39:
1609:
1328:
1961:
1864:
1798:
1744:
1163:
1108:
1053:
860:
813:
728:
681:
593:
546:
1638:
764:
632:
998:
1966:
This property is useful when the specific volume and either temperature or pressure are known, in which case the missing third property can be computed directly.
1339:
497:
1712:
1227:
836:
789:
704:
657:
569:
522:
461:
1317:
1350:
1877:). Both the reduced temperature and the reduced pressure are often used in thermodynamical formulas like the Peng–Robinson equation of state.
920:
1631:
1218:
454:
332:
1679:
887:
1895:
270:
1402:
1376:
897:
351:
2101:
2077:
2011:
303:
1455:
926:
325:
1672:
1664:
1624:
1555:
87:
1450:
1530:
1303:
280:
915:
118:
108:
1818:
1752:
123:
113:
1445:
1407:
1371:
83:
1200:
948:
394:
207:
197:
1612:
1440:
1237:
940:
879:
415:
404:
70:
1869:
where the actual temperature and critical temperature are expressed in absolute temperature scales (either
1668:
1545:
1465:
1262:
346:
100:
75:
1480:
1057:
370:
216:
65:
1809:
1560:
1485:
1475:
275:
149:
137:
1505:
1500:
1267:
289:
255:
250:
163:
1885:
The reduced specific volume (or "pseudo-reduced specific volume") of a fluid is computed from the
2044:
1975:
1720:
1683:
1682:, a model designed to provide reasonable accuracy near the critical point. They are also used to
1594:
1257:
1205:
1118:
1063:
1008:
421:
308:
260:
245:
235:
44:
38:
1252:
842:
795:
710:
663:
575:
528:
2073:
2007:
1715:
1589:
1550:
1540:
1112:
910:
746:
738:
611:
240:
230:
172:
2036:
1510:
1495:
1435:
1430:
1247:
1242:
968:
892:
360:
225:
1660:
1460:
1308:
962:
603:
426:
187:
154:
1686:, which describe the behaviour of physical quantities near continuous phase transitions.
479:
2061:
1697:
1652:
1515:
1285:
821:
774:
689:
642:
554:
507:
385:
265:
202:
192:
60:
30:
2095:
1886:
1874:
1584:
902:
471:
432:
144:
2048:
1667:. These dimensionless thermodynamic coordinates, taken together with a substance's
1535:
1520:
1470:
953:
17:
2069:
1490:
298:
2082:
1579:
1525:
1808:
The reduced temperature of a fluid is its actual temperature, divided by its
2027:
Peng, DY & Robinson, DB (1976). "A New Two-Constant
Equation of State".
177:
1293:
1210:
1002:
410:
182:
2040:
399:
1870:
1956:{\displaystyle v_{\rm {r}}={\frac {vp_{\rm {c}}}{RT_{\rm {c}}}}\,}
375:
1694:
The reduced pressure is defined as its actual pressure
1889:
at the substance's critical pressure and temperature:
1898:
1821:
1755:
1723:
1700:
1121:
1066:
1011:
971:
845:
824:
798:
777:
749:
713:
692:
666:
645:
614:
578:
557:
531:
510:
482:
2029:Industrial and Engineering Chemistry: Fundamentals
1955:
1858:
1792:
1738:
1706:
1157:
1102:
1047:
992:
854:
830:
807:
783:
758:
722:
698:
675:
651:
626:
587:
563:
540:
516:
491:
1859:{\displaystyle T_{\rm {r}}={T \over T_{\rm {c}}}}
1793:{\displaystyle p_{\rm {r}}={p \over p_{\rm {c}}}}
1671:, provide the basis for the simplest form of the
1678:Reduced properties are also used to define the
1663:scaled by the fluid's state properties at its
1632:
8:
2002:Cengel, Yunus A.; Boles, Michael A. (2002).
1639:
1625:
1188:
340:
159:
37:
26:
1952:
1942:
1941:
1925:
1924:
1914:
1904:
1903:
1897:
1847:
1846:
1837:
1827:
1826:
1820:
1781:
1780:
1771:
1761:
1760:
1754:
1729:
1728:
1722:
1699:
1120:
1065:
1010:
970:
844:
823:
797:
776:
748:
712:
691:
665:
644:
613:
577:
556:
530:
509:
481:
2006:. Boston: McGraw-Hill. pp. 91–93.
2004:Thermodynamics: an engineering approach
1997:
1995:
1993:
1991:
1987:
1385:
1362:
1316:
1276:
1226:
1191:
384:
359:
288:
215:
162:
29:
7:
2070:World Scientific (Singapore, 2001)
1943:
1926:
1905:
1848:
1828:
1782:
1762:
1730:
846:
799:
714:
667:
579:
532:
352:Intensive and extensive properties
25:
2066:Critical Properties of φ-Theories
1608:
1607:
927:Table of thermodynamic equations
1680:Peng–Robinson equation of state
1673:theorem of corresponding states
1403:Maxwell's thermodynamic surface
2064:and Verena Schulte-Frohlinde,
1137:
1125:
1082:
1070:
1027:
1015:
987:
975:
1:
1304:Mechanical equivalent of heat
916:Onsager reciprocal relations
1739:{\displaystyle p_{\rm {c}}}
1408:Entropy as energy dispersal
1219:"Perpetual motion" machines
1158:{\displaystyle G(T,p)=H-TS}
1103:{\displaystyle A(T,V)=U-TS}
1048:{\displaystyle H(S,p)=U+pV}
2118:
855:{\displaystyle \partial T}
808:{\displaystyle \partial V}
723:{\displaystyle \partial p}
676:{\displaystyle \partial V}
588:{\displaystyle \partial T}
541:{\displaystyle \partial S}
1329:An Inquiry Concerning the
2102:Thermodynamic properties
1659:of a fluid are a set of
1342:Heterogeneous Substances
759:{\displaystyle \alpha =}
627:{\displaystyle \beta =-}
1881:Reduced specific volume
1957:
1860:
1794:
1740:
1708:
1669:compressibility factor
1159:
1104:
1049:
994:
993:{\displaystyle U(S,V)}
856:
832:
809:
785:
760:
724:
700:
677:
653:
628:
589:
565:
542:
518:
493:
472:Specific heat capacity
76:Quantum thermodynamics
1958:
1861:
1795:
1741:
1709:
1340:On the Equilibrium of
1160:
1105:
1058:Helmholtz free energy
1050:
995:
857:
833:
810:
786:
761:
725:
701:
678:
654:
629:
590:
566:
543:
519:
494:
1896:
1819:
1810:critical temperature
1753:
1721:
1698:
1353:Motive Power of Fire
1119:
1064:
1009:
969:
921:Bridgman's equations
898:Fundamental relation
843:
822:
796:
775:
747:
711:
690:
664:
643:
612:
576:
555:
529:
508:
480:
2041:10.1021/i160057a011
1804:Reduced temperature
1331:Source ... Friction
1263:Loschmidt's paradox
455:Material properties
333:Conjugate variables
18:Reduced temperature
1976:Departure function
1953:
1856:
1790:
1736:
1704:
1684:critical exponents
1657:reduced properties
1595:Order and disorder
1351:Reflections on the
1258:Heat death paradox
1155:
1100:
1045:
990:
852:
828:
805:
781:
756:
720:
696:
673:
649:
624:
585:
561:
538:
514:
492:{\displaystyle c=}
489:
462:Property databases
438:Reduced properties
422:Chemical potential
386:Functions of state
309:Thermal efficiency
45:Carnot heat engine
1950:
1854:
1788:
1716:critical pressure
1707:{\displaystyle p}
1649:
1648:
1590:Self-organization
1415:
1414:
1113:Gibbs free energy
911:Maxwell relations
869:
868:
865:
864:
831:{\displaystyle V}
784:{\displaystyle 1}
739:Thermal expansion
733:
732:
699:{\displaystyle V}
652:{\displaystyle 1}
598:
597:
564:{\displaystyle N}
517:{\displaystyle T}
445:
444:
361:Process functions
347:Property diagrams
326:System properties
316:
315:
281:Endoreversibility
173:Equation of state
16:(Redirected from
2109:
2086:
2081:(Read online at
2059:
2053:
2052:
2024:
2018:
2017:
1999:
1962:
1960:
1959:
1954:
1951:
1949:
1948:
1947:
1946:
1932:
1931:
1930:
1929:
1915:
1910:
1909:
1908:
1865:
1863:
1862:
1857:
1855:
1853:
1852:
1851:
1838:
1833:
1832:
1831:
1799:
1797:
1796:
1791:
1789:
1787:
1786:
1785:
1772:
1767:
1766:
1765:
1745:
1743:
1742:
1737:
1735:
1734:
1733:
1713:
1711:
1710:
1705:
1690:Reduced pressure
1641:
1634:
1627:
1611:
1610:
1318:Key publications
1299:
1298:("living force")
1248:Brownian ratchet
1243:Entropy and life
1238:Entropy and time
1189:
1164:
1162:
1161:
1156:
1109:
1107:
1106:
1101:
1054:
1052:
1051:
1046:
999:
997:
996:
991:
893:Clausius theorem
888:Carnot's theorem
861:
859:
858:
853:
837:
835:
834:
829:
814:
812:
811:
806:
790:
788:
787:
782:
769:
768:
765:
763:
762:
757:
729:
727:
726:
721:
705:
703:
702:
697:
682:
680:
679:
674:
658:
656:
655:
650:
637:
636:
633:
631:
630:
625:
594:
592:
591:
586:
570:
568:
567:
562:
547:
545:
544:
539:
523:
521:
520:
515:
502:
501:
498:
496:
495:
490:
468:
467:
341:
160:
41:
27:
21:
2117:
2116:
2112:
2111:
2110:
2108:
2107:
2106:
2092:
2091:
2090:
2089:
2060:
2056:
2026:
2025:
2021:
2014:
2001:
2000:
1989:
1984:
1972:
1937:
1933:
1920:
1916:
1899:
1894:
1893:
1883:
1842:
1822:
1817:
1816:
1806:
1776:
1756:
1751:
1750:
1724:
1719:
1718:
1714:divided by its
1696:
1695:
1692:
1661:state variables
1645:
1600:
1599:
1575:
1567:
1566:
1565:
1425:
1417:
1416:
1395:
1381:
1356:
1352:
1345:
1341:
1334:
1330:
1297:
1290:
1272:
1253:Maxwell's demon
1215:
1186:
1185:
1169:
1168:
1167:
1117:
1116:
1115:
1062:
1061:
1060:
1007:
1006:
1005:
967:
966:
965:
963:Internal energy
958:
943:
933:
932:
907:
882:
872:
871:
870:
841:
840:
820:
819:
794:
793:
773:
772:
745:
744:
709:
708:
688:
687:
662:
661:
641:
640:
610:
609:
604:Compressibility
574:
573:
553:
552:
527:
526:
506:
505:
478:
477:
457:
447:
446:
427:Particle number
380:
339:
328:
318:
317:
276:Irreversibility
188:State of matter
155:Isolated system
140:
130:
129:
128:
103:
93:
92:
88:Non-equilibrium
80:
55:
47:
23:
22:
15:
12:
11:
5:
2115:
2113:
2105:
2104:
2094:
2093:
2088:
2087:
2062:Hagen Kleinert
2054:
2019:
2012:
1986:
1985:
1983:
1980:
1979:
1978:
1971:
1968:
1964:
1963:
1945:
1940:
1936:
1928:
1923:
1919:
1913:
1907:
1902:
1882:
1879:
1867:
1866:
1850:
1845:
1841:
1836:
1830:
1825:
1805:
1802:
1801:
1800:
1784:
1779:
1775:
1770:
1764:
1759:
1732:
1727:
1703:
1691:
1688:
1665:critical point
1653:thermodynamics
1647:
1646:
1644:
1643:
1636:
1629:
1621:
1618:
1617:
1616:
1615:
1602:
1601:
1598:
1597:
1592:
1587:
1582:
1576:
1573:
1572:
1569:
1568:
1564:
1563:
1558:
1553:
1548:
1543:
1538:
1533:
1528:
1523:
1518:
1513:
1508:
1503:
1498:
1493:
1488:
1483:
1478:
1473:
1468:
1463:
1458:
1453:
1448:
1443:
1438:
1433:
1427:
1426:
1423:
1422:
1419:
1418:
1413:
1412:
1411:
1410:
1405:
1397:
1396:
1394:
1393:
1390:
1386:
1383:
1382:
1380:
1379:
1374:
1372:Thermodynamics
1368:
1365:
1364:
1360:
1359:
1358:
1357:
1348:
1346:
1337:
1335:
1326:
1321:
1320:
1314:
1313:
1312:
1311:
1306:
1301:
1289:
1288:
1286:Caloric theory
1282:
1279:
1278:
1274:
1273:
1271:
1270:
1265:
1260:
1255:
1250:
1245:
1240:
1234:
1231:
1230:
1224:
1223:
1222:
1221:
1214:
1213:
1208:
1203:
1197:
1194:
1193:
1187:
1184:
1183:
1180:
1176:
1175:
1174:
1171:
1170:
1166:
1165:
1154:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1130:
1127:
1124:
1110:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1078:
1075:
1072:
1069:
1055:
1044:
1041:
1038:
1035:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1000:
989:
986:
983:
980:
977:
974:
959:
957:
956:
951:
945:
944:
939:
938:
935:
934:
931:
930:
923:
918:
913:
906:
905:
900:
895:
890:
884:
883:
878:
877:
874:
873:
867:
866:
863:
862:
851:
848:
838:
827:
816:
815:
804:
801:
791:
780:
766:
755:
752:
742:
735:
734:
731:
730:
719:
716:
706:
695:
684:
683:
672:
669:
659:
648:
634:
623:
620:
617:
607:
600:
599:
596:
595:
584:
581:
571:
560:
549:
548:
537:
534:
524:
513:
499:
488:
485:
475:
466:
465:
464:
458:
453:
452:
449:
448:
443:
442:
441:
440:
435:
430:
419:
408:
389:
388:
382:
381:
379:
378:
373:
367:
364:
363:
357:
356:
355:
354:
349:
330:
329:
324:
323:
320:
319:
314:
313:
312:
311:
306:
301:
293:
292:
286:
285:
284:
283:
278:
273:
268:
266:Free expansion
263:
258:
253:
248:
243:
238:
233:
228:
220:
219:
213:
212:
211:
210:
205:
203:Control volume
200:
195:
193:Phase (matter)
190:
185:
180:
175:
167:
166:
158:
157:
152:
147:
141:
136:
135:
132:
131:
127:
126:
121:
116:
111:
105:
104:
99:
98:
95:
94:
91:
90:
79:
78:
73:
68:
63:
57:
56:
53:
52:
49:
48:
43:The classical
42:
34:
33:
31:Thermodynamics
24:
14:
13:
10:
9:
6:
4:
3:
2:
2114:
2103:
2100:
2099:
2097:
2085:
2083:
2079:
2078:981-02-4658-7
2075:
2071:
2067:
2063:
2058:
2055:
2050:
2046:
2042:
2038:
2034:
2030:
2023:
2020:
2015:
2013:0-07-121688-X
2009:
2005:
1998:
1996:
1994:
1992:
1988:
1981:
1977:
1974:
1973:
1969:
1967:
1938:
1934:
1921:
1917:
1911:
1900:
1892:
1891:
1890:
1888:
1887:ideal gas law
1880:
1878:
1876:
1872:
1843:
1839:
1834:
1823:
1815:
1814:
1813:
1811:
1803:
1777:
1773:
1768:
1757:
1749:
1748:
1747:
1725:
1717:
1701:
1689:
1687:
1685:
1681:
1676:
1674:
1670:
1666:
1662:
1658:
1654:
1642:
1637:
1635:
1630:
1628:
1623:
1622:
1620:
1619:
1614:
1606:
1605:
1604:
1603:
1596:
1593:
1591:
1588:
1586:
1585:Self-assembly
1583:
1581:
1578:
1577:
1571:
1570:
1562:
1559:
1557:
1556:van der Waals
1554:
1552:
1549:
1547:
1544:
1542:
1539:
1537:
1534:
1532:
1529:
1527:
1524:
1522:
1519:
1517:
1514:
1512:
1509:
1507:
1504:
1502:
1499:
1497:
1494:
1492:
1489:
1487:
1484:
1482:
1481:von Helmholtz
1479:
1477:
1474:
1472:
1469:
1467:
1464:
1462:
1459:
1457:
1454:
1452:
1449:
1447:
1444:
1442:
1439:
1437:
1434:
1432:
1429:
1428:
1421:
1420:
1409:
1406:
1404:
1401:
1400:
1399:
1398:
1391:
1388:
1387:
1384:
1378:
1375:
1373:
1370:
1369:
1367:
1366:
1361:
1355:
1354:
1347:
1344:
1343:
1336:
1333:
1332:
1325:
1324:
1323:
1322:
1319:
1315:
1310:
1307:
1305:
1302:
1300:
1296:
1292:
1291:
1287:
1284:
1283:
1281:
1280:
1275:
1269:
1266:
1264:
1261:
1259:
1256:
1254:
1251:
1249:
1246:
1244:
1241:
1239:
1236:
1235:
1233:
1232:
1229:
1225:
1220:
1217:
1216:
1212:
1209:
1207:
1204:
1202:
1199:
1198:
1196:
1195:
1190:
1181:
1178:
1177:
1173:
1172:
1152:
1149:
1146:
1143:
1140:
1134:
1131:
1128:
1122:
1114:
1111:
1097:
1094:
1091:
1088:
1085:
1079:
1076:
1073:
1067:
1059:
1056:
1042:
1039:
1036:
1033:
1030:
1024:
1021:
1018:
1012:
1004:
1001:
984:
981:
978:
972:
964:
961:
960:
955:
952:
950:
947:
946:
942:
937:
936:
929:
928:
924:
922:
919:
917:
914:
912:
909:
908:
904:
903:Ideal gas law
901:
899:
896:
894:
891:
889:
886:
885:
881:
876:
875:
849:
839:
825:
818:
817:
802:
792:
778:
771:
770:
767:
753:
750:
743:
740:
737:
736:
717:
707:
693:
686:
685:
670:
660:
646:
639:
638:
635:
621:
618:
615:
608:
605:
602:
601:
582:
572:
558:
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550:
535:
525:
511:
504:
503:
500:
486:
483:
476:
473:
470:
469:
463:
460:
459:
456:
451:
450:
439:
436:
434:
433:Vapor quality
431:
429:
428:
423:
420:
418:
417:
412:
409:
406:
402:
401:
396:
393:
392:
391:
390:
387:
383:
377:
374:
372:
369:
368:
366:
365:
362:
358:
353:
350:
348:
345:
344:
343:
342:
338:
334:
327:
322:
321:
310:
307:
305:
302:
300:
297:
296:
295:
294:
291:
287:
282:
279:
277:
274:
272:
271:Reversibility
269:
267:
264:
262:
259:
257:
254:
252:
249:
247:
244:
242:
239:
237:
234:
232:
229:
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218:
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209:
206:
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196:
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186:
184:
181:
179:
176:
174:
171:
170:
169:
168:
165:
161:
156:
153:
151:
148:
146:
145:Closed system
143:
142:
139:
134:
133:
125:
122:
120:
117:
115:
112:
110:
107:
106:
102:
97:
96:
89:
85:
82:
81:
77:
74:
72:
69:
67:
64:
62:
59:
58:
51:
50:
46:
40:
36:
35:
32:
28:
19:
2080:
2065:
2057:
2032:
2028:
2022:
2003:
1965:
1884:
1868:
1807:
1693:
1677:
1656:
1650:
1446:Carathéodory
1377:Heat engines
1349:
1338:
1327:
1309:Motive power
1294:
954:Free entropy
925:
437:
425:
424: /
414:
413: /
405:introduction
398:
397: /
336:
299:Heat engines
86: /
1268:Synergetics
949:Free energy
395:Temperature
256:Quasistatic
251:Isenthalpic
208:Instruments
198:Equilibrium
150:Open system
84:Equilibrium
66:Statistical
1982:References
1580:Nucleation
1424:Scientists
1228:Philosophy
941:Potentials
304:Heat pumps
261:Polytropic
246:Isentropic
236:Isothermal
2035:: 59–64.
1561:Waterston
1511:von Mayer
1466:de Donder
1456:Clapeyron
1436:Boltzmann
1431:Bernoulli
1392:Education
1363:Timelines
1147:−
1092:−
880:Equations
847:∂
800:∂
751:α
715:∂
668:∂
622:−
616:β
580:∂
533:∂
241:Adiabatic
231:Isochoric
217:Processes
178:Ideal gas
61:Classical
2096:Category
2068:, pp.8,
2049:98225845
1970:See also
1613:Category
1551:Thompson
1461:Clausius
1441:Bridgman
1295:Vis viva
1277:Theories
1211:Gas laws
1003:Enthalpy
411:Pressure
226:Isobaric
183:Real gas
71:Chemical
54:Branches
1875:Rankine
1536:Smeaton
1531:Rankine
1521:Onsager
1506:Maxwell
1501:Massieu
1206:Entropy
1201:General
1192:History
1182:Culture
1179:History
403: (
400:Entropy
337:italics
138:Systems
2076:
2047:
2010:
1871:Kelvin
1655:, the
1526:Planck
1516:Nernst
1491:Kelvin
1451:Carnot
741:
606:
474:
416:Volume
331:Note:
290:Cycles
119:Second
109:Zeroth
2045:S2CID
1574:Other
1541:Stahl
1496:Lewis
1486:Joule
1476:Gibbs
1471:Duhem
164:State
124:Third
114:First
2074:ISBN
2008:ISBN
1546:Tait
376:Heat
371:Work
101:Laws
2072:;
2037:doi
1873:or
1651:In
1389:Art
335:in
2098::
2043:.
2033:15
2031:.
1990:^
1812::
1746::
1675:.
2084:)
2051:.
2039::
2016:.
1944:c
1939:T
1935:R
1927:c
1922:p
1918:v
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1906:r
1901:v
1849:c
1844:T
1840:T
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1829:r
1824:T
1783:c
1778:p
1774:p
1769:=
1763:r
1758:p
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1726:p
1702:p
1640:e
1633:t
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1153:S
1150:T
1144:H
1141:=
1138:)
1135:p
1132:,
1129:T
1126:(
1123:G
1098:S
1095:T
1089:U
1086:=
1083:)
1080:V
1077:,
1074:T
1071:(
1068:A
1043:V
1040:p
1037:+
1034:U
1031:=
1028:)
1025:p
1022:,
1019:S
1016:(
1013:H
988:)
985:V
982:,
979:S
976:(
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826:V
803:V
779:1
754:=
718:p
694:V
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619:=
583:T
559:N
536:S
512:T
487:=
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407:)
20:)
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