 452.3 462.3 472.3 482.3 492.3 502.3 512.3 522.3 532.3 542.3 552.3 562.3 V 0.02 1.20 1.22 1.24 1.26 1.29 1.32 1.34 1.36 1.38 1.41 1.43 1.45 1.47 h 419.5 1207.4 1217.8 1226.6 1234.4 1241.4 1247.8 1253.9 1259.7 1265.3 1270.7 1276.1 1281.4 1286.6 n 0.6178 1.4915 1.5029 1.5124 1.5209 1.5282 1.5353 1.5417 1.5476 1.5533 1.5588 1.5642 1.5695 1.5747 400 t 444.7 454.7 464.7 474.7 484.7 494.7 504.7 514.7 524.7 534.7 544.7 554.7 564.7 V 0.02 1.17 1.19 1.21 1.23 1.26 1.28 1.31 1.33 1.35 1.37 1.40 1.42 1.44 h 422.2 1207.7 1218.3 1227.2 1235.1 1242.1 1248.6 1254.7 1260.5 1266.1 1271.5 1276.9 1282.2 1287.5 n 0.6208 1.4894 1.5010 1.5107 1.5192 1.5267 1.5336 1.5399 1.5459 1.5516 1.5571 1.5625 1.5678 1.5730 450 t 456.5 466.5 476.5 486.5 496.5 506.5 516.5 526.5 536.5 546.5 556.5 566.5 576.5 V 0.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.19 1.21 1.23 1.25 1.27 1.29 h 435. 1209. 1221. 1231. 1239. 1246. 1252. 1258. 1264. 1270. 1276. 1281. 1286. 1291. n 0.635 1.479 1.492 1.502 1.511 1.519 1.526 1.532 1.538 1.544 1.549 1.554 1.560 1.565 500 t 467.2 477.2 487.2 497.2 507.2 517.2 527.2 537.2 547.2 557.2 567.2 577.2 587.2 V 0.02 0.93 0.95 0.97 0.99 1.01 1.03 1.05 1.07 1.09 1.11 1.13 1.15 1.17 h 448. 1210. 1223. 1233. 1242. 1249. 1256. 1262. 1268. 1274. 1279. 1285. 1290. 1295. n 0.648 1.471 1.486 1.497 1.506 1.513 1.520 1.526 1.532 1.538 1.543 1.549 1.554 1.559 550 t 477.2 487.2 497.2 507.2 517.2 527.2 537.2 547.2 557.2 567.2 577.2 587.2 J97.2 V 0.02 0.85 0.87 0.89 0.91 0.93 0.94 0.96 0.98 1.00 1.01 1.03 1.05 1.07 h 458. 1210. 1225. 1236. 1245. 1253. 1260. 1266. 1272. 1277. 1283. 1288. 1293. 1299. n 0.659 1.462 1.479 1.491 1.501 1.509 1.516 1.522 1.528 1.533 1.539 1.544 1.549 1.554 600 t 486.4 496.4 506.4 516.4 526.4 536.4 546.4 556.4 566.4 576.4 586.4 596.4 606.4 V 0.02 0.78 0.79 0.81 0.83 0.85 0.86 0.88 0.90 0.92 0.93 0.95 0.97 0.98 h 469. 1211. 1228. 1240. 1250. 1257. 1264. 1270. 1276. 1282. 1288. 1293. 1298. 1304. n 0.670 1.454 1.473 1.486 1.496 1.504 1.510 1.516 1.522 1.528 1.533 1.538 1.543 1.548 Degrees of Superheat 130° 140' 150° 160° 170° 180° 190° 200° 250° 300° 350° 400° 500° 600° ''ibT 553.4 563.4 573.4 583.4 593.4 603.4 613.4 623.4 673.4 723.4 773.4 823.4 923 4 1023 4 t 320 1.80 1.82 1.85 1.87 1.90 1.92 1.94 1.96 2.08 2.19 2.30 2 41 2 61 2 81 v 1285.6 1290.7 1295.9 1301.0 1306.1 1311.1 1316.2 1321.3 1346.3 1371.3 1396.1 1420 8 1470 3 1520 h 1.5935 1.5986 1.6036 1.6085 1.6133 1.6181 1.6228 1.6276 1.d503 1.6717 1.6922 1.7120 1.7491 1.7898 n 556.3 566.3 576.3 586.3 596.3 606.3 616.3 626.3 676.3 726.3 776.3 826.3 926 3 1026 3 t 330 1.75 1.77 1.80 1.82 1.84 1.86 1.89 1,91 2.02 2.13 2.24 2.34 2 54 2 74 v 1286.5 1291.7 1296.8 1301.9 1307.0 1312.1 1317.2 1322.2 1347.3 1372.3 1397.1 14219 14715 15212 h 1.5913 1.5964 1.6014 1.6063 1.6111 1.6159 1.6206 1.6253 1.6480 1.6694 1.6899 1.7097 1.7467 1.7814 n 559.1 569.1 579.1 589.1 599.1 609.1 619.1 629.1 679.1 729.1 779.1 829 1 929 1 1029 1 t 340 1.70 1.72 1.75 1.77 1.79 1.81 1.84 1.86 1.97 2.08 2.18 2 28 2^7 2 67 v 1287.4 1292.6 1297.8 1302.9 1308.0 1313.0 1318.1 1323 2 1348.3 1373.3 1398.2 1423 K 72 6 1522 3 h 1.5892 1.5942 1.5992 1.6041 1.6089 1.6137 1.6184 1.6231 1.6458 1.6671 1.6876 1.7074 1.7444 1.7790 n 561.9 571.9 581.9 591.9 601.9 611.9 621.9 631.9 681.9 731.9 781.9 831 9 931 9 1031 9 t 350 1.65 1.68 1.70 1.72 1.74 1.77 1.79 1.81 1.92 2.02 2.12 2 22 2 41 2 60 V 1288.3 1293.5 1298.7 1303.8 1308.9 1313.9 1319.0 1324.1 1349.3 1374.3 1399.2 1424 1473 7 1523 5 h 1.5871 1.5921 1.5971 1.6020 1.6068 1.6116 1.6163 1.6210 1.6436 1.6650 1.6854 1.7052 1.7422 1.7767 n 564.6 574.6 584.6 594.6 604.6 614.6 624.6 634.6 684.6 734.6 784.6 834 6 934 6 1034 6 t 360 1.61 1.63 1.65 1.68 1.70 1.72 1.74 1.76 1.87 1.97 2.07 2.16 2 35 2 53 V 1289.2 1294.4 1299.6 1304.7 1309.8 1314.9 1319.9 1325.0 1350.2 1375.3 1400.2 1425 1474 8 1^24 6 h 1.5852 1.5902 1.5951 1.6000 1.6048 1.6096 1.6143 1.6190 1.6415 1.6629 1.6833 1.7031 1.7400 1.7745 n 567.2 577.2 587.2 597.2 607.2 617.2 627.2 637.2 687.2 737.2 787.2 837 2 937 2 1037 2 t 370 1.57 1.59 1.61 1.64 1.66 1.68 1.70 1.72 1.82 1.92 2.02 2.11 2 30 2 47 v 1290.1 1295.3 1300.4 1305.6 1310.7 1315.8 1320.8 1325.9 1351.1 1376.2 1401.2 1426.1 1475 8 1525 7 h 1.5833 1.5883 1.5933 1.5982 1.6030 1.6077 1.6124 1.6171 1.6396 1.6610 1.6814 1.7011 1.7380 1.7725 n 569.8 579.8 589.8 599.8 609.8 619.8 629.8 639.8 689.8 739.8 789.8 839.8 939.8 1039.8 t 380 1.53 1.55 1.58 1.60 1.62 1.64 1.66 1.68 1.78 1.88 1.97 2.06 2 24 2 41 v 1290.9 1296.1 1301.3 1306.5 1311.6 1316.7 1321.7 1326.8 1352.0 1377.1 1402.1 1427.0 1476.9 1526 8 h 1.5816 1.5866 1.5915 1.5964 1.6012 1.6059 1.6106 1.6153 1.6378 1.6591 1.6795 1.6992 1.7361 1.7705 n 572.3 582.3 592.3 602.3 612.3 622.3 632.3 642.3 692.3 742.3 792.3 842.3 942 3 1042 3 t 390 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.74 1.83 1.92 2.01 2.19 2 35 v 1291.8 1297.0 1302.2 1307.3 1312.4 1317.5 1322.6 1327.7 1353.0 1378.1 1403.1 1428.0 1477.9 1527.9 h 1.5798 1.5848 1.5897 1.5946 1.5994 1.6041 1.6088 1.6135 1.6360 1.6573 1.6777 1.6973 1.7342 1.7685 n 574.7 584.7 594.7 604.7 614.7 624.7 634.7 644.7 694.7 744.7 794.7 844.7 944.7 1044.7 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.70 1.79 1.88 1.97 2.14 2.30 t400 1292.7 1297.9 1303.0 1308.2 1313.3 1318.4 1323.5 1328.6 1353.9 1379.1 1404.1 1429.0 1478.9 1528.9 h 1.5781 1.5821 1.5880 1.5929 1.5977 1.6024 1.6070 1.6117 1.6342 1.6554 1.6758 1.6955 1.7323 1.7666 „ 536.5 596.5 606.5 616.5 626.5 636.5 646.5 656.5 706.5 756.5 806.5 856.5 956.5 1056.5 t 450 1.31 1.33 1.35 1.36 1.38 1.40 1.42 1.44 1.53 1.61 1.69 1.77 1.93 2.07 v 1297. 1302. 1307. 1312. 1317. 1323. 1328. 1333. 1358. 1383. 1409. 1434. 1484. 1534. h 1.570 1.575 1.580 1.585 1.589 1.594 1.599 1.603 1.626 1.647 1.667 1.687 1.723 1.758 n 597.2 607.2 617.2 627.2 637.2 6-V7.2 657.2 667.2 717.2 767.2 817.2 867.2 %7.2 1067.2 t 500 1.19 1.20 1.22 1.24 1.26 1.27 1.29 1.31 1.39 1.47 1.54 1.62 1.76 1.89 V 1300. 1306. 1311. 1316. 1321. 1327. 1332. 1337. 1362. 1388. 1413. 1438. 1489. 1539. h 1.564 1.569 1.574 1.579 1.584 1.589 1.594 1.598 1.620 1.641 1.661 1.680 1.716 1.751 n 607.2 617.2 627.2 637.2 647.2 657.2 667.2 677.2 727.2 777.2 827.2 877.2 977.2 1077.2 t 550 1.08 1.10 1.11 1.13 1.15 1.16 1.18 1.20 1.27 1.34 1.42 1.49 1.62 1.74 V 1304. 1309. 1315. 1320. 1325. 1330. 1336. 1341. 1366. 1392. 1417. 1442. 1493. 1543. h 1.559 1.564 1.569 1.574 1.579 1.583 1.588 1.592 1.615 1.636 1.656 1.675 1.711 1.746 n 616.4 626.4 636.4 (A6A 656.4 666.4 676.4 686.4 736.4 786.4 836.4 886.4 986.4 1086.4 t 600 1.00 1.02 1.03 1.05 1.06 1.08 1.09 1.11 1.18 1.25 1.31 1.38 1.50 1.62 V 1309. 1314. 1319. 1325. 1330. 1335. 1340. 1346. 1371. 1397. 1422. 1448. 1499. 1550. h 1.SS3 1.SS8 1.563 1.568 1.573 1.577 1.582 1.586 1.608 1.629 1.649 1.668 1.704 1.739 n (65) Table 4. Increase in Total Heat and in Entropy for Steam Superheated above 600° „ From 600" Fahr. superheat to . Prflss Press lbs." 700° 800° 900° 1000° 1100° 1200° 1300° 1400° 1500° 1600° 1700° 1800° 1900° 2000° ibs.' 1 Ah 47. 95. 143. 192. 242. 292. 343. 394. 446. 500. 554. 610. 667. 726. Ah 1 An 0.039 0.075 0.110 0.142 0.172 0.202 0.230 0.257 0.283 0.308 0.333 0357 0.381 0.404 An 15 Ah 48. 96. 145. 194. 244. 295. 347. 400. 453. 508. 564. 621. 680. 741. Ah 15 An 0.036 0.070 0.102 0.133 0.162 0.190 0.216 0.242 0.268 0.292 0.316 0.340 0364 0.387 An 25 Ah 48. 96. 145. 195. 246. 297. 349. 402. 455. 510. 566. 624. 684. 745. Ah 26 An 0.036 0.069 0.101 0.131 0.160 0.188 0.214 0.240 0.266 0.290 0.313 0337 0.361 0384 An 50 Ah 48. 97. 146. 196. 247. 299. 351. 404. 459. 514, 571. 630. 690. 752. Ah 50 An 0.035 0.068 0.099 0.128 0.156 0.184 0.210 0.236 0.260 0.285 0308 0332 0.355 0378 An 75 Ah 48. 97. 147. 197. 248. 300. 353. 406. 461. 517. 574. 633. 694. 756. Ah 75 An 0.035 0.067 0.098 0.127 0.154 0.182 0.208 0.234 0.258 0.283 0306 0330 0353 0376 An 100 Ah 48. 98. 148. 198. 249. 301. 354. 408. 463. 519. 577. 636. 697. 759. Ah 100 An 0.034 0.066 0.097 0.126 0.153 0.181 0.207 0.232 0.256 0.281 0304 0328 0351 0374 An 150 Ah 49. 99. 149. 200. 251. 303. 356. 411. 467. 524. 582. 642. 703. 765. Ah 150 An 0.034 0.065 0.095 0.124 0.151 0.178 0.204 0.229 0.253 0.277 0301 0324 0.347 0370 An 200 Ah 49. 99. 150. 201. 253. 305. 358. 413. 470. 527. 586. 646. 708. 771. Ah 200 An 0.033 0.065 0.094 0.123 0.150 0.177 0.203 0.228 0.252 0.276 0.300 0323 0346 0.369 An 250 Ah 50. 100. 151. 202. 254. 306. 360. 415. 472. 530. 589. 649. 712. 776. Ah 250 An 0.033 0.064 0.094 0.122 0.150 0.176 0.202 0.226 0.251 0.275 0.298 0.322 0.345 0.368 An 300 Ah 50. 100. 151. 203. 255. 308. 362. 417. 474. 532. 591. 652. 715. 780. Ah 300 An 0.033 0.064 0.093 0.122 0.149 0.175 0.201 0.225 0.250 0.274 0.297 0.320 0344 0367 An 400 Ah 50. 101. 152. 204. 257. 311. 365. 421. 478. 537. 597. 659. 722. 787. Ah 400 An 0.032 0.063 0.092 0.120 0.147 0.173 0.199 0.223 0.248 0.271 0.295 0318 0.341 0.364 An 500 Ah 51. 102. 154. 206. 259. 313. 368. 424. 482. 541. 602. 664. 728. 794. Ah 500 An 0.032 0.063 0.092 0.120 0.147 0.173 0.198 0.222 0.247 0.270 0.294 0317 0.340 0.363 An 600 Ah 51. 103. 155. 208. 261. 315. 371. 427. 485. 545. 606. 669. 734. 800. Ah 600 An 0.032 0.062 0.091 0.119 0.146 0.172 0.197 0.222 0.246 0.270 0.293 0317 0.340 0363 An This talile gives, either directly or by interpolation, the excess of the total heat or entropy at any given pressnre and super- heat above that at the same pressure and 600° superheat. The actual total heat or entropy is obtained by adding this 'ncrement to the corresponding value in the GOC column of Table 3. (66) Table 5. Boiling Points For Thermometer Calibrations English Units F.ess. n.ofHg. Temp. , Fahr. Press, in. of Hg Temp. . Fahr. Press, in. of Hg Temp, , Fahr. Press, in. of Hg Temp. ;, Fahr. Press, in. of Hg Temp, ;. Fahr. 22.0 .2 .4 .6 .8 190.95 197.37 197.79 198.21 198.63 25.0 .2 .4 .6 .8 203.10 203.48 203.86 204.24 204.62 28.0 .1 .2 .3 .4 208.67 208.85 209.03 209.20 209.37 29.5 .6 .7 .8 .9 211.27 211.44 211.62 211.79 211.96 31.0 .1 .2 .3 .4 213.80 213.96 214.13 214.29 214.46 23.0 .2 .4 .6 .8 199.05 199.47 199.89 200.31 200.72 26.0 .2 .4 .6 .8 205.00 205.38 205.75 206.12 206.49 28.5 .6 .7 .8 .9 209.55 209.73 209.91 210.08 210.25 30.0 .1 .2 .3 .4 212.13 212.30 212.47 212.64 212.81 31.5 .6 .7 .8 .9 214.62 214.79 214.95 215.11 215.27 24.0 .2 .4 .6 .8 201.13 201.54 201.94 202.33 202.72 27.0 .2 .4 .6 .8 206.86 207.23 207.59 207.95 208.31 29.0 .1 .2 .3 .4 210.42 210.59 210.76 210.93 211.10 30.5 .6 .7 .8 .9 212.97 213.13 213.30 213.46 213.63 32.0 .2 .4 .6 .8 215.43 215.75 216.08 216.40 216.72 Metric Units Press. Temp. Press. Temp. Press. Temp. Press, Temp, Press, Temp. Tim, of Hg. Cent. mm. of Hg. Cent. mm. ofHg. Cent, mm, of 1 Hg. Cent. mm. ofHg. Cent, 550 91,19 700 97.71 726 98.68 750 99.63 775 100.55 60 91.67 1 97.75 6 98.72 1 99.66 6 100.59 70 92.14 2 97.79 7 98.76 2 99.70 7 100.62 80 92.60 3 97.83 8 98.80 3 99.74 8 100.66 90 93.06 4 97.87 9 98.84 4 99.78 9 100.69 600 93.51 705 97.91 730 98.87 755 99.81 780 100.73 05 93.73 6 97.95 1 98.91 6 99.85 1 100.77 10 93.96 7 97.99 2 98.95 7 99.89 2 100.80 15 94.18 8 98.03 3 98.99 8 99.92 3 100.84 20 94.40 9 98.07 4 99.03 9 99.96 4 100.87 625 94.61 710 98.10 735 99.06 760 100.00 785 100.91 30 94.83 1 98.14 6 99.10 1 100.04 6 100.95 35 95.04 2 98.18 7 99.14 2 100.07 7 100.98 40 95.25 3 98.22 8 99.18 3 100.11 8 101.02 45 95.47 4 98.26 9 99.21 4 100.15 9 101.05 650 95.68 715 98.30 740 99.25 765 100.18 790 101.09 65 95.89 6 98.34 1 99.29 6 100.22 1 101.12 60 96.10 7 98.38 2 99.33 7 100.26 2 101.16 65 96.30 8 98.41 3 99.36 8 100.29 3 101.20 70 96.51 9 98.45 4 99.40 9 100.33 4 101.23 675 96.71 720 98.49 745 99.44 770 100.37 795 101.27 80 96.91 1 98.53 6 99.48 1 100.40 6 101.30 85 97.12 2 98.57 7 99.51 2 100.44 7 101.34 90 97.32 3 98.61 8 99.55 3 100.48 8 101.37 96 97.52 4 98.65 9 99.59 4 100.51 9 101.41 (67) %^^ fil^^%^ Table 6. Thermal Properties of Water At Saturation Pressure Temp. Fahr, 20° 30 40 Press, lbs. 0.06 0.08 Specific Volume ft.=/lb. cm.^gr. 0.01603 0.01602 1.00101 1.00022 Density Ibs./fU grs./cm.' 0.99899 0.99978 62.37 62.42 144 Apv' B. t. u. 0.000 0.000 Specific Heat 1.0168 1.0098 0.12 0.01602 1.00000 62.43 1.00000 0.000 1.0045 Temp. Fahr. 20° 30 40 50° 60 70 80 90 0.18 0.26 0.36 0.51 0.70 0.01602 0.01603 0.01605 0.01607 0.01610 1.00027 1.00096 1.00201 1.00338 1.00504 62.42 62.37 62.30 62.22 62.11 0.99973 0.99904 0.99799 0.99663 0.99498 0.001 0.001 0.001 0.002 0.002 1.0012 0.9990 0.9977 0.9970 0.9967 60° 60 70 80 90 100° 0.95 0.01613 1.00698 62.00 0.99307 0.003 0.9967 100° 110 1.27 0.01616 1.00915 61.86 0.99093 0.004 0.9970 110 120 1.69 0.01620 1.01157 61.71 0.98857 0.005 0.9974 120 130 2.22 0.01625 1.01420 61.55 0.98600 0.007 0.9979 130 140 2.89 0.01629 1.01705 61.38 0.98324 0.009 0.9986 140 150° 160 170 180 190 200° 210 220 230 240 300° 310 320 330 340 3.71 4.74 5.99 7.51 9.34 11.52 14.13 17.19 20.77 24.97 250° 29.82 260 35.42 270 41.85 280 49.18 290 57.55 67.00 77.67 89.63 103.0 118.0 0.01634 1.02011 0.01639 1.02337 0.01645 1.02682 0.01651 1.03047 0.01657 1.03431 0.01663 0.01670 0.01677 0.01684 0.01692 0.01700 0.01708 0.01716 0.01725 0.01735 0.01744 0.01754 0.01765 0.01776 0.01788 1.03835 1.04256 1.0469 1.0515 1.0562 1.0611 1.0662 1.0715 1.0771 1.0830 1.0890 1.0953 1.1019 1.1088 1.1160 61.20 0.98029 61.00 0.97717 60.80 0.97388 60.58 0.97043 60.36 0.96683 60.12 59.88 59.63 59.37 59.11 58.83 58.55 58.26 57.96 57.65 57.33 57.00 56.66 56.30 55.94 0.96307 0.95917 0.9552 0.9510 0.9468 0.9425 0.9379 0.9332 0.9284 0.9234 0.9183 0.9130 0.9075 0.9019 0.8961 0.011 0.014 0.018 0.023 0.029 0.036 0.044 0.054 0.065 0.078 0.094 0.112 0.133 0.157 0.185 0.217 0.254 0.295 0.340 0.391 0.9994 1.0002 1.0010 1.0019 1.0029 1.0039 1.0050 1.007* 1.009* 1.012* 1.029 1.032 1.035 1.038 1.041 150° 160 170 180 190 200° 210 220 230 240 1.015* 250° 1.018 260 1.021 270 1.023 280 1.026 290 300' 310 320 330 340 * Values below 220^ from mean curve described on page 89. Values above 250' from Bieterici's formula. The four values indicated are selected so as to give a smooth transition. (68) Table 6 : Water Temp. Press. Specific Volume Density 144 Apv' Specific Temp. Fahr. lbs. ft.Vlb. cm.s/gr. Ibs./ft.^ grs./cm.' B.t. u. Heat Fahr. 350° 135. 0.01800 1.1235 55.57 0.8902 0.448 1.045 350° 360 153. 0.01812 1.1313 55.18 0.8840 0.513 1.048 360 370 173. 0.01825 1.1396 54.78 0.8776 0.586 1.052 370 380 196. 0.01839 1.1483 54.36 0.8709 0.666 1.056 380 390 220. 0.01854 1.1573 53.94 0.8642 0.756 1.060 390 400° 247. 0.0187 1.167 53.5 0.857 0.86 1.064 400° 410 276. 0.0189 1.177 53.0 0.850 0.96 1.068 410 420 308. 0.0190 1.187 52.6 0.843 1.09 1.072 420 430 343. 0.0192 1.197 52.2 0.835 1.22 1.077 430 440 381. 0.0194 1.208 51.7 0.828 1.36 1.082 440 450° 422. 0.0195 1.220 51.2 0.820 1.52 1.086 450° 460 466. 0.0197 1.232 50.7 0.812 1.70 1.091 460 470 514. 0.0199 1.244 50.2 0.804 1.89 1.096 470 480 565. 0.0201 1.256 49.7 0.796 2.10 1.101 480 490 620. 0.0203 1.269 49.2 0.787 2.33 1.106 490 500° 679. 0.0206 1.283 48.7 0.779 2.58 1.112 500° 510 743. 0.0208 1.297 48.1 0.771 2.86 1.117 510 520 810. 0.0210 1.312 47.6 0.763 3.15 1.123 520 530 883. 0.0213 1.329 47.0 0.755 3.48 1.128 530 540 960. 0.0216 1.35 46.3 0.74 3.8 1.134 540 550° 1043. 0.0219 1.37 45.6 0.73 4.2 1.140 550° 560 1130. 0.0223 1.39 44.9 0.71 4.7 1.146 560 570 1224. 0.0227 1.42 44.1 0.70 5.2 1.152 570 580 1323. 0.0231 1.44 43.3 0.69 5.7 1.158 580 590 1428. 0.0235 1.46 42.6 0.68 6.2 1.165 590 600° 1540. 0.024 1.49 41.8 0.67 6.8 1.172 600° 610 1658. 0.024* 1.52* 41.0* 0.66* 7.5* 610 620 1783. 0.025 1.55 40.2 0.65 8.2 620 630 1916. 0.025 1.59 39.4 0.64 9.0 630 640 2056. 0.026 1.63 38.5 0.62 9.9 640 650° 2204. 0.027 1.67 37.5 0.60 10.9 650° 660 2361. 0.027 1.72 36.4 0.58 12.0 660 670 2526. 0.028 1.78 35.2 0.56 13.3 670 690 2883. 0.031 1.95 32.1 0.51 16.6 690 706.1 3200. 0.050 3.11 20.1 0.32 29.5 706. J * The specific volumes and densities below 600^ were tnken from the 3rd (1905) edition of Landolt and Bornstein's " Physikalische Tabellen," These and the following values were obtained by the method described on page 103. (69) Temperature Conversion Tables TABLE OF EQUIVALENT TEMPERATURES Cent. Fahr. Cent. Fahr. Cent. Fahr. Cent. Fahr. Cent. Fahr. Cent. Fahi. Cent. Fahr. -25° -13° 50° 122° 125° 257° 200° 392° 275° 527° 350° 662° 425° 797° -20 - 4 55 131 130 266 205 401 280 536 355 671 430 806 -15 + 5 60 140 135 275 210 410 285 545 360 680 435 815 -10 14 65 149 140 284 215 419 290 554 365 689 440 824 - 5 23 70 158 145 293 220 428 295 563 370 698 445 833 0° 32° 75° 167° 150° 302° 225° 437° 300° 572° 375° 707° 450° 842° 5 41 80 176 155 311 230 446 305 581 380 716 455 851 10 50 85 185 160 320 235 455 310 590 385 725 460 860 15 59 90 194 165 329 240 464 315 599 390 734 465 869 20 68 95 203 170 338 245 473 320 608 395 743 470 878 25° 77° 100° 212° 175° 347° 250° 482° 325° 617° 400° 752° 475° 887° 30 86 105 221 180 356 255 491 330 626 405 761 480 896 35 95 110 230 185 365 260 500 335 635 410 770 485 905 40 104 115 239 190 374 265 509 340 644 415 779 490 914 45 113 120 248 195 383 270 518 345 653 420 788 495 923 TABLE OF VALUES FOR INTERPOLATION IN ABOVE 1°C=1.8°K 4°(;= 7.2°F 7°('=12.6°F 1°K = 0.55°(! 4°F = 2.22°C 7°F=3.88°C 2 =3.6 5 = 9.0 8 =14.4 2 =1.11 5 =2.77 8 =4.44 3 =5.4 6 =10.8 9 =16.2 3 =1.66 6 =3.33 9 =5.00 All decimals are exact. All decimals are repeating decimals. Length area and volume 1 cm. -= 03937* inchos, IoK = -1-59 517 1 inch = 2 54001 cm., loK==0-40 483 1 metpr = 3. 28083 ft-, 051 598 1 ft. = 0-30480 m., 1-48 402 1 sq. cm. = 015500 wi. in., 1-19 033 1 Bq. in. = 6-4516 .■f Hr. - 0-491170 Ibs./in.MiU, 32°), 1-89 123 K (standiini) = 32-1740 {*■■ »oc.-', 1-50 750 lib. = 0453592 l«-= 2-88 081 29-921 in. of 11^.. 1-47 598 33.93 ft. of 11,/) (al&r 1.53 061 14-696 lbH/ill.2, 1-16 721 1-0333 kK./cm.2, 0-01421 1.0133 megiibars.t 0.00 573 (70) I 1 mcgaV)ar= 10" dynes per sq. cm. Conversion Table Energy 1 ft. lb. = 32 174 ft. poundals,log = = 1 50 750 ft. poundal = 3 = 13826 kg. meters, I 14 068 kg. meter = 7 = 1 3558 Joules, t 13 220 L Joule t = 0. = 1 2861X10' mean B. t. u.. 3 10 929 mean H. t. u = 777 = 3241 gr. calories, I 51 068 gr. calorie = 3- = 7 145 XIO^ lb. °C. cals.. 4 85 402 L lb. °C. cal. = 1- = 1 3381X10^ liter atmos, 2 12 647 liter atmo = 74. = 4 7253X10' cii. ft. atmos. 4 67 443 cu. ft. atmo = 2. = 5 0505X10 ' H. P. hours. 7 70 333 H. P. hour = 1- = 5 1206X10" chev. vap. hrs.. 7 70 932 ] chev. vap. hr = 1 ■= 3 7662X10' watt hours 4 57 590 ] watt hour = 2 ] Joulet = 10197 kg. meters, log = = 1 00 848 kg. meter = 9- = 73756 ft. lbs., I 86 780 L ft. lb. = 1- - 23 730 ft. pounfials. 1 37 530 ft. poundal = 4- = 9 486 XIO' mean B. t. u., 4 97 709 mean B.t.u. = 1. = 2390 gr. calories, I 37 848 L gr. calorie = 4- = 5 270 XIO" lb. °C. cal.. 4 72 181 I lb. °C. cal. = 1 = 9 8690X10' liter atmos. 3 99 427 liter atmo = 1 = 3 4852X10 ' cu. ft. atmos. 4 54 223 cu. ft. atmo = 2 = 3 7251X10-' H. P. hours, 7 57 113 H. P. hour = 2 = 3 7767X10-'' chev. vap. hrs.. 7 57 711 chev. vap. hr = 2 = 2 7778X10-' watt hours. 4 44 370 watt hour = 3 1 B. t. u. = 2 5200 XIO^ gr. calories, log = = 2 40 139 gr. calorie = 3 = 5556 lb. °C. cal.. I 74 473 L lb. °C. cal. = 1- = 777 5+ ft. lbs.. 2 89 071 ] ft. lb. = 1 = 2 5016 X?0' ft. poundals. 4 39 822 ] ft. poundal = 3- = 1 0750X10= kg. meters. 2 03 139 ] kg. meter = 9. = 1 0542X10' Joules, t 3 02 291 ] Joulet = 9- = 10 404 liter atmos. 1 01 719 ] liter atmo = 9. = 3674 cu. ft. atmos. I 56 514 ] cu. ft. atmo = 2 = 3 927 X10-' H. P. hours. 4 59 405 H. P. hour = 2. = 3 981 X10-' chev. vap. hrs.. 4 60 003 ] chev. vap. hr = 2 = 2928 watt hours. I 46 661 watt hour = 3- 1 gr. cal. = 3 9683 X10-' mean B.t.u., log = = 3 59 861 ] mean B.t.u = 2- = 2 2046X10 ' lb. ''C. cal.. 3 34 333 lb. °C. cal. = 4. = 3 086 ft. lbs.. 48 932 L ft. lb. = 0. = 99 27 ft. poundals. 1 99 682 ft. poundal = 1. = 4266 kg. meters. 1 63 000 kg. meter = 2- = 1834 Joules, t 62 153 Joulet = 0- =- 1286X10-' liter atmos, 2 61 579 liter atmo = 24. = 4580X10-' cu. ft. atmos. 3 16 374 cu. ft. atmo = 6. = 5583X10-' H. P. hours, 6 19 265 ] H. P. hour = 6. ■= 5800X10-' chev. vap. hrs.. 6 19 864 ] chev. vap. hr = 6. = 1821X10-' watt hours. '3 06 522 1 watt hour = 8. 1081X10-' ft. Ib.v 2330 73756 5+ 086 3996X10' 735 1163X10' 98* X10« 9529X10' 6552X10' 80665* Joules 3558 2140X10' 0542X10' 1834 8976X10' 0133X10' 8693X10' 6845X10" 6478X10' 6* X 10' 9683X10' B.t.u. 8* 2861X10' 997 XIO' 302 XIO' 486 X10-' " 612 XIO' 722 547 XIO' 512 XIO' 415 5200X10' gr. cal. 5359X10' 3241 0073X10' 3442 2390 22 859 XIO' 417 X10» 329 X10« 605 XIO' log =5 I 2 3 1 3 6 6 t log = log = 3 5 5 3 i 2 3 3 log =2 2 I 5 I 1 2 5 5 2 49 250 85 932 86 780 89 071 48 932 14 598 87 353 32 557 29 667 29 068 42 410 99 152 13 220 62 470 02 291 62 153 27 818 00 573 45 777 42 887 42 288 55 630 59 861 25 527 10 929 60 178 96 861 97 709 98 281 43 486 40 595 39 996 53 339 40 139 65 667 51 068 00 318 37 000 37 848 38 421 83 626 80 735 80 135 93 478 Power 1 horse power (H. P.) is 550 ft. lbs. per second. 1 watt is 1 Joule per .second or 10' ergs per second. 1 kilowatt (K. VV.) is 1000 watts. 1 cheval-vapeur, or pferdekraft, or "continental horse power," is 75 kg. meters per second. 1 poacelet is 100 kg. meters per second. 1 K. W. = 1.3410 TI. P.. log = 0.12 743 - 1.3597 rlli'V. vap., 0.13 343 ■= 10197 poncelets, 000 849 = 737.56 It. Ibs./sec, 2-86 780 = 101. 97 kg. m./sec, 2. 00 848 • 9486 B. t. u./sec, 1.97 709 = 23904 gr. cals. /sec. 2.37 848 1 H. P. = 7457 K. W.. log = = I87 257 = 1 0139 chev. vap., 000 599 = 7604 poncelets. 1. 88 105 -550 • ft. lbs. /.sec. 2.74 036 = 76 040 kg. in. /sec. 188 104 = 7074 B. t. u./sec. , 1.84 965 -=178 25 gr. cal. /sec , 2.25 104 • Exact valnoi by definition. t 1 Jonle= 10' erg8. (71) Logarithms to the Base 10 1334 5 6789 iO 1.00 0.0000 0004 0009 0013 0017 0022 0026 0030 0035 0039 0043 1.01 0043 0048 0052 0056 0060 0065 0069 0073 0077 0082 0086 1.02 0086 0090 0095 0099 0103 0107 0111 0116 0120 0124 0128 1.03 0128 0133 0137 0141 0145 0149 0154 0158 0162 0166 0170 1.04 0170 0175 0179 0183 0187 0191 0195 0199 0204 0208 0212 1.05 0212 0216 0220 0224 0228 0233 0237 0241 0245 0249 0253 1.06 0253 0257 0261 0265 0269 0273 0278 0282 0286 0290 0294 1.07 0294 0298 0302 0306 0310 0314 0318 0322 0326 0330 0334 1.08 0334 0338 0342 0346 0350 0354 0358 0362 0366 0370 0374 1.09 0374 0378 0382 0386 0390 0394 0398 0402 0406 0410 0414 1.10 0.0414 0418 0422 0426 0430 0434 0438 0441 0445 0449 0453 1.11 0453 0457 0461 0465 0469 0473 0477 0481 0484 0488 0492 1.12 0492 0496 0500 0504 0508 0512 0515 0519 0523 0527 0531 1.13 0531 0535 0538 0542 0546 0550 0554 0558 0561 0565 0569 1.14 0569 0573 0577 0580 0584 0588 0592 0596 0599 0603 0607 1.15 0607 0611 0615 0618 0622 0626 0630 0633 0637 0641 0645 1.16 0645 0648 0652 0656 0660 0663 0667 0671 0674 0678 0682 1.17 0682 0686 0689 0693 0697 0700 0704 0708 0711 0715 0719 1.18 0719 0722 0726 0730 0734 0737 0741 0745 0748 0752 0755 1.19 0755 0759 0763 0766 0770 0774 0777 0781 0785 0788 0792 1.20 0.0792 0795 0799 0803 0806 0810 0813 0817 0821 0824 0828 1.21 0828 0831 0835 0839 0842 0846 0849 0853 0856 0860 0864 1.22 0864 0867 0871 0874 0878 0881 0885 0888 0892 0896 0899 1.23 0899 0903 0906 0910 0913 0917 0920 0924 0927 0931 0934 1.24 0934 0938 0941 0945 0948 0952 0955 0959 0962 0966 0969 1.25 0969 0973 0976 0980 0983 0986 0990 0993 0997 1000 1004 1.26 1004 1007 1011 1014 1017 1021 1024 1028 1031 1035 1038 1.27 1038 1041 1045 1048 1052 1055 1059 1062 1065 1069 1072 1.28 1072 1075 1079 1082 1086 1089 1092 1096 1099 1103 1106 1.29 1106 1109 1113 1116 1119 1123 1126 1129 1133 1136 1139 1.30 0.1139 1143 1146 1149 1153 1156 1159 1163 1166 1169 1173 1.31 1173 1176 1179 1183 1186 1189 1193 1196 1199 1202 1206 1.32 1206 1209 1212 1216 1219 1222 1225 1229 1232 1235 1239 1.33 1239 1242 1245 1248 1252 1255 1258 1261 1265 1268 1271 1.34 1271 1274 1278 1281 1284 1287 1290 1294 1297 1300 1303 1.35 1303 1307 1310 1313 1316 1319 1323 1326 1329 1332 1335 1.36 1335 1339 1342 1345 1348 1351 1355 1358 1361 1364 1367 1.37 1367 1370 1374 1377 1380 1383 1386 1389 1392 1396 1399 1.38 1399 1402 1405 1408 1411 1414 1418 1421 1424 1427 1430 1.39 1430 1433 1436 1440 1443 1446 1449 1452 1455 1458 1461 1.40 0.1461 1464 1467 1471 1474 1477 1480 1483 1486 1489 1492 1.41 1492 1495 1498 1501 1504 1508 1511 1514 1517 1520 1523 1.42 1523 1526 1529 1532 1535 1538 1541 1544 1547 1550 1553 1.43 1553 1556 1559 1562 1565 1569 1572 1575 1578 1581 1584 1.44 1584 1587 1590 1593 1596 1599 1602 1605 1608 1611 1614 1.45 1614 1617 1620 1623 1626 1629 1632 1635 1638 1641 1644 1.46 1644 1647 1649 1652 1655 1658 1661 1664 1667 1670 1673 1.47 1673 1676 1679 1682 1685 1688 1691 1694 1697 1700 1703 1.48 1703 1706 1708 1711 1714 1717 1720 1723 1726 1729 1732 1.49 1732 1735 1738 1741 1744 1746 1749 1752 1755 1758 1761 (72) Logarithms to the Base 10 8 10 1.50 0.1761 1764 1767 1770 1772 1775 1778 1781 1784 1787 1790 1.51 1790 1793 1796 1798 1801 1804 1807 1810 1813 1816 1818 1.52 1818 1821 1824 1827 1830 1833 1836 1838 1841 1844 1847 1.S3 1847 1850 1853 1855 1858 1861 1864 1867 1870 1872 1875 1.54 1875 1878 1881 1884 1886 1889 1892 1895 1898 1901 1903 1.55 1903 1906 1909 1912 1915 1917 1920 1923 1926 1928 1931 1.56 1931 1934 1937 1940 1942 1945 1948 1951 1953 1956 1959 1.57 1959 1952 1965 1967 1970 1973 1976 1978 1981 1984 1987 1.58 1987 1989 1992 1995 1998 2000 2003 2006 2009 2011 2014 1.59 2014 2017 2019 2022 2025 2028 2030 2033 2036 2038 2041 1.60 0.2041 2044 2047 2049 2052 2055 2057 2060 2063 2066 2068 1.61 2068 2071 2074 2076 2079 2082 2084 2087 2090 2092 2095 1.62 2095 2093 2101 2103 2106 2109 2111 2114 2117 2119 2122 1.63 2122 2125 2127 2130 2133 2135 2138 2140 2143 2146 2148 1.64 2148 2151 2154 2156 2159 2162 2164 2167 2170 2172 2175 1.65 2175 2177 2180 2183 2185 2188 2191 2193 2196 2198 2201 1.66 2201 2204 2206 2209 2212 2214 2217 2219 2222 2225 2227 1.67 2227 2230 2232 2235 2238 2240 2243 2245 2248 2251 2253 1.68 2253 2256 2258 2261 2263 2266 2269 2271 2274 2276 2279 1.69 2279 2281 2284 2287 2289 2292 2294 2297 2299 2302 2304 1.70 0.2304 2307 2310 2312 2315 2317 2320 2322 2325 2327 2330 1.71 2330 2333 2335 2338 2340 2343 2345 2348 2350 2353 2355 1.72 2355 2358 2360 2363 2365 2368 2370 2373 2375 2378 2380 1.73 2380 2383 2385 2388 2390 2393 2395 2398 2400 2403 2405 1.74 2405 2408 2410 2413 2415 2418 2420 2423 2425 2428 2430 1.75 2430 2433 2435 2438 2440 2443 2445 2448 2450 2453 2455 1.76 2455 2458 2460 2463 2465 2467 2470 2472 2475 2477 2480 1.77 2480 2482 2485 2487 2490 2492 2494 2497 2499 2502 2504 1.78 2504 2507 2509 2512 2514 2516 2519 2521 2524 2526 2529 1.79 2529 2531 2533 2536 2538 2541 2543 2545 2548 2550 2553 1.80 0.2553 2555 2558 2560 2562 2565 2567 2570 2572 2574 2577 1.81 2577 2579 2582 2584 2586 2589 2591 2594 2596 2598 2601 1.82 2601 2603 2605 2608 2610 2613 2615 2617 2620 2622 2625 1.83 2625 2627 2629 2632 2634 2636 2639 2641 2643 2646 2648 1.84 2648 2651 2653 2655 2658 2660 2662 2665 2667 2669 2672 1.85 2672 2674 2676 2679 2681 2683 2686 2688 2690 2693 2695 1.86 2695 2697 2700 2702 2704 2707 2709 2711 2714 2716 2718 1.87 2718 2721 2723 2725 2728 2730 2732 2735 2737 2739 2742 1.88 2742 2744 2746 2749 2751 2753 2755 2758 2760 2762 2765 1.89 2765 2767 2769 2772 2774 2776 2778 2781 2783 2785 2788 190 2788 2790 2792 2794 2797 2799 2801 2804 2806 2803 2810 1.91 2810 2813 2815 2817 2819 2822 2824 2826 2828 2831 2833 1.92 2833 2835 2838 2840 2842 2844 2847 2849 2851 2853 2856 1.93 2856 2858 2860 2862 2865 2867 2869 2871 2874 2876 2878 1.94 2878 2880 2882 2885 2887 2889 2891 2894 2896 2898 2900 1.95 2900 2903 2905 2907 2909 2911 2914 2916 2918 2920 2923 1.96 2923 2925 2927 2929 2931 2934 2936 2938 2940 2942 2945 1.97 2945 2947 2949 2951 2953 2956 2958 2960 2962 2964 2967 1.98 2967 2969 2971 2973 2975 2978 2980 2982 2984 2986 2989 1.99 2989 2991 2993 2995 2997 2999 3002 3004 3006 3008 3010 (73) Logarithms to the Base 10 These two pajres give the common logarithms of numbers between 1 and 10, correct to four places. Moving tlie decimal point n places to the right (or left) in the number is equivalent to adding «, (or — /i) to the logarithm. Thus, log 0.017453=0 2419 — 2 [=2.2419]. To facilitate interpolation, the tenths of the tabular differences are given at the end of each line, so that the differences themselves need not be considered. In using these aids, first find the nearest tabular entry, and then add (to move to the right) or subtract (to move to the left), as the case may require. Pages 72-77 are reprinted by permission, with unimportant changes, from Huntington's " Four Place Tables." Tenths of the Tabular Difference 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 1.0 0.0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 0414 1.1 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 0792 1.2 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 1139 1.3 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 1461 To avoid interpo- 1.4 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 1761 lation In the first 1.5 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 2041 ten lines, i use the 1.6 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 2304 special tablu un um preceding page. 1.7 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 2553 1.8 2553 2577 2601 2625 2648 2672 2695 2718 2742 2765 2788 1.9 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 3010 3.0 0.3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 3222 2 4 6 8 11 2.1 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 3424 2 4 6 8 10 2.2 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 3617 2 4 6 8 10 2.3 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 3802 2 4 5 7 9 2.4 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 3979 2 4 5 7 9 2.5 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 4150 2 3 5 7 9 2.6 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 4314 2 3 5 7 8 2.7 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 4472 2 3 5 6 8 2.8 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 4624 2 3 5 6 8 2.9 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 4771 1 3 4 6 7 3.0 0.4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 4914 3 4 6 7 3.1 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 5051 3 4 6 7 3.2 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 5185 3 4 5 7 3.3 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 5315 3 4 5 6 3.4 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 5441 3 4 5 6 3.5 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 5563 2 4 5 6 3.6 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 5682 2 4 5 6 3.7 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 5798 2 3 5 6 3.8 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 5911 2 3 5 6 3.9 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 6021 2 3 4 6 4.0 0.6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 6128 2 3 4 5 4.1 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 6232 2 3 4 5 4.2 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 6335 2 3 4 5 4.3 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 6435 2 3 4 5 4.4 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 6532 2 3 4 5 4.5 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 6628 2 3 4 5 4.6 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 6721 2 3 4 5 4.7 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 6812 2 3 4 5 4.8 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 6902 2 3 4 4 4.9 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 6990 2 3 4 4 (74) Logarithms to the Base 10 Tenths of the Tabular DitterencE 1234 5 6789 10 12346 5.0 0G990 6998 7007 7016 7024 7033 7042 7050 7059 7067 7076 12 3 3 4 5 1 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 7160 12 3 3 4 S2 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 7243 12 2 3 4 5 3 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 7324 12 2 3 4 5^4 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 7404 12 2 3 4 5 5 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 7482 12 2 3 4 5*6 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 7559 12 2 3 4 5 7 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 7634 12 2 3 4 5*8 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 7709 112 3 4 5.9 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 7782 112 3 4 6.0 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 7853 112 3 4 6 1 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 7924 112 3 4 6 2 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 7993 112 3 3 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 8062 112 3 3 6.4 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 8129 112 3 3 6 5 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 8195 112 3 3 6 6 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 8261 112 3 3 6 7 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 8325 112 3 3 6 8 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 8388 112 3 3 6.9 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 8451 112 3 3 7.0 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 8513 112 2 3 7 1 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 8573 112 2 3 7 2 8573 8579 8585 8591 8597 8603 8609 86l5 8621 8627 8633 112 2 3 7 3 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 8692 112 2 3 7.4 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 8751 112 2 3 7 5 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 8808 112 2 3 7 6 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 8865 112 2 3 7 7 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 8921 112 2 3 7.8 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 8976 112 2 3 7.9 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 9031 112 2 3 8.0 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 9085 112 2 3 8 1 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 9138 112 2 3 8 2 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 9191 112 2 3 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 9243 112 2 3 8.4 9243 9248 9253 9258 9263 9269 9274 9279 9284 92S9 9294 112 2 3 8 5 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 9345 112 2 3 8*6 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 9395 112 2 3 8 7 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 9445 112 2 88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 9494 112 2 8".9 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 9542 112 2 9.0 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 9590 112 2 9 1 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 9638 112 2 9*2 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 9685 112 2 9*3 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 9731 112 2 9^4 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 9777 112 2 9 5 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 9823 112 2 9*6 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 9868 112 2 9 7 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 9912 112 2 98 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 9956 112 2 g'g 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 112 2 175) Logarithms to the Base e 1 These two pages give the natural (hy- 2 perbolic, or Napierian) logarithms of 3 numbers between 1 and 10, correct to 4 four places. Moving the decimal point 5 n places to the right (or left) in the num- 6 ber is equivalent to adding n times 2.3026 7 (or n times 3.6974) to the logarithm. 8 9 2.3026 4.6052 6.9078 9.2103 11.5129 13.8155 16.1181 18.4207 20.7233 1 0.6974-3 2 0.3948-5 3 0.0922-7 4 0.7897-10 5 0.4871-12 6 0.1845-14 7 0.8819-17 8 0.5793-19 9 0.2767-21 Tenths of th8 Tabular Oifferencfl 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 1.0 0.0000 0100 0198 0296 0392 0488 0583 0677 0770 0862 0.0953 10 19 29 38 48 1.1 0953 1044 1133 1222 1310 1398 1484 1570 1655 1740 1823 9 17 26 35 44 1.2 1823 1906 1989 2070 2151 2231 2311 2390 2469 2546 2624 8 16 24 32 40 1.3 2624 2700 2776 2852 2927 3001 3075 3148 3221 3293 3365 7 15 22 30 37 1.4 3365 3436 3507 3577 3646 3716 3784 3853 3920 3988 4055 7 14 21 28 34 1.5 4035 4121 4187 4253 4318 4383 4447 4511 4574 4637 4700 6 13 19 26 32 1.6 4700 4762 4824 4886 4947 5008 5068 5128 5188 5247 5306 6 12 18 24 30 1.7 5306 5365 5423 5481 5539 5596 5653 5710 5766 5822 5878 6 11 17 23 29 1.8 5878 5933 5988 6043 6098 6152 6206 6259 6313 6366 6419 5 11 16 22 27 1.9 6419 6471 6523 6575 6627 6678 6729 6780 6831 6881 0.6931 5 10 15 21 26 3.0 0.6931 6981 7031 7080 7129 7178 7227 7275 7324 7372 7419 5 10 15 20 24 2.1 7419 7467 7514 7561 7608 7655 7701 7747 7793 7839 7885 5 9 14 19 23 2.2 7885 7930 7975 8020 8065 8109 8154 8198 8242 8286 8329 4 9 13 18 22 2.3 8329 8372 8416 8459 8502 8544 8587 8629 8671 8713 8755 4 9 13 17 21 2.4 8755 8796 8838 8879 8920 8961 9002 9042 9083 9123 9163 4 8 12 16 20 2.5 9163 9203 9243 9282 9322 9361 9400 9439 9478 9517 9555 4 8 12 16 20 2.6 9555 9594 9632 9670 9708 9746 9783 9821 9858 9895 0.9933 4 8 11 15 19 2.7 0.9933 9969. [0006 0043 0080 0116 0152 0188 0225 0260 1.0296 4 7 11 15 18 2.8 1.0296 0332 0367 0403 0438 0473 0508 0543 0578 0613 0647 4 7 1114 18 2.9 0647 0682 0716 0750 0784 0818 0852 0886 0919 0953 1.0986 3 7 10 14 17 3.0 1.0986 1019 1053 1086 1119 1151 1184 1217 1249 1282 1314 3 7 10 13 16 3.1 1314 1346 1378 1410 1442 1474 1506 1537 1569 1600 1632 3 6 10 13 16 3.2 1632 1663 1694 1725 1756 1787 1817 1848 1878 1909 1939 3 6 9 12 15 3.3 1939 1969 2000 2030 2060 2090 2119 2149 2179 2208 2238 3 6 9 12 15 3.4 2238 2267 2296 2326 2355 2384 2413 2442 2470 2499 2528 3 6 9 1214 3.5 2528 2556 2585 2613 2641 2669 2698 2726 2754 2782 2809 3 6 8 1114 3.6 2809 2837 2865 2892 2920 2947 2975 3002 3029 3056 3083 3 5 8 1114 3.7 3083 3110 3137 3164 3191 3218 3244 3271 3297 3324 3350 3 5 8 1113 3.8 3350 3376 3403 3429 3455 3481 3507 3533 3558 3584 3610 3 5 8 1013 3.9 3610 3635 3661 3686 3712 3737 3762 3788 3813 3838 1.3863 3 5 8 1013 4.0 1.3863 3888 3913 3938 3962 3987 4012 4036 4061 4085 4110 2 5 7 10 12 4,1 4110 4134 4159 4183 4207 4231 4255 4279 4303 4327 4351 2 5 7 1012 4.2 4351 4375 4398 4422 4446 4469 4493 4516 4540 4563 4586 2 5 7 912 4.3 4586 4609 4633 4656 4679 4702 4725 4748 4770 4793 4816 2 5 7 911 4.4 4816 4839 4861 4884 4907 4929 4951 4974 4996 5019 5041 2 4 7 911 4.5 5041 5063 5085 5107 5129 5151 5173 5195 5217 5239 5261 2 4 7 911 4.6 5261 5282 5304 5326 5347 5369 5390 5412 5433 5454 5476 2 4 6 911 4.7 5476 5497 5518 5539 5560 5581 5602 5623 5644 5665 5686 2 4 6 811 4.8 5686 5707 5728 5748 5769 5790 5810 5831 5851 5872 5892 2 4 6 810 4.9 5892 5913 5933 5953 5974 5994 6014 C76^ 6034 6054 6074 1.6094 2 4 6 810 Logarithms *o the Base e 5.0 1.6094 6114 6134 6154 6174 S.l 6292 6312 6332 6351 6371 5.2 6487 6506 6525 6544 6563 5.3 6677 6696 6715 6734 6752 5.4 6864 6882 6901 6919 6938 5.5 7047 7066 7084 7102 7120 5.6 7228 7246 7263 7281 7299 5.7 7405 7422 7440 7457 7475 5.8 7579 7596 7613 7630 7647 5.9 7750 7766 7783 7800 7817 6.0 1.7918 7934 7951 7967 7984 6.1 8083 8099 8116 8132 8148 6.2 8245 8262 8278 8294 8310 6.3 8405 8421 8437 8453 8469 6.4 8563 8579 8594 8610 8625 6.5 3718 8733 8749 8764 8779 6.6 8871 8886 8901 8916 8931 6.7 9021 9036 9051 9066 9081 6.8 9169 9184 9199 9213 9228 6.9 9315 9330 9344 9359 9373 7.0 1.9459 9473 9488 9502 9516 7.1 9601 9615 9629 9643 9657 7.2 9741 9755 9769 9782 9796 7.3 1.9879 9892 9906 9920 9933 7.4 2.0015 0028 0042 0055 0069 7.5 0149 0162 0176 0189 0202 7.6 0281 0295 0308 0321 0334 7.7 0412 0425 0438 0451 0464 7.8 0541 0554 0567 0580 0592 7.9 0669 0681 0694 0707 0719 8.0 2.0794 0807 0819 0832 0844 8.1 0919 0931 0943 0956 0968 8.2 1041 1054 1066 1078 1090 8.3 1163 1175 1187 1199 1211 8.4 1282 1294 1306 1318 1330 8.5 1401 1412 1424 1436 1448 8.6 1518 1529 1541 1552 1564 8.7 1633 1645 1656 1668 1679 8.8 1748 1759 1770 1782 1793 8.9 1861 1872 1883 1894 1905 9.0 2.1972 1983 1994 2006 2017 9.1 2083 2094 2105 2116 2127 9.2 2192 2203 2214 2225 2235 9.3 2300 2311 2322 2332 2343 9.4 2407 2418 2428 2439 2450 9.5 2513 2523 2534 2544 2555 9.6 2618 2628 2638 2649 2659 9.7 2721 2732 2742 2752 2762 9.8 2824 2834 2844 2854 2865 9.9 2925 2935 2946 2956 2966 6194 6390 6582 6771 6956 7138 7317 7492 7664 7834 8001 8165 8326 8485 8641 8795 8946 9095 9242 9387 9530 9671 9810 9947 0082 0215 0347 0477 0605 0732 0857 0980 1102 1223 1342 1459 1576 1691 1804 1917 2028 2138 2246 2354 2460 2565 2670 2773 2875 Tenths of the Tatiular Difference 6 7 8 9 10 1 2 3 4 5 6214 6233 6253 6273 6292 2 4 6 8 10 6409 6429 6448 6467 6487 2 4 6 8 10 6601 6620 6639 6658 6677 2 4 6 8 10 6790 6808 6827 6845 6864 2 4 6 7 9 6974 6993 7011 7029 7047 2 4 6 7 9 7156 7174 7192 7210 7228 2 4 5 7 9 7334 7352 7370 7387 7405 2 4 5 7 9 7509 7527 7544 7561 7579 2 3 5 7 9 7681 7699 7716 7733 7750 2 3 5 7 9 7851 7867 7884 7901 1.7918 2 3 5 7 8 8017 8034 8050 8066 8083 2 3 5 7 8 8181 8197 8213 8229 8245 2 3 5 7 8 8342 8358 8374 8390 8405 2 3 5 6 8 8500 8516 8532 8547 8563 2 3 5 6 8 8656 8672 8687 8703 8718 2 3 5 6 8 8810 8825 8840 8856 8871 2 3 5 6 8 8961 8976 8991 9006 9021 2 3 5 6 8 9110 9125 9140 9155 9169 3 4 6 7 9257 9272 9286 9301 9315 3 4 6 7 9402 9416 9430 9445 1.9459 3 4 6 7 9544 9559 9573 9587 9601 3 4 6 7 9685 9699 9713 9727 9741 3 4 6 7 9824 9838 9851 9865 1.9879 3 4 6 7 9961 9974 9988j0001 2.0015 3 4 5 7 0096 0109 0122 0136 0149 3 4 5 7 0229 0242 0255 0268 0281 3 4 5 7 0360 0373 0386 0399 0412 3 4 5 7 0490 0503 0516 0528 0541 3 4 5 6 0618 0631 0643 0656 0669 3 4 5 6 0744 0757 0769 0782 2.0794 3 4 5 6 0869 0882 0894 0906 0919 2 4 5 6 0992 1005 1017 1029 1041 2 4 5 6 1114 1126 1138 1150 1163 2 4 5 6 1235 1247 1258 1270 1282 2 4 5 6 1353 1365 1377 1389 1401 2 4 5 6 1471 1483 1494 1506 1518 2 4 5 6 1587 1599 1610 1622 1633 2 3 5 6 1702 1713 1725 1736 1748 2 3 5 6 1815 1827 1838 1849 1861 2 3 5 6 1928 1939 1950 1961 2.1972 2 3 4 6 2039 2050 2061 2072 2083 2 3 4 6 2148 2159 2170 2181 2192 2 3 4 5 2257 2268 2279 2289 2300 2 3 4 5 2364 2375 2386 2396 2407 2 3 4 5 2471 2481 2492 2502 2513 2 3 4 5 2576 2586 2597 2607 2618 2 3 4 5 2680 2690 2701 2711 2721 2 3 4 5 2783 2793 2803 2814 2824 2 3 4 5 2885 2895 2905 2915 2925 2 3 4 5 (77) PART II THE USE OF THE DIAGRAMS The steam tables give values of the simultaneous physical coordinates (or proper- ties) of steam, such as the pressure, specific volume, temperature, entropy, total heat, and internal energy. When certain of these physical coordinates are known, the remainder can be obtained from the tables, either directly, or by an interpolation. The values tabulated are for dry and saturated steam and for superheated steam; if the steam is wet, its properties must be calculated. The simultaneous properties of steam can also be shown by the use of a steam diagram. The diagram may be drawn on a plane which has any independent pair of the properties as its coordinates; for example, the ordinates and abscissae may be, respectively, pressures and specific volumes, or temperatures and entropies, or total heats and entropies, or total heats and pressures. Each point on such a plane repre- sents steam in a perfectly definite condition : that is, with all its physical coordinates fixed. On such a plane it is possible to plot a steam diagram, or chart, consisting of a number of curves, each of which goes through all points on the plane having a cer- tain constant value of some one physical coordinate. If a well-selected and sufficient number of such curves is drawn for each physical coordinate, then, for any point on the plane, all the properties of steam can be determined by reading the corre- sponding ordinate and abscissa, and by interpolation in the plotted families of curves. For example, on a pressure-volume plane on which families of constant entropy curves, and of constant total heat curves, are drawn, there can be read ofif by inspec- tion the pressure, volume, entropy, and total heat, corresponding to any point on the plane. The families of curves which are drawn may include curves of constant dryness factor (quality) of saturated steam; consequently the diagram may give by inspection the properties of wet steam. This is an advantage over the tables. Of the various planes on which these diagrams may be drawn, some are more con- venient than others. Any one of them will serve if the only purpose in view is to find single values of physical coordinates. For this purpose, the relative advantages of the various planes is a question only of the accuracy and ease with which the desired quantities can be read. A diagram may, however, have uses other than merely showing the simultaneous properties of steam. It may be used for the solution of certain problems, if the proper plane is chosen and the necessary families of curves are drawn on it. It should be clearly borne in mind that the choice of a plane for this purpose has no relation to the choice of a plane on which to represent the cycle of operations of a steam (78J THE USE OF THE DIAGRAMS engine or other steam appliance. For tlie latter purpose two special planes are of particular value, (i) the pressure-volume plane, and (2) the temperature-entropy plane. The pressure-volume plane shows the amount of external work done while the steam is going through any series of changes; the temperature-entropy plane, in a similar way, shows the heat added to or abstracted from the steam. To find the work done or the heat exchange, it is only necessary that the steam cycle should be drawn on those planes; the presence of families of curves of the physical co- ordinates is of no use in finding those quantities. In other words, the plane alone is required for that purpose, not a steam diagram on that plane. A steam diagram on the pressure-volume plane, or on the temperature-entropy plane, does not offer any particular advantages over other diagrams for finding steam quantities. For the solution of many problems of common occurrence such a dia- gram is decidedly less useful and convenient than a diagram in which the total heat of steam is one of the coordinates. By the total heat of steam is meant the sum of its internal energy, E, and of the heat equivalent of the product of its pressure and specific volume, or H = E -|- 144 Apv. (It should be noted that total heat defined in this way differs slightly from the total heat as found in Regnault's investigations of saturated steam and as usually given in steam tables; for a discussion of this, see page loi.) The total heat of steam is a quantity which enters into a large number of problems. It represents the energy (other than kinetic energy) entering any piece of apparatus with every pound of steam that goes to it, and the energy (other than kinetic) leav- ing it with every pound of steam that leaves it. In most steam appliances, under steady conditions of operation, the weight of steam entering per unit of time is equal to the weight of steam leaving. In such an appliance if H^ is the total heat of one pound of the entering steam, and H^ is the total heat of one pound of the leaving steam, then H, — H^ is the energy given up in the apparatus by each pound of steam. In a steam engine H^ — H^ is the sum of the work done and of the external heat-losses; in a boiler its value is negative and represents the heat supply per pound of steam formed; in a non-conducting steam nozzle it is the heat that is converted into ki- netic energy; in a throttling calorimeter its value is zero because there is no external work done, no heat conduction, and no change in kinetic energy. On a steam diagram on which the ordinates are total heats, the quantity H_ — H, is represented by the vertical drop between the points representing the entering and leaving conditions. Vertical distances measure the energy given up in a steam appliance, with a constant scale all over the diagram. In flow of steam problems, this constancy of scale permits the immediate graphical determination of the velocity of flow by merely transferring the vertical distance H, — H, to a velocity scale at the side of the diagram. It is in this respect especially that a total heat-entropy diagram is greatly superior to a temperature-entropy diagram. (79) THE USE OF THE DIAGRAMS Two diagrams are presented, both with total heats as ordinates. By the superposi- tion of three families of curves it would have been possible to give all the data on one diagram; but that would have led to confusion if the curves had been as closely spaced as is requisite for accurate interpolation. The diagrams give information as to the total heat, entropy, and specific volume of wxt and of superheated steam, within a pressure range from .5 to 600 lbs. per sq, in., and for steam in any condition between a quality of about .7 and a superheat of about 600° F. If the properties of water or the latent heat of steam come into the problem, the tables must be used to supplement the readings from the diagrams. The principal advantages of the diagrams over the tables are that they give the properties of wet steam, and that they permit an expeditious solution of many problems without calculation and with a degree of accuracy^ which is sufficient for the ordinary purposes of the engineer. The method of solution of some of the more commonly occurring problems is given below. Properties of Steam The two diagrams give the values of five of the physical coordinates of steam: pressure, quality," entropy, total heat, and specific volume. If any two of these coordinates are known, the remaining three can be found by inspection. In some cases it will be more expeditious (and it will always be more accurate) to use the tables instead of the diagrams, but in other cases, as when wet steam is used, the diagrams will save time and calculation. Pressures, qualities, and total heats can be found on both diagrams; if entropy is involved. Diagram I must be used; if specific volume is involved, Diagram II must be used. The pressure scale on the top of Diagram II is more open than the pressure scale of Diagram I, and consequently somewhat greater accuracy is obtainable by using Diagram II in cases where either diagram can be used. The method of finding a desired quantity is the same in all cases. The point of intersection of the lines (actual or interpolated) representing the two known quantities is located on the appropriate diagram; the position of this point with reference to the lines representing the desired quantity determines the actual value of that quantity. Examples. I. A vessel of 4 cu. ft. capacity contains 0.2 lbs. of water and 0.8 lbs. of steam. What is the pressure? ' The accuracy of a two-color diagram depends on the accuracy of registration of the two print- ings. The original drawings showed in no place an error of as much as -5V inch. The photographic reproduction of these drawings has resulted in minor local distortions, which in the lower corners of Diagram II amount to J,j inch. This is the maximum distortion, and it occurs in the least important part of the diagram. ^ In what follows, the word quality means, the dryness factor if the steam is saturated, the number of degrees of superheat if the steam is superheated. Pressures, throughout, are absolute pressures. (80) THE USE OF THE DIAGRAMS The intersection of the steam quality line, .80, with the specific volume line, 4 cu. ft., on Diagram II, occurs at a steam pressure of 87 lbs. per sq. in. abs. 2. Measurements from an indicator card show that at a certain instant during expansion the volume of the steam is 1.6 cu. ft. and the pressure 40 lbs. per sq. in. abs. If the weight of steam in the cylinder is 0.20 lbs., what is the quality of the steam at that instant? 1.6 The specific volume of the steam is — =8 cu. ft. From Diagram II, .20 steam of that volume and of 40 lbs. pressure has a quality of .764. 3. What is the entropy of i lb. of steam at too lbs. pressure and a tempera- ture of 450° F. ? From the table on Diagram I, the temperature of saturated steam at 100 lbs. pressure is seen to be 328° F.; the steam is consequently superheated 450—328 = 122° F. From Diagram I, steam at 100 lbs. pressure, superheated 122° F., has an entropy 1.678. 4. An indicator (pressure- volume) card is to be redrawn on the temperature- entropy plane. What are the temperature and entropy corresponding to the condition defined in example 2 ? Steam at 40 lbs. pressure has a temperature of 267° F., or 267-1-460 = 727° abs. The entropy is seen, by Diagram I, to be 1.373. 5. What is the heat supply per lb. of steam to a boiler with feed water at 100° F., generating steam at 160 lbs. pressure and of a quality .99? The total heat of steam (Diagram II) at 160 lbs. pressure and quality .99 is 1186 B. t. u.; the feed water contains approximately 100 — 32=68 B. t. u. The heat supply per lb. of steam is consequently 1186 — 68 = 1118 B. t. u. 6. What is the volume of 5 lbs. of steam at i lb. pressure and a quality .80? The specific volume (Diagram II) is 265 cu. ft.; the volume of 5 lbs. is consequently 5x266 = 1330 cu. ft. Internal Energy The internal energy of steam of known pressure, p, and specific volume, v, is given bv the equation ^ _, Example 7. A cylinder contains 1 lb. of steam at a pressure of 80 lbs. per sq. in. and occupying a volume of 7 cu. ft. What is the internal energy of the steam ? The total heat of the steam (Diagram II) is 1274 B. t. u. The internal energy is 00 t^ . ^•' 1274— .1852x80x7 = 1170 B.t.u. (81) 10555 THE USE OF THE DIAGRAMS Adiabatic Expansion During adiabatic expansion, entropy is constant. Vertical lines on Diagram I are lines of constant entropy. A vertical line is consequently the locus of the points representing the condition of steam which is expanding adiabatically. Two of the three quantities, pressure, specific volume, and quality, will generally be known at some one point on the adiabatic curve; this suffices for finding the entropy. When the entropy and one other property of the steam are known, the condition of the steam is fixed. To find the quality of steam which has expanded adiabatically to some known pressure, locate the intersection of the known entropy and pressure lines; its position with reference to the constant quality lines gives the desired quality. Example 8. Steam at 1 20 lbs. pressure, superheated 100° F., expands adiabatically. Find its quality and the ratio of expansion when the pressure reaches 15 lbs. per sq. in. The entropy of the steam (Diagram I) is 1.651; at 15 lbs. pressure, steam of the same entropy has a quality .928. The initial volume (Diagram H) was 4.33 cu. ft.; the final volume is 24.4 cu. ft. The ratio of expansion is .24.4 4-33 I'o find the pressure of steam which has expanded adiabatically to a known quality, locate the intersection of the known entropy and quaUty lines. The desired pressure is given by the position of the intersection with reference to the constant pressure lines. Example 9. Steam at a pressure of 150 lbs. per sq. in., superheated 60° F., expands adiabatically. At what pressure will the steam become dry and saturated? The entropy (Diagram I) is 1.6105 ; the corresponding entropy line crosses the dry and saturated steam line at 90 lbs. pressure. To find the pressure and quality of steam which has expanded adiabatically to a known volume, requires the use of both diagrams. The desired pressure and quality lie on the known constant entropy line of Diagram I, and on the known constant specific volume line of Diagram II. Find by inspection of fhe two diagrams the one pair of simultaneous values of pressure and quality which are common to both lines; or, assume various final pressures, find the corresponding final volumes, and inter- polate. Example 10. Steam of 140 lbs. pressure, superheated 120° F., expands adia- l)atically with a ratio of expansion of 6. What are the pressure and quality at the end of expansion? The initial specific volume (Diagram II) is 3.85 cu. ft.; the final specific volume is 6x3.85=23.10 cu. ft. The entropy (Diagram I) is 1.6503. With (82) THE USE OF THE DIAGRAMS this entropy, steam at 17 lbs. has a quality .934 corresponding to a volume of 21.8 cu. ft.; at 15 lbs. the quality is .927, and volume 24.4. The final pressure is evidently between 15 and 17 lbs. At 16 lbs. the quality is .931 and volume 23.0. By interpolation the desired pressure is 15.9 lbs. per sq. in., and the corresponding quality .930. Work done during Adiabatic Expansion The work done during adiabatic expansion cannot be taken directly from the diagrams. It is equal in amount but opposite in sign to the change of internal energy during expansion. The simplest way of obtaining the work done from the diagrams is to find H^ — H^ for adiabatic expansion, and to subtract from it the second term in the equation given. Example 11. How much work is done on unit mass of steam at 15 lbs. pressure and quality .90 when it is compressed adiabatically to one-fourth its origi- nal volume? By a process similar to that given in example 10, the pressure at the end of compression is found to be 72 lbs. per sq. in., and the corresponding quality .988. The volumes at the beginning and end of the compression are 23.62 and 5.905 cu. ft. respectively. The work done by the steam is H-H-iAAA{p^v^^p^v^) = 1054-1169-. 1852(15x23. 62 -72x5-905) = -115-13 = -128 B. t. u. or the work done on the steam is 128 B. t. u. Work done in the Rankine Ideal Cycle In the Rankine cycle, steam is admitted at a constant pressure, expands adia- batically to the back pressure and is exhausted against a constant back pressure. The engine is supposed to have no clearance. It is an ideal steam-engine cycle, with no internal friction, no heat losses and no free or imperfectly resisted expan- sion. In such a cycle all the energy that is taken from the steam must be con- verted into work. The work done per lb. of steam is consequently H^ — H^. As the only expansion that takes place is adiabatic, the steam that is leaving has the same entropy as the entering steam. To find the work done by unit mass of steam, in a Rankine cycle admitting steam of known qualitv and pressure, and expanding to a known back pressure, locate the (83) THE USE OF THE DIAGRAMS point representing the quality and pressure of the admission steam, and measure the vertical distance from this point to the known back pressure line. This distance represents the work done in B. t. u. Example 12. Steam initially at 150 lbs. pressure, superheated 150° F., goes through a Rankine cycle with a back pressure of 2 lbs. per sq. in. How much work is done by unit mass of steam? The total heat of steam at 150 lbs. pressure, superheated 150° F. (Dia- gram I), is 1275 B. t. u. Steam of the same entropy at 2 lbs. abs. pressure has a total heat of 964 B. t. u. The work of the Rankine cycle is 1275-964=311 B. t.u. The Flow of Steam In a steam engine the resistance to expansion is ofifered by the piston, and the useful work is done on the piston; in a steam nozzle the resistance to expansion is offered by the steam which is ahead, and consequently the work is done on the steam, and results in giving it kinetic energy. If steam is admitted to a properly designed, non-conducting nozzle without inter- nal friction, it will expand adiabatically. Since there is no heat loss, and no external work done, all the energy that is taken from the steam must be converted into kinetic energy. The kinetic energy of the escaping steam is consequently H^ — H^. The velocity corresponding to this kinetic energy of unit mass of steam can be read directly from the scale to the left of Diagram I. It is evident that the kinetic energy of the escaping steam is equal to the work that would have been done by the steam in a Rankine cycle with the same back pressure. To find the velocity with which steam escapes from a properly designed friction- less nozzle, measure with a pair of compasses the change in the total heat of the steam during adiabatic expansion and transfer this measurement to the veloci*^^y scale. Example 13. Steam at 100 lbs. pressure, superheated 60° F., expands in a nozzle to a pressure of 2 lbs. per sq. in. What is its final velocity? The change in the total heat is 1219—954 = 266 B. t. u. This is seen by the scale on Diagram I to correspond to a velocity of 3650 ft. per second. Example 14. A four-stage impulse turbine supplied with steam as in example 13 and with expansion to the same pressure, is designed for equal velocity of steam in each of the stages. What is that velocity? .266 The kinetic energy of the steam in each stage is — =66.5 B. t. u. This corresponds to a velocity of 1825 ft. per second. (84) THE USE OF THE DIAGRAMS Designing a Nozzle The design of a steam nozzle for a desired weight flow is determined by the throat (smallest cross section) of the nozzle. The pressure at the throat will be about .58 of the initial pressure whenever the ratio of the final pressure to the initial pressure is less than that quantity; for ratios greater than .58 the throat pressure is the same as the final pressure. To determine the throat area, find the velocity of the steam at the throat from Diagram I and its specific volume from Diagram II. The specific volume multiplied by the desired weight flow in lbs. per second is the volume flowing per second past the throat. This volume divided by the velocity at the throat is equal to the area of the throat, in square feet. Example 15. 50 lbs. of steam at 160 lbs. pressure, superheated 100° F., flow per minute through a nozzle into the atmosphere (15 lbs. per sq. in.). \\'hat is the smallest cross section of the nozzle? The entropy of the steam is 1.629 ^^^ i^^ total heat 1251 B. t. u. At the throat the pressure is approximately i6ox.58=92.8 lbs. per sq. in.; the total heat is 1202 B. t. u., and the specific volume is 4.98. The kinetic energy at the throat is 1251 — 1202=49 B. t. u., which corresponds to a velocity of 1575 ft. per second. The volume flowing per second past the throat IS — X4. 98=4. 15 cu. ft. The throat area is consequently X 60 1575 144 = .380 sq. ins. Throttling If steam expands through a small orifice (or a porous plug) without the addition or abstraction of heat, and is brought finally to its initial velocity, its total heat will be unchanged. This must be the case because none of the heat is converted into exter- nal work or kinetic energy and no heat is added or abstracted, so that H^ — H^=o. The process is called throttling, and occurs when steam goes through a reducing valve and also in the throttling calorimeter. Horizontal lines on Diagrams I and II are lines of constant total heat and consequently show the changes in the condition of steam which result from throttling. Example 16. Steam at 200 lbs. pressure, quality .99, passes through a reducing valve. At what pressure must the valve be set in order to discharge dry and saturated steam? Inspection of Diagram I or II shows that dry and saturated steam at 119 lbs. has the same total heat as steam at 200 lbs. and quality .99. Example 17. Steam in a throttling calorimeter has a pressure of 17 lbs. per sq. in. and a temperature of 265° F. The initial pressure of the steam was 100 lbs. per sq. in. What was its initial quality? (85) THE USE OF THE DIAGRAMS .Saturated steam at 17 lbs. has a temperature of 219° F.; the superheat in the calorimeter is consequently 265 — 219=46° F. The initial quality of the steam is seen by inspection to be .987, Hirn's Analysis In making Hirn's analysis of the performance of a steam engine it is necessary to find (from the measured pressure, volume, and weight of steam acting) the internal energy of the steam in the cylinder at admission, cut off, release, and compression. These quantities are readily found by the method already outlined. Temperature-Entropy Diagram In redrawing an indicator (pressure-volume) diagram on the temperature-entropy plane, the assumption is made that the whole of the working substance remains in the cylinder throughout the cycle, and that heat is added to and abstracted from it while it is in the cylinder. That is, the boiler, cyHnder, and condenser operations are all assumed to take place in the cylinder. It is most convenient, moreover, to draw the diagram for unit mass of steam, which is readily done after determining the proper scale of volumes for the indicator diagram. The process then becomes extremely simple : the temperature and entropy corresponding to a series of points on the indi- cator diagram are found as in example 4 and are plotted. It should be noted, however, that the diagrams do not give information for qualities below about .7. Consequently some of the points on the temperature-entropy diagram must be calculated. Other Problems Many special problems of less common occurrence than the foregoing can be easily solved by the use of the diagrams. For example, suppose it is proposed to spray into a gas-engine cylinder a certain weight of water at a certain instant, and it is desired to know what will be the resulting pressure and temperature in the cylinder. The partial pressure, temperature and total heat of the steam formed will be repre- sented by the coordinates of some point on a definite constant specific volume line on Diagram II; the exact position of the point on the line can easily be determined from the conditions of the problem by trial and interpolation. (86) PART III DISCUSSION OF SOURCES The computation of a steam table requires as its foundation experimental data of several different kinds. The most important are: 1. An evaluation of the absolute thermodynamic scale; 2. Data on the variation of the specific heat of water with temperature; 3. Data on the mechanical equivalent of heat; 4. Data on the pressure-temperature relation for saturated steam; 5. Data on the specific heat of superheated steam; 6. Data on the specific volume of superheated steam; 7. Data on the total heat of saturated steam. Each of these subjects will be discussed in a separate section. Besides them one needs: A comparison of the fundamental units of length and of weight in the English and metric systems; Data on the density of water at various temperatures; A value for the density of mercury at the temperature of melting ice. In each of these last three cases there are trustworthy values so generally accepted as to need no discussion. § I. Absolute Temperature An evaluation of the absolute thermodynamic scale is necessary because of the use which must be made of absolute temperatures in the computation of entropies. Two distinct problems are involved. The first is the determination of the absolute tem- perature of melting ice, that is, the location of the absolute zero; and the second is the determination, degree by degree, of the difference between the absolute scale and that of the nitrogen-in-glass thermometer which is the usual standard in scien- tific work. For the present purpose the second of these problems need not be con- sidered, for the variation of the nitrogen thermometer from the absolute scale is no- where greater than a twentieth of a degree Fahrenheit between 0° and 400°; above 400° even considerably larger errors in the temperature scale would be within the limit of error of the rest of the experimental data. The determination of the absolute zero has recently been most satisfactorily accom- plished. Three papers may be mentioned, which will themselves give references to many more, namely those of Berthelot,* Buckingham,^ and Rose Innes.^ Berthelot worked by two very different methods, the first based on the fact that as the pressure ' Trav. et Mem. Bur. Int., voi. 13 (iqo^). ' Bui. of the Bur. of Stan., vol. 3 (1907), pp. 237-293 (Reprint No. 57). ' Phil. Mag. (6), vol. 15 (1908), pp. 301-316. (87) DISCUSSION OF SOURCES (§§i, 2) in a gas thermometer approaches zero, the gas becomes more and more perfect, and the second based on the Joule-Thomson effect. Buckingham worked only from the Joule-Thomson effect. Rose-Innes also used the Joule-Thomson observations, but supplemented them as far as possible by much more accurate recent data on coeffi- cients of expansion. The values which these investigators give for the temperature of the ice-point are : — Author Berthelot <( Buckingham Rose-Innes Year 1903 1907 1Q08 Method Extrapolation to p=o Joule-Thomson effect Final Value Gases FOR ICE-POINT H. and N2 491.54° F. ^2, Nz, CO2 and air. 4QI-63 a a u (( u 491.71 Hz and Nz 491.64 J.-T. eflfect and other data Of these values the last is probably the best. Incidentally, it agrees almost exactly with the mean of the other three. Since the temperature of melting ice on the ordi- nary Fahrenheit scale is 32°, the value that must be added to temperatures on the ordinary scale to reduce them to absolute temperatures is 49i°.64-32°.oo=459°.64. 80° 40° 60° 80° my 120* 140" 160^ i8(r 800° , 220° Fig. I. — The specific heat of water between tlie freezing and boiling points according to Barnes [B]- Dieterici (Z>) and Liidin (Z,). The dotted curve is (2 B + D)/^. §2. The Variation of the Specific Heat of Water with Temperature The only sets of experiments available over the whole range from 32° to 212° F. are those of Liidin,' Barnes,^ and Dieterici.^ Since this part of the discussion is con- cerned only with the shape of the curve of variation of the specific heat, c, with tem- * Inaug. Diss., Zurich, 1895: recomputed, Fortsch. d. Phys- vol. 56" (1900), p. 304. ' Phil. Trans., vol. 199A (1002), pp. 149-263. ' Wied. Ann., (4) vol. 16 (1905), pp. 593-620. (88) DISCUSSION OF SOURCES (§2) perature, and not with its height, the actual values of each of these observers have been multiplied by such a constant as to make the average value of c between 32° and 212° exactly i. This is equivalent to expressing each set of values in terms of the well-known Bunsen or mean calorie, if the temperatures are on the Centigrade scale, or in terms of a corresponding mean B.t.u., if the temperatures are on the Fahren- heit scale. The resulting curves are oq shown in Figure i. Liidin's values are generally regarded as the least trustworthy, partly because of the difficulties inherent in calorimetry by the method of mixtures, and partly because his maximum just below the boiling point is not corroborated by either of the other observers, or by Regnault, either for water or for any other liquid. Of the other two pieces of work, Dieterici's is not as convincing as the extraordinarily good work of Barnes as regards either perfection of method or con- sistency of results. Barnes' values have therefore been given most weight in arriving at a representa- tive curve. Liidin's values have been given no direct weight whatever, but the fact that his curve and Dieterici's both differ from that of Barnes in the same direction throughout en- courages one to give to Dieterici's values rather more weight in com- j)arison with Barnes' than might otherwise have seemed desirable.^ The values finally chosen are a mean between those of Barnes and those of Dieterici, giving the former twice as much weight as the latter. The curve repre- senting these mean values is dotted in Figure i, and its ordinates are tabulated in the sixth column of Table 6 at the end of Part I of this book. The values there given for temperatures below the freezing point are from the work of Barnes and Cooke.' The values of the heat of the liquid, in Tables i, 2 and 3, were obtained D17 Fig. 2. — A large scale drawing of a piece out of the lower left-hand corner of the steam dome on the ordinary pv plane, illustrating the meaning of "the heat of the liquid." Abscissse are in cu. ft. ; ordinates are in lbs. per sq. in. ; temperatures are on the Fahrenlieit scale. by a step by step, numerical evaluation of the integral ' See also p. gi. - Phys. Rev., vol. 15 (1902), pp. 65-72 'SI dt. (89) DISCUSSION OF SOURCES (§2) It should be noticed that between 32° and 212° F. there are two theoretically distinct sets of numbers which could properly be given under the heading " the heat of the liquid " in a steam table, according to whether water at 32° and atmospheric pres- sure, or water at 32° and the pressure of its saturated vapor, is used as the zero of total heat. Figure 2 represents, drawn to scale, but much magnified, the lower left- hand corner of the steam dome on the usual pv plane. According to the first scheme, water at the point b is chosen as the zero of total heat, and the values of h which cor- respond to temperatures between 32° and 212° are those along the line be. According to the second scheme, water at the point a is the zero of total heats, and the values of h given are those along the water-line ac. Since the internal energy, e, of water at b is very nearly the same as that of water at a, practically all of the difference between the h at b and the h at a comes in the second term of the usual equation h=e-\- 144 Apv. Graphically, this difference is the equivalent in heat units of the area of the rectangle between the vertical line ab of Figure 2 and the p axis; and in general the differ- ence between the two possible values of h at any temperature is the area of a similar rectangle to the left of some vertical line between ac and be. A comparison of the two possible sets of h values with each other, and with the values of e along the same two lines, is given in the following table. The "mean B. t. u.," which is the heat unit employed, is, by definition, the one hundred and eightieth part of the change in total heat along be. Description Value at 32° 212° Range e along ac e along be h along ac h along be 0.00000 0.00002 0.00026 0.04362 179.99813 179.99813 180.04362 180.04362 179.99813 I 79.99811 180.04336 180.00000 The distinction between the two possible sets of h values is of practical importance only in accurate calorimetry by the method of mixtures, and for that purpose // values along be are preferable. They are given to two decimal places in Table i to facilitate this use of them. As a matter of convenience they have been reduced to b as the zero state, and satisfy the unusual but equally permissible equation of definition h—e + 144 Apv— 0.04362 At high temperatures only values on the second scheme are possible, so that, in careful thinking, different interpretations of the phrase "heat of the liquid" are necessary in different temperature ranges. Above 212° there are available only two investigations, Dieterici's and Regnault's.^ The latter's observations were by the method of mixtures, the mean temperature of the cold water in the calorimeter varying from 55° to 70° F. Since the specific heat of ' M^m. de I'Inst. de France, vol. 21 (1847), pp. 729-748. (90) DISCUSSION OF SOURCES (§2) water changes rapidly with the temperature in that range, it has seemed worth while to recompute Regnault's results on the basis of the curve just obtained for c below 212°. Figure 3 shows on a large scale the difference between the recomputed heat of the liquid from Regnault's data and that on the assumption that r is constant and equal to one. In other words, ordinates in Figure 3 are the increments that must be added to the mere temperature difference (/— 212) to give, for any temperature /, the heat of the liquid above that at 212°. The curve R, representing Regnault's observa- tions, does not approach zero at 212° as it should, which means that Regnault's experi- ments are inherently inconsistent with the c curve adopted above for the range from 32° to 212°. Regnault's experiments require the curve to be lower at room tempera- •200° 300° 400" •"IG. 3. — The heat of the liquid (/i) above the boiling point. Abscissse are temperatures on the Fahrenheit scale. Ordinates are A// in B. t. u. where A/i is what must be added to (/ — 32) to give /i. The recom- puted results of Regnault's forty experiments are represented by small circles, and their means, in six groups, by large circles (curve A*); curved?' is curve R scaled down to pass through o at ^=212^. Curve /* is Peabody's recomputation of Regnault's curve, also scaled down to pass through o at ^ = 212°. Curve D represents Dieterici's formula and is the one used in this book. The black dots are five of Dieterici's twenty experimental means. The middle one of the five shown is the most inconsistent of the whole twenty. Dieterici's formula represents fairly well his other values at temperatures above 400^ F. jures and consequently higher near the boiling point than is the mean cur\ie chosen above — that is, they require a curve still more like Dieterici's and still 1*^55 like Barnes' than that chosen, thus justifying the decision that Dieterici's results should have a weight of at least one in three. Perhaps they should have had even more weight, but the work of Barnes has always been regarded as of such extraordinary e.xcellence that this has not seemed best at the present time. If Regnault's values are multiplied by such a constant factor as will make them ap- proach zero at 212°, his curve lies below either Dieterici's or that marked P in Figure 3, (91) DISCUSSION OF SOURCES (§§2, 3) which represents Peabody's version of Regnault's experiments/ but turns sharply up across Peabody's curve toward Dieterici's near 400° F. The arbitrary nature of this scaling-down process is, however, an argument against the acceptance of the resulting curve. Dieterici's curve is also open to objection in that his observed points do not lie as near it as might be wished, especially in the temperature range of Figure 3. The posi- tion of his curve is fixed largely by the points at higher temperatures. The whole subject is still, therefore, in an unsatisfactory condition above 212°. Fortunately it makes very little difference in the properties of saturated steam which values are used for the heat of the liquid. For instance, the whole of the outstanding discrepancy at 400° would make about a thirtieth of one per cent difference in the entropy of saturated steam at that temperature. The values of Dieterici above 212° have, therefore, been chosen because of the great range covered by his experiments, even though this involves a slight discontinuity in dh/dl^c at 212°. His formula for the mean specific heat from 32° F. to 1° F. may be written Cw=o.9983— 0.000 028 8(/— 32)-|-o.ooo 002 i33(/-32)2 mean B. t. u. Strictly speaking, this formula leads to values, not of h, but of e, but the differ- ence is, in general, smaller than the outstanding uncertainties in either, being 0.046 B.t.u. at 212°, about 0.2 B.t. u. at 300°, and only 0.85 B.t.u. at 400°. Neglecting it, as has been done in these tables at temperatures below 450°, simply means using as standard a compromise (namely curve D on Figure 3) between the true Dieterici curve, which would lie somewhat higher than curve D, and Regnault's results as represented by either curve R or curve P. Above 450°, where the differ- ence between e and h gets big, it has been allowed for. §3. The Mechanical Equivalent of Heat The values of the specific heat of water discussed in the last section are in thermal units; some one of them must now be determined in mechanical units. For this purpose there are available the experiments of Rowland," and of Reynolds and Moor- by,"* by whom mechanical work was transformed directly into heat, and the experi- ments of GrifiEiths,* of Schuster and Gannon,^ and of Barnes,^ by whom electrical energy was changed into heat. These investigations have recently been discussed by Smith,^ who accepts as most trustworthy the mean of the values of Reynolds and Moorby and of Barnes, namely I mean calorie =4. 1834 x 10^ ergs. ' Reduced to mean B.t.u. by subtracting a seventh of one per cent ' Proc. Amer. Acad., vol. 15 (1880), pp. 75-200. * Phil. Trans., vol. 190A (1898), pp. 301-422. * Phil. Trans., vol. 184A (1893), pp. 361-504. ^ Phil. Trans., vol. 186A (1895), pp. 415-467. ' Phil. Trans., vol. 199A (1902), pp. 149-263. ' Monthly Weather Review, October, 1907. (92) DISCUSSION OF SOURCES (§§3, 4) To change this into English units, one needs the conversion factor^ I kg. = 2.204622 lbs. and a value of the gravitation constant g for which ^=980.665 cms. per sec.^ has been adopted as standard by international agreement.^ The result is I mean B. t. u. =777. 54 standard ft. lbs. This value has been used in these tables. §4. Pressures and Temperatures of Saturated Steam The classical experiments on this subject were performed by Regnault ^ in the year 1847, and are even now models of accuracy. They covered the range from —27° to 363° F. They have been recomputed with slightly var}^'ing results by several au- thors, among whom are Broch,^ Peabody,^ and Henning.® Since Regnault's time, many other investigations have been published, eleven of which are carefully dis- cussed by Henning.^ He uses as a standard of reference a formula of Thiesen,^ which expresses p in mms. of mercury (at 0° C.) as a function of / in degrees Centigrade, as follows: — P (/-i- 273) log —-=5. 409 (/-ICO) -0.508x10-^ ((36s -/)4- 265*). 700 The deviations, from this formula, of Regnault's obsen'ations and of those of the eleven later investigators are plotted on a large scale in Henning's paper, and a correction curve for the formula obtained graphically. The conclusions reached in this paper were the basis of the original computations for these tables. The use of Thiesen's formula is greatly facilitated by a table in Henning's paper, giving p in mms. of mercury for every degree from 0° to 200° C. More recently, in August, 1908, Holborn and Henning have published the results of new experiments at the Reichsanstalt covering the range from 125° to 400° F. with extraordinary precision, and have proposed a new correction curve for Thiesen's ' See Fischer, Bui. of the Bur. of Stan., vol i (1904-5), p. 380. * Troisieme Conf. gen. des poids et mes., 1901, pp. 66-68. ' Mem. de I'Inst. de France, vol. 21 (1847), pp. 465-633; for a most excellent account in English of these experiments see Risteen, The Locomotive, published by the Hartford Steam Boiler Inspec- tion and Insurance Co., vol. 26 (July, 1906), pp. 85-94. * Trav. et Mem. Bur. Int., vol. lA (1881), pp. 19-39. * Steam Tables, yth ed. (1907), pp. 2-6. ' Wied. Ann., (4) vol. 22 (1907), pp. 609-630. Loc. cit.; see also Risteen, The Locomotive, vol. 26 (1907), pp. 183-190, 246-254; and voi. ay (1908), pp. 54-62. - Wied. Ann., N. F., vol. 67 (1899), p. 692. (93) DISCUSSION OF SOURCES (§4) formula based on their own work down to 125° F. and on Thiesen's experiments near the freezing point. Above 212° the new curve, Henning's 1907 curve, and the curve which represents Henning's recomputation of Regnault's observations, all agree within a twentieth of a degree Fahrenheit, so that the pressure-temperature relation may be regarded as satisfactorily known. Below 212° the new saturation temperatures run slightly higher than those of the 1907 paper, the greatest change being 0.12° F. at a pressure of i lb. Those parts of the tables which are affected by the change have been j-ecomputed and corrected in page proof. 5' A' .2° .1' 0" -J" Fig. 4. — Correction curve for Thiesen's formula, according to Holborn and Henning (1908). Abscissae are temperatures ; ordinates are A^ = ^'obs. — ^calc. To make Thiesen's formula available in English units, one needs the density of mercury at o° C. According to Thiesen and Scheel ^ I cu. cm. of Hg. at o° C. weighs 13.59545 grs. In the computation of the condenser vacuum column in Table i, giving p in inches of mercury, one needs also I meter=39.37 U. S. standard inches.^ Thiesen's formula, expressed in English units, is / / / / / / / / / y y .'' ^ -^ ^ y K 0" 2( )0'' 300° . 40 (/ + 459-6) log 14.70 = 5.409 (/-2i2)-8.7ixio-'° ((689-/)" -4770, where p is in lbs. per sq. in. and / is in ordinary Fahrenheit degrees. The correc- tion curve of the 1908 paper of Holborn and Henning is plotted in English units in Figure 4, in which ordinates are A/=observed temperature minus the i in Thiesen's 1 Z. S. f. Instrkde., vol. 18 (1898), p. 138. ^ This is the legal definition of the U. S. standard inch. See Fischer, Bui. of the Bur. of Stan. vol. I (1904-5), pp. 365-381, particularly p. 380. (94) i6.8 16.8 48.6 46.6 47-1 109.7 107.1 112. 5 186.7 189.0 207.7 DISCUSSION OF SOURCES (§§4, 5) formula. To use this curve to get the pressure corresponding to a given temperature /°, one first subtracts from that / the A/ given by the curve, and then substitutes the remainder in Thiesen's formula. At the very high temperatures considered at the end of Table i, three researches are available, namely those of Battelli,^ of Cailletet and Colardeau,- and of Knipp.^ The results of these observers are not in good agreement, as the following table shows. The values of Cailletet and Colardeau were used in the preparation of Table i.* Tkmp. Pressure :n Atmosphbrbs According to Fahr. Battelli C and C. Knipp 400° 500° 600° 680° §5. The Specific Heat of Superheated Steam Here, as before, the classical research is that of Regnault,^ published in the year 1862. Contrary to an assumption sometimes seen in the literature, his work does not even seem to prove that the specific heat at constant pressure (C^) of superheated steam is independent of either the pressure or the temperature, for he made only four series of experiments, and these were all at atmospheric pressure and covered nearly the same temperature range. He worked by the method of mixtures, injecting a known weight, first of slightly superheated steam, and then of highly superheated steam, into a calorimeter filled with water at room temperature. His computations are in error because, instead of weighing the cold water in the calorimeter, he measured it volumetrically in a suitable cast-iron tank. His justification of this was that although, by reason of the thermal expansion of the water as compared with that of the tank, there was less water by weight at room temperature than at 0° C, which was his stand- ard temperature, nevertheless the fact (which he thought to be true at low as well as at high temperatures) that the specific heat of water increased with the temperature, made the water in the calorimeter more effective thermally, gram for gram, and just about made up for neglecting its change of density. But we now know that at room temperatures the specific heat of water decreases with rising temperature. His data have, therefore, been recomputed, using his own value for the expansion coefficient of his sheet-iron tanks and modern data for the density and specific heat of water. This slightly reduces each of his four values of C^ to the following figures: — ' Mem. d. R. Ace. d. Sc, Turin (2), vol. 43 (1892), pp. 63-98; see also Ann. de Chem. et de Phys. (6), vol. 26 (1892), pp. 410-425; and especially Risteen, The Locomotive, vol. 26 (October, 1906), pp. 116-126, and vol. 26 (July, 1907), pp. 213-219. ' Joum. de Phys. (2), vol. 10 (1891), pp. 333-340; also Ann. de Chem. et de Phys., vol. 25 (1892), pp. 519-534; also Physikalische Revue, vol. i (1892), pp. 14-21; ajso a short note in C. R. vol. 112 (1891), pp. 563-565; see Risteen, The Locomotive, vol. 26 (July, 1907), pp. 219-221. ' Phys. Rev., vol. 11(1900), pp. 141-144. * Mem. de ITnst. de France, vol. 26 (1862), pp. 167-178. * See page 4. (95) Temp. Range (0°) R's Value of Cp New Value ok Cp 127. 7-231. 1 (0.46881)1 (0.4655) 137.7-225.9 0.481 1 1 0.4769 I 24.3-210.4 0.48080 0.4736 122. 8-216.0 0.47963 0.4780 Mean of last three 0.48051 0.4762 DISCUSSION OF SOURCES (§s) Series i. Series 2. Series 3. Series 4. It will be seen presently that the new figures agree better with modern work than do the older ones. It is only within a few years that reliable determinations of Cp at other pressures than I atmosphere have been made. The best of these are probably those of Knob- lauch and Jakob,- which were carried out with great care by the electrical method. Steam from a boiler was superheated in an apparatus consisting of a long pipe some inches in diameter filled with a dense grid of resistance wire, wound on insulating frames. The energy necessary for superheating was introduced electrically in the first sections of this pipe and the rest of the resistance wire served to mix the steam and bring it into a homogeneous state. It then passed into a calorimeter where a small amount of additional energy was introduced electrically, careful measurements being made of the temperatures of the steam when entering and leaving this calori- meter. The losses due to radiation and conduction were determined by separate experiments. The Cp of the steam in the calorimeter could then be easily computed. The results of these experiments have been used as the basis for the computation of these tables. They have, however, been modified in two respects. In the first place, the curve giving the Cp of steam at atmospheric pressure has been lowered in the high temperature region, so as to agree better with the values obtained by Hol- born and Henning^ at very high temperatures. Their work, like Regnault's, was only at atmospheric pressure, but they reached temperatures as high as 2450° F., and others by different methods have gone even higher. All these results agree in giving smaller values of Cp than an extrapolation of Knoblauch and Jakob's atmospheric curve would indicate. It has therefore been lowered so as to join continuously with the curve of Holborn and Henning.* The high * " . . . les resultats de la premiere serie, qui m'inspirent moins de confiance que les autres. . . ." Regnault, p. 178. 2 Forischarb., Berlin, Hefte 35 and 36 (1906), pp. iog-152. ' Wied, Ann., (4) vol. 18 (1905), pp. 739-756; and (4) vol. 23 (1907), pp. 809-845. * (Note added, June, 191 2). The propriety of this change in the original curve of Knoblauch and Jakob has been justified since the first copies of this book were printed by the results of a new investigation by Knoblauch and Mollier (Z. V. D. I., 191 1, pp. 665-674) covering the same range of pressure as their earlier investigation, but extending to over 1000° F. This work shows that their former Cp curve for i atmosphere rose too sharply near 650° F. and that the true curve lies nearly as it was drawn in figure 5. Their results run a little higher, however, than Holborn and Henning's, and it is therefore possible that the values of C/ used in this book for the highest temperatures are a little too low. No error of commercial importance is involved. m DISCUSSION OF SOURCES (§5) 1. 00 Op §8 3 ^0 8 )0 -I ■- .' - 260 l_^ / ' / 2O0I A 1 / \ 1 - / \ mill IB A llllll 1 \ \ \M\\\ / \ \0 m 1 ^°°/ \ A\ m \ / \ \A \\\\\ 7J k \ \^ n\\^ ^ ^^^ 7^ \ \^\ ^:^ "v^ ^^ ==S — 3 /J ~-^ ^^c ~^^^ ^^ iizrr: 6^ ^ '"" ~° — — { ;_ : ^-^ == =^ .44 ^= l< )0' 2 JO- 3( )0- 4 DO- 500- 6( 30- 7 30- 8 DO- 9 DO Fig. 5. — The specific heat at constant pressure of superlieated steam as used in this book, extrapolated from Knoblauch's data. The saturation line is drawn according to his formula, and the curves at moderate pres- sures and superheats follow iiis curves as nearly as possible. The curves at very low pressures close to saturation are higher than Knoblauch's curves because of thermodynamic evidence, and because of Reg- nault's results at atmospheric pressure. The 15 lb. curve at higli superheats follows Holborn and Hen- ning's curve. The other curves are spaced at very high superheats in accordance with information derived from the Joule-Thomson effect. (97) DISCUSSION OF SOURCES (§§5,6,7) temperature ends of the other curves, for pressure higher than 15 lbs., have then been spaced in accordance with information which can be derived from a study of the Joule-Thomson effect in superheated steam and in other vapors.^ The second modification of Knoblauch's curves is at the low temperature end of the 15 lb. curve and those near it. These run lower than even the recomputed results of Regnault's observations, to which considerable importance may well be attached in the present unsettled state of the subject. There are also certain theoretical con- siderations based on the thermodynamics of the Joule-Thomson effect which seem to set 0.45 as a lower limit to the lower end of the saturation line on the C^ diagram, a value also somewhat higher than Knoblauch's. For these reasons, the curves below 100 lbs. have all been slightly raised on the C^ diagram. The difference at 15 lbs. is only 0.007 B. t. u. The finally accepted values of C^, which were used in the preparation of these tables, are plotted in Figure 5. They have received additional confirmation from the fact that all of seven different kinds of large scale steam diagrams which have been plotted in the course of this work, and particularly the total heat-temperature diagram on which the lines of constant pressure seem to be very sensitive to inconsistencies in the assumed values of C., ran more smoothly with these values of C^ than with cer- tain other suggested values which were first tried. §6. The Specific Volume of Superheated Steam Of the various sets of values of the specific volume of superheated steam at different pressures and temperatures, that of Knoblauch, Linde and Klebe ^ seems to be the best, and has been used in this work.^ Linde's characteristic equation,* expressing T' as a function of p and /, may be written /1 50,300,000 \ ^7;=o.5962 r-/>(i + o.ooi4 P)[ y~i 0-0833 j, where p is in lbs. per sq. in., v is in cu. ft., and r=/-|-459.6 is the absolute temper- ature on the Fahrenheit scale. §7. The Total Heat of Saturated Steam It is in their values for the total heat of saturated steam that these tables differ most essentially from all that have preceded them. It has been the custom for makers of steam tables to use Regnault's classic formula,^ now sixty-one years old, which gives as the total heat of saturated steam B. = 1091.7 -I- 0.305 (/ - 32). ' Davis, Proc. Am. Acad., vol. 44 (1909). ^ Forscharb., Berlin, Heft 21 (1905), pp. 33-55. ' But see p. 103. * Forscharb., Berlin, Heft 21 (1905), pp. 64-69. ' Mem. de I'lnst. de France, vol. 21 (1847), pp. 635-728. m DISCUSSION OF SOURCES (§7) It has for some time been known that this formula was considerably in error, especially at low temperatures, and it is worth noticing that of the eight other vapors studied by Regnault, five gave curves of the second degree, concave downward, for i? as a function of /. Since Regnault 's time, measurements of great value, either of the total heat itself, or of the heat of vaporization, which amounts to the same thing, have been made at various temperatures between 32° and 212° F. by Dieterici, Smith, Griffiths, Henning and Joly, all of which have been admirably discussed by Smith in the paper previ- ously referred to/ Their values as recomputed by him are given in the following table: — Obskrvbr C. Dieterici, Konigl. Tech. Hochschule, Hanover, Germany. Wied. Ann., vol. 37 (1889), pp. 494-508.^ A. W. Smith, University of Michigan, U. S. A. Phys. Rev., vol. 25 (1907), pp. 145-170. E. H. Griffiths, Cambridge, England. Phil. Trans., vol. 186A (1895), pp. 261-341. F. Henning, Reichsanstalt, Berlin, Germany. Wied. Ann., (4) vol. 21 (1906), pp. 849-8^ Temperature Total Heat Degrees Fahr. B. T.V. 32.0 1073-4 57-1 1084.7 70.1 1090.7 82.5 1096.2 103.6 IIO4.6 86.0 1097.8 104-3 IIO4.9 76.9 1094.5* 103.9 IIO4.2* 121. 7 IIII.2* 86.2 1097.6* 120.5 III4.4 148.7 II24.7 171. 2 "34-5 192.7 1144.0 213.1 1151.1 211. 9 II50.0 J. Joly, Trinity College, Dublin, Ireland. In an appendix to Griffiths' paper above (p. 322). * These four values were considered by the experimenters less reliable than their other results. These values have been plotted on a large scale and a graph drawn representing satisfactorily practically all of them, from which the values used in this book at tem- peratures below 212° were then read off. Regnault 's formula, and those tables which are based on it, are right at 170° F., but are too high by 18 B. t. u. at 32° F. Above 212°, Regnault's values may be replaced by a second degree equation re- cently proposed by one of the present authors ^ on the basis of a recomputation of the throttling experiments of Grindley, Griessmann and Peake, with the help of the C. measurements of Knoblauch and Jakob, already referred to. The method used is illustrated by Figure 6, the left-hand half of which represents a throttling curve of the * Monthly Weather Review, October, 1907. ' See also Wied. Ann., (4) vol. 16 (1905), pp. 593—620. ^ Davis, Proc. Am. Soc. of Mech. Engs., vol. 30 (November, 1908), pp. 1419-1432. (99) DISCUSSION OF SOURCES (§7) sort published in the papers mentioned. Supposedly dry and saturated steam at the pressure and temperature corresponding to the point A is first throttled to a lower pressure and temperature corresponding to the point B; then in a later experiment in the same run, it is throttled from exactly the same initial condition A to the con- dition C; then to D and so on. The well-known law of throttling is that the total heat in the condition B, or C, or D, is equal to that in the initial condition A. The point B represents superheated steam at the pressure p^; the point B' repre- sents saturated steam at the same pressure; the amount of superheat at B is the known temperature there minus the temperature at B', which can be taken from a steam table. Also, by definition, the total heat at B equals that of saturated steam at the same pressure (point B') plus the amount of heat required to superheat it at constant pressure from B' to B. This is the integral of C^ from B' to B, or simply the mean C. from saturation multiplied by the known superheat. If C. is known, this integral or increment in the total heat between B' and B is easily evaluated. The value obtained is not only the difference between the total heat of saturated steam at B' and that of superheated steam at B; it is also the difference between the total heat of saturated steam at B' and that of saturated steam at A; that is, be- tween the two corresponding ordinates of a curve giving the total heat of saturated steam as a function of the temperature. To draw a piece of this curve, one chooses arbitrarily some horizontal line such as xy in Figure 6, and lays off below it, at the proper temperatures, the distances bb', cc', dd', etc., which represent on the desired i?-scale the integrals or total heat differences between B' and B, C and C, D' and Z>, etc. The curve ab'c'd' is an isolated piece of the true curve of total heat against temperature. The relative height of its points, that is, its shape, is accurately de- termined; its absolute height above the assumed zero of total heat, namely, water at 32° and atmospheric pressure, is not yet known. In the paper referred to, twenty-four overlapping pieces of this sort were super- posed and gave a well-defined curve. Its height was then so determined as to make it pass through the mean of the values near the boiling point of Henning and of Joly, each reduced to 212°. The resulting curve leads to the formula i7 = ii5o.3-Ho.3745(/-2i2)-o.ooo55o(/-2i2)^ It agrees satisfactorily, in the range from 212° to 400° F., with the values which Linde * computes from the volume measurements of Knoblauch, Linde and Klebe, and also with the values recently proposed by Henning^ on the basis of an extrapolation of a formula representing his results below 212°.^ It is certainly much better than Reg- nault's formula, and is probably within a tenth of one percent of the truth throughout the range considered. If it be even that much in error, it is probably because it runs too low at the high temperatures. It has been used for the range above 212° in these ' Forscharb., Berlin, Heft 21 (1905), pp. 69-72. * Wied. Ann., (4) vol. 21 (1906), p. 870. ' See also Peabody. Proc. Am. Soc. of Mech. Engs., vol. 31 (1909). (100) DISCUSSION OF SOURCES (57) tables. It shows that Regnault's formula, and those tables which are based on it, are too high by 6 B. t. u. at 175°, are right at 280°, and are too low at higher tempera- tures, the error increasing as the square of (/— 175). It has been pointed out ^ that the "total heat of saturated steam" obtained in this way is, rigorously, slightly different from that measured by Regnault. The new H is defined by the equation already mentioned in section 2, H=E-\- 1/^^ Apv— 0.0^ mean B.t.u., where E is the internal energy of the saturated steam and v is its volume. Regnault's H was smaller by the amount of the feed-pump work required to force water at the Fig. 6. — Showing how the total heat curve ab'c'd' is obtained from a throttling curve, ABCD. temperature 0} the room into an enclosure against the pressure of the high tempera- ture steam under investigation. Regnault's H gives accurately the heat required to turn feed water under pressure at his room temperature into steam in the delivery pipe, but is not as useful for other purposes as the H defined above; furthermore, it is not an accurately definable concept, depending as it does not only on the tem- perature of the saturated steam itself, but also on the temperature of the feed water. It is desirable, therefore, to displace it in both scientific and technical thinking by an H defined as above. This is the usual practice abroad. From H it is easy to compute L, the latent heat of evaporation, by subtracting h, the heat of the liquid. . ^^ , In many places in Tables i and 2, the values given for H, h and L will fail to satisfy this equation by one unit in the last place. This is because they were made to satisfy it when carried to an extra decimal place, the discrepancy coming in when the extra place was dropped. * Heck, Jour, of the Aro, Soc. of Mech. Engs., vol. 31 (1909), p. 301. ClOl) DISCUSSION OF SOURCES (§§7, 8) At the end of Table i, an attempt has been made to obtain by an extrapolation at least a qualitative idea of the variation of L and H with temperature in the range between 400° and the critical point. For this purpose L is easier to work with than H, because its behavior at the critical temperature itself is definitely known, at least if the usually accepted ideas about the critical point are assumed to be correct. These demand that at that point L=o and dLldt=m.\rm'S, infinity. As to H, it can be proved on the same hypotheses that