657:
2414:(1805–1869) found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. In other words, the ratio of the rates of effusion of two gases at the same temperature and pressure is given by the inverse ratio of the square roots of the masses of the gas particles.
999:
1243:
2395:
At constant pressure and temperature, the root-mean-square speed and therefore the effusion rate are inversely proportional to the square root of the molecular weight. Gases with a lower molecular weight effuse more rapidly than gases with a higher molecular weight, so that the
851:
2493:
2199:
1113:
683:
Under these conditions, essentially all molecules which arrive at the hole continue and pass through the hole, since collisions between molecules in the region of the hole are negligible. Conversely, when the diameter is larger than the
2300:
1755:
1651:
1326:
1448:
815:
1887:
664:. Effusion occurs through an orifice smaller than the mean free path of the particles in motion, whereas diffusion occurs through an opening in which multiple particles can flow through simultaneously.
2559:
The effusion rate for a gas depends directly on the average velocity of its particles. Thus, the faster the gas particles are moving, the more likely they are to pass through the effusion orifice.
2420:
1118:
856:
994:{\displaystyle {\begin{aligned}Q_{\text{effusion}}&=J_{\text{impingement}}\times A\\&={\frac {PA}{\sqrt {2\pi mk_{B}T}}}\\&={\frac {PAN_{A}}{\sqrt {2\pi MRT}}}\end{aligned}}}
80:
2094:
2365:
2047:
1506:
1099:
1539:
1252:
2330:
1782:
2102:
1913:
2550:
2523:
1960:
1052:
2210:
2385:
2008:
1984:
1933:
1805:
1471:
1364:
1021:
844:
756:
1656:
1552:
2579:. The vapor slowly effuses through a pinhole, and the loss of mass is proportional to the vapor pressure and can be used to determine this pressure. The
1238:{\displaystyle {\begin{aligned}{\overline {v_{x}}}&={\overline {v_{y}}}=0\\{\overline {v_{z}}}&={\sqrt {\frac {\pi k_{B}T}{2m}}}.\end{aligned}}}
748:
1372:
629:
2620:
1817:
1546:
2702:
2488:{\displaystyle {{\mbox{Rate of effusion of gas}}_{1} \over {\mbox{Rate of effusion of gas}}_{2}}={\sqrt {M_{2} \over M_{1}}}}
744:
2726:
2681:
2608:
622:
2584:
36:
672:
is the process in which a gas escapes from a container through a hole of diameter considerably smaller than the
2576:
2055:
595:
296:
133:
615:
336:
222:
2744:
291:
200:
83:
747:. The number of atomic or molecular collisions with a wall of a container per unit area per unit time (
712:
650:
207:
680:
and the escape of the gas is due to the pressure difference between the container and the exterior.
2335:
2017:
1476:
502:
497:
286:
279:
112:
1061:
2411:
2194:{\displaystyle \Phi _{V}={\frac {\Delta Pd^{2}}{P_{\rm {avg}}}}{\sqrt {\frac {\pi k_{B}T}{32m}}}}
1515:
1339:
565:
560:
229:
2583:
can also be determined by measuring the vapor pressure as a function of temperature, using the
2308:
1760:
1509:
819:
assuming mean free path is much greater than pinhole diameter and the gas can be treated as an
117:
1895:
2295:{\displaystyle \Phi _{V}={\frac {\Delta Pd^{2}}{P_{\rm {avg}}}}{\sqrt {\frac {\pi RT}{32M}}}}
2014:. Assuming the pressure difference between the two sides of the barrier is much smaller than
540:
158:
2641:
2528:
2501:
2011:
1938:
1030:
716:
378:
195:
175:
163:
107:
8:
2580:
661:
580:
428:
321:
27:
2575:
of a solid with very low vapor pressure. Such a solid forms a vapor at low pressure by
2370:
1993:
1969:
1918:
1790:
1750:{\textstyle v_{\rm {rms}}={\sqrt {3\pi /8}}\ v_{\rm {avg}}\approx 1.085\ v_{\rm {avg}}}
1646:{\textstyle v_{\rm {avg}}={\sqrt {8/3\pi }}\ v_{\rm {rms}}\approx 0.921\ v_{\rm {rms}}}
1542:
1456:
1349:
1006:
829:
743:
Effusion from an equilibrated container into outside vacuum can be calculated based on
600:
234:
190:
185:
1247:
Combined with the effusive flow rate, the recoil/thrust force on the system itself is
2722:
2698:
2677:
2604:
1963:
1055:
708:
217:
168:
1321:{\displaystyle F=m{\overline {v_{z}}}{\times }Q_{\text{effusion}}={\frac {PA}{2}}.}
846:
on the container is punched to become a small hole, the effusive flow rate will be
720:
555:
530:
443:
418:
413:
368:
2553:
2404:
2096:), it is possible to express effusion flow as a volumetric flow rate as follows:
545:
469:
433:
383:
314:
303:
248:
150:
2603:
K.J. Laidler and J.H. Meiser, Physical
Chemistry, Benjamin/Cummings 1982, p.18.
1330:
An example is the recoil force on a balloon with a small hole flying in vacuum.
735:
word, effundo, which means "shed, pour forth, pour out, utter, lavish, waste."
2749:
2572:
1343:
700:
685:
673:
550:
408:
373:
274:
180:
2738:
590:
423:
2669:
2568:
1987:
1443:{\displaystyle {\frac {1}{2}}mv_{\rm {rms}}^{2}={\frac {3}{2}}k_{\rm {B}}T}
1102:
689:
660:
The image on the left shows effusion, whereas the image on the right shows
575:
570:
535:
267:
810:{\displaystyle J_{\text{impingement}}={\frac {P}{\sqrt {2\pi mk_{B}T}}}.}
585:
488:
2400:
of lighter molecules passing through the hole per unit time is greater.
1785:
1024:
507:
403:
2697:. Boston: Houghton Mifflin Harcourt Publishing Company. p. 164.
1882:{\displaystyle \Phi _{N}={\frac {\Delta PAN_{A}}{\sqrt {2\pi MRT}}}.}
820:
479:
474:
308:
2552:
represent the molar masses of the gases. This equation is known as
643:
458:
363:
343:
329:
212:
704:
353:
732:
257:
2367:
is the average pressure on either side of the orifice, and
656:
1811:
of molecules passing through the hole per second) is then
1545:. The average molecular speed can be calculated from the
393:
2442:
2428:
1659:
1555:
676:
of the molecules. Such a hole is often described as a
2531:
2504:
2423:
2373:
2338:
2311:
2213:
2105:
2058:
2020:
1996:
1972:
1941:
1921:
1898:
1820:
1793:
1763:
1518:
1479:
1459:
1375:
1352:
1255:
1116:
1064:
1033:
1009:
854:
832:
759:
39:
1915:is the gas pressure difference across the barrier,
2544:
2517:
2487:
2379:
2359:
2324:
2294:
2193:
2088:
2041:
2002:
1978:
1954:
1927:
1907:
1881:
1799:
1776:
1749:
1645:
1533:
1500:
1465:
1442:
1358:
1320:
1237:
1093:
1046:
1015:
993:
838:
809:
74:
2736:
2049:, the average absolute pressure in the system (
16:Process of a gas escaping through a small hole
2390:
1108:The average velocity of effused particles is
623:
75:{\displaystyle J=-D{\frac {d\varphi }{dx}}}
630:
616:
2089:{\displaystyle \Delta P\ll P_{\rm {avg}}}
2332:is the volumetric flow rate of the gas,
1333:
655:
2692:
2737:
699:refers to accumulation of fluid in an
2665:
2663:
1807:effuses (typically expressed as the
731:The word effusion derives from the
13:
2676:(8th ed., W.H.Freeman 2006) p.756
2660:
2613:
2351:
2348:
2345:
2313:
2259:
2256:
2253:
2230:
2215:
2151:
2148:
2145:
2122:
2107:
2080:
2077:
2074:
2059:
2033:
2030:
2027:
1899:
1837:
1822:
1765:
1741:
1738:
1735:
1714:
1711:
1708:
1672:
1669:
1666:
1637:
1634:
1631:
1610:
1607:
1604:
1568:
1565:
1562:
1525:
1492:
1489:
1486:
1431:
1401:
1398:
1395:
14:
2761:
2642:"Low-Pressure Effusion of Gases"
738:
2562:
2403:
2711:
2686:
2634:
2597:
1:
2719:Physical Methods in Chemistry
2590:
2360:{\displaystyle P_{\rm {avg}}}
2042:{\displaystyle P_{\rm {avg}}}
1501:{\displaystyle v_{\rm {rms}}}
1473:is the mass of one molecule,
2621:"5.62 Physical Chemistry II"
1277:
1184:
1157:
1133:
1094:{\displaystyle R=N_{A}k_{B}}
726:
707:. Specific examples include
7:
2693:Zumdahl, Steven S. (2008).
2585:Clausius–Clapeyron relation
1534:{\displaystyle k_{\rm {B}}}
1346:for a gas at a temperature
695:In medical terminology, an
688:of the gas, flow obeys the
10:
2766:
2721:(W.B.Saunders 1977) p.563
2391:Effect of molecular weight
1547:Maxwell speed distribution
668:In physics and chemistry,
648:
641:
2325:{\displaystyle \Phi _{V}}
1935:is the area of the hole,
1777:{\displaystyle \Phi _{N}}
651:Effusion (disambiguation)
2554:Graham's law of effusion
1908:{\displaystyle \Delta P}
642:Not to be confused with
134:Clausius–Duhem (entropy)
84:Fick's laws of diffusion
2571:is used to measure the
2444:Rate of effusion of gas
2430:Rate of effusion of gas
1340:kinetic theory of gases
292:Navier–Stokes equations
230:Material failure theory
2546:
2519:
2489:
2387:is the hole diameter.
2381:
2361:
2326:
2296:
2195:
2090:
2043:
2004:
1980:
1956:
1929:
1909:
1883:
1801:
1778:
1751:
1647:
1535:
1512:of the molecules, and
1510:root-mean-square speed
1502:
1467:
1444:
1360:
1322:
1239:
1095:
1048:
1017:
995:
840:
811:
665:
76:
2547:
2545:{\displaystyle M_{2}}
2520:
2518:{\displaystyle M_{1}}
2490:
2382:
2362:
2327:
2297:
2196:
2091:
2044:
2005:
1981:
1957:
1955:{\displaystyle N_{A}}
1930:
1910:
1884:
1802:
1779:
1752:
1648:
1536:
1503:
1468:
1445:
1361:
1334:Measures of flow rate
1323:
1240:
1096:
1049:
1047:{\displaystyle N_{A}}
1018:
996:
841:
812:
659:
287:Bernoulli's principle
280:Archimedes' principle
77:
2672:and Julio de Paula,
2529:
2502:
2421:
2371:
2336:
2309:
2211:
2103:
2056:
2018:
2012:absolute temperature
1994:
1970:
1939:
1919:
1896:
1818:
1791:
1761:
1657:
1553:
1516:
1477:
1457:
1373:
1350:
1253:
1114:
1062:
1031:
1007:
852:
830:
757:
649:For other uses, see
379:Cohesion (chemistry)
201:Infinitesimal strain
37:
2695:Chemical Principles
2581:heat of sublimation
1653:(or, equivalently,
1411:
297:Poiseuille equation
28:Continuum mechanics
22:Part of a series on
2745:Physical chemistry
2674:Physical Chemistry
2628:MIT OpenCourseWare
2542:
2515:
2485:
2446:
2432:
2377:
2357:
2322:
2292:
2191:
2086:
2039:
2000:
1976:
1952:
1925:
1905:
1879:
1797:
1784:at which a gas of
1774:
1747:
1643:
1543:Boltzmann constant
1531:
1498:
1463:
1440:
1389:
1356:
1318:
1235:
1233:
1091:
1044:
1013:
991:
989:
836:
807:
703:, usually without
666:
503:Magnetorheological
498:Electrorheological
235:Fracture mechanics
72:
2704:978-0-547-19626-8
2646:www.chem.hope.edu
2483:
2482:
2454:
2445:
2431:
2410:Scottish chemist
2380:{\displaystyle d}
2290:
2289:
2265:
2189:
2188:
2157:
2003:{\displaystyle T}
1979:{\displaystyle R}
1964:Avogadro constant
1928:{\displaystyle A}
1874:
1873:
1800:{\displaystyle M}
1728:
1701:
1697:
1624:
1597:
1593:
1466:{\displaystyle m}
1423:
1384:
1359:{\displaystyle T}
1338:According to the
1313:
1294:
1280:
1226:
1225:
1187:
1160:
1136:
1056:Avogadro constant
1016:{\displaystyle M}
985:
984:
936:
935:
883:
866:
839:{\displaystyle A}
802:
801:
767:
721:pleural effusions
640:
639:
515:
514:
449:
448:
218:Contact mechanics
141:
140:
70:
2757:
2729:
2715:
2709:
2708:
2690:
2684:
2667:
2658:
2657:
2655:
2653:
2638:
2632:
2631:
2625:
2617:
2611:
2601:
2551:
2549:
2548:
2543:
2541:
2540:
2524:
2522:
2521:
2516:
2514:
2513:
2494:
2492:
2491:
2486:
2484:
2481:
2480:
2471:
2470:
2461:
2460:
2455:
2453:
2452:
2447:
2443:
2439:
2438:
2433:
2429:
2425:
2386:
2384:
2383:
2378:
2366:
2364:
2363:
2358:
2356:
2355:
2354:
2331:
2329:
2328:
2323:
2321:
2320:
2301:
2299:
2298:
2293:
2291:
2288:
2280:
2269:
2268:
2266:
2264:
2263:
2262:
2246:
2245:
2244:
2228:
2223:
2222:
2200:
2198:
2197:
2192:
2190:
2187:
2179:
2175:
2174:
2161:
2160:
2158:
2156:
2155:
2154:
2138:
2137:
2136:
2120:
2115:
2114:
2095:
2093:
2092:
2087:
2085:
2084:
2083:
2048:
2046:
2045:
2040:
2038:
2037:
2036:
2009:
2007:
2006:
2001:
1985:
1983:
1982:
1977:
1961:
1959:
1958:
1953:
1951:
1950:
1934:
1932:
1931:
1926:
1914:
1912:
1911:
1906:
1888:
1886:
1885:
1880:
1875:
1857:
1856:
1855:
1854:
1835:
1830:
1829:
1806:
1804:
1803:
1798:
1783:
1781:
1780:
1775:
1773:
1772:
1756:
1754:
1753:
1748:
1746:
1745:
1744:
1726:
1719:
1718:
1717:
1699:
1698:
1693:
1682:
1677:
1676:
1675:
1652:
1650:
1649:
1644:
1642:
1641:
1640:
1622:
1615:
1614:
1613:
1595:
1594:
1586:
1578:
1573:
1572:
1571:
1540:
1538:
1537:
1532:
1530:
1529:
1528:
1507:
1505:
1504:
1499:
1497:
1496:
1495:
1472:
1470:
1469:
1464:
1449:
1447:
1446:
1441:
1436:
1435:
1434:
1424:
1416:
1410:
1405:
1404:
1385:
1377:
1365:
1363:
1362:
1357:
1327:
1325:
1324:
1319:
1314:
1309:
1301:
1296:
1295:
1292:
1286:
1281:
1276:
1275:
1266:
1244:
1242:
1241:
1236:
1234:
1227:
1224:
1216:
1212:
1211:
1198:
1197:
1188:
1183:
1182:
1173:
1161:
1156:
1155:
1146:
1137:
1132:
1131:
1122:
1100:
1098:
1097:
1092:
1090:
1089:
1080:
1079:
1053:
1051:
1050:
1045:
1043:
1042:
1022:
1020:
1019:
1014:
1000:
998:
997:
992:
990:
986:
968:
967:
966:
965:
949:
941:
937:
931:
930:
912:
911:
903:
895:
885:
884:
881:
868:
867:
864:
845:
843:
842:
837:
826:If a small area
816:
814:
813:
808:
803:
797:
796:
778:
774:
769:
768:
765:
749:impingement rate
632:
625:
618:
464:
463:
429:Gay-Lussac's law
419:Combined gas law
369:Capillary action
254:
253:
97:
96:
81:
79:
78:
73:
71:
69:
61:
53:
19:
18:
2765:
2764:
2760:
2759:
2758:
2756:
2755:
2754:
2735:
2734:
2733:
2732:
2716:
2712:
2705:
2691:
2687:
2668:
2661:
2651:
2649:
2640:
2639:
2635:
2623:
2619:
2618:
2614:
2602:
2598:
2593:
2573:vapor pressures
2565:
2536:
2532:
2530:
2527:
2526:
2509:
2505:
2503:
2500:
2499:
2476:
2472:
2466:
2462:
2459:
2448:
2441:
2440:
2434:
2427:
2426:
2424:
2422:
2419:
2418:
2408:
2393:
2372:
2369:
2368:
2344:
2343:
2339:
2337:
2334:
2333:
2316:
2312:
2310:
2307:
2306:
2281:
2270:
2267:
2252:
2251:
2247:
2240:
2236:
2229:
2227:
2218:
2214:
2212:
2209:
2208:
2180:
2170:
2166:
2162:
2159:
2144:
2143:
2139:
2132:
2128:
2121:
2119:
2110:
2106:
2104:
2101:
2100:
2073:
2072:
2068:
2057:
2054:
2053:
2026:
2025:
2021:
2019:
2016:
2015:
1995:
1992:
1991:
1971:
1968:
1967:
1946:
1942:
1940:
1937:
1936:
1920:
1917:
1916:
1897:
1894:
1893:
1850:
1846:
1836:
1834:
1825:
1821:
1819:
1816:
1815:
1792:
1789:
1788:
1768:
1764:
1762:
1759:
1758:
1734:
1733:
1729:
1707:
1706:
1702:
1689:
1681:
1665:
1664:
1660:
1658:
1655:
1654:
1630:
1629:
1625:
1603:
1602:
1598:
1582:
1577:
1561:
1560:
1556:
1554:
1551:
1550:
1524:
1523:
1519:
1517:
1514:
1513:
1485:
1484:
1480:
1478:
1475:
1474:
1458:
1455:
1454:
1430:
1429:
1425:
1415:
1406:
1394:
1393:
1376:
1374:
1371:
1370:
1351:
1348:
1347:
1336:
1302:
1300:
1291:
1287:
1282:
1271:
1267:
1265:
1254:
1251:
1250:
1232:
1231:
1217:
1207:
1203:
1199:
1196:
1189:
1178:
1174:
1172:
1169:
1168:
1151:
1147:
1145:
1138:
1127:
1123:
1121:
1117:
1115:
1112:
1111:
1085:
1081:
1075:
1071:
1063:
1060:
1059:
1038:
1034:
1032:
1029:
1028:
1008:
1005:
1004:
988:
987:
961:
957:
950:
948:
939:
938:
926:
922:
904:
902:
893:
892:
880:
876:
869:
863:
859:
855:
853:
850:
849:
831:
828:
827:
792:
788:
773:
764:
760:
758:
755:
754:
751:) is given by:
741:
729:
654:
647:
636:
607:
606:
605:
525:
517:
516:
470:Viscoelasticity
461:
451:
450:
438:
388:
384:Surface tension
348:
251:
249:Fluid mechanics
241:
240:
239:
153:
151:Solid mechanics
143:
142:
94:
86:
62:
54:
52:
38:
35:
34:
17:
12:
11:
5:
2763:
2753:
2752:
2747:
2731:
2730:
2710:
2703:
2685:
2659:
2648:. Hope College
2633:
2612:
2595:
2594:
2592:
2589:
2564:
2561:
2539:
2535:
2512:
2508:
2496:
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2243:
2239:
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2232:
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2217:
2202:
2201:
2186:
2183:
2178:
2173:
2169:
2165:
2153:
2150:
2147:
2142:
2135:
2131:
2127:
2124:
2118:
2113:
2109:
2082:
2079:
2076:
2071:
2067:
2064:
2061:
2035:
2032:
2029:
2024:
1999:
1975:
1949:
1945:
1924:
1904:
1901:
1890:
1889:
1878:
1872:
1869:
1866:
1863:
1860:
1853:
1849:
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1824:
1796:
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1725:
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1716:
1713:
1710:
1705:
1696:
1692:
1688:
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1680:
1674:
1671:
1668:
1663:
1639:
1636:
1633:
1628:
1621:
1618:
1612:
1609:
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1601:
1592:
1589:
1585:
1581:
1576:
1570:
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1564:
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1527:
1522:
1494:
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1462:
1451:
1450:
1439:
1433:
1428:
1422:
1419:
1414:
1409:
1403:
1400:
1397:
1392:
1388:
1383:
1380:
1355:
1344:kinetic energy
1335:
1332:
1317:
1312:
1308:
1305:
1299:
1290:
1285:
1279:
1274:
1270:
1264:
1261:
1258:
1230:
1223:
1220:
1215:
1210:
1206:
1202:
1195:
1192:
1190:
1186:
1181:
1177:
1171:
1170:
1167:
1164:
1159:
1154:
1150:
1144:
1141:
1139:
1135:
1130:
1126:
1120:
1119:
1088:
1084:
1078:
1074:
1070:
1067:
1041:
1037:
1012:
983:
980:
977:
974:
971:
964:
960:
956:
953:
947:
944:
942:
940:
934:
929:
925:
921:
918:
915:
910:
907:
901:
898:
896:
894:
891:
888:
879:
875:
872:
870:
862:
858:
857:
835:
806:
800:
795:
791:
787:
784:
781:
777:
772:
763:
745:kinetic theory
740:
737:
728:
725:
701:anatomic space
686:mean free path
674:mean free path
638:
637:
635:
634:
627:
620:
612:
609:
608:
604:
603:
598:
593:
588:
583:
578:
573:
568:
563:
558:
553:
548:
543:
538:
533:
527:
526:
523:
522:
519:
518:
513:
512:
511:
510:
505:
500:
492:
491:
485:
484:
483:
482:
477:
472:
462:
457:
456:
453:
452:
447:
446:
440:
439:
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431:
426:
421:
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411:
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389:
387:
386:
381:
376:
374:Chromatography
371:
366:
360:
357:
356:
350:
349:
347:
346:
327:
326:
325:
306:
294:
289:
277:
264:
261:
260:
252:
247:
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227:
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183:
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155:
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145:
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139:
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128:
127:
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122:
121:
120:
115:
110:
102:
101:
95:
92:
91:
88:
87:
82:
68:
65:
60:
57:
51:
48:
45:
42:
31:
30:
24:
23:
15:
9:
6:
4:
3:
2:
2762:
2751:
2748:
2746:
2743:
2742:
2740:
2728:
2727:0-7216-3184-3
2724:
2720:
2714:
2706:
2700:
2696:
2689:
2683:
2682:0-7167-8759-8
2679:
2675:
2671:
2666:
2664:
2647:
2643:
2637:
2629:
2622:
2616:
2610:
2609:0-8053-5682-7
2606:
2600:
2596:
2588:
2586:
2582:
2578:
2574:
2570:
2560:
2557:
2555:
2537:
2533:
2510:
2506:
2477:
2473:
2467:
2463:
2456:
2449:
2435:
2417:
2416:
2415:
2413:
2412:Thomas Graham
2406:
2401:
2399:
2388:
2374:
2340:
2317:
2285:
2282:
2277:
2274:
2271:
2248:
2241:
2237:
2233:
2224:
2219:
2207:
2206:
2205:
2184:
2181:
2176:
2171:
2167:
2163:
2140:
2133:
2129:
2125:
2116:
2111:
2099:
2098:
2097:
2069:
2065:
2062:
2052:
2022:
2013:
1997:
1989:
1973:
1965:
1947:
1943:
1922:
1902:
1876:
1870:
1867:
1864:
1861:
1858:
1851:
1847:
1843:
1840:
1831:
1826:
1814:
1813:
1812:
1810:
1794:
1787:
1769:
1730:
1723:
1720:
1703:
1694:
1690:
1686:
1683:
1678:
1661:
1626:
1619:
1616:
1599:
1590:
1587:
1583:
1579:
1574:
1557:
1548:
1544:
1520:
1511:
1481:
1460:
1437:
1426:
1420:
1417:
1412:
1407:
1390:
1386:
1381:
1378:
1369:
1368:
1367:
1353:
1345:
1341:
1331:
1328:
1315:
1310:
1306:
1303:
1297:
1288:
1283:
1272:
1268:
1262:
1259:
1256:
1248:
1245:
1228:
1221:
1218:
1213:
1208:
1204:
1200:
1193:
1191:
1179:
1175:
1165:
1162:
1152:
1148:
1142:
1140:
1128:
1124:
1109:
1106:
1104:
1086:
1082:
1076:
1072:
1068:
1065:
1057:
1039:
1035:
1026:
1010:
1001:
981:
978:
975:
972:
969:
962:
958:
954:
951:
945:
943:
932:
927:
923:
919:
916:
913:
908:
905:
899:
897:
889:
886:
877:
873:
871:
860:
847:
833:
824:
822:
817:
804:
798:
793:
789:
785:
782:
779:
775:
770:
761:
752:
750:
746:
739:Into a vacuum
736:
734:
724:
722:
718:
714:
710:
706:
702:
698:
693:
691:
687:
681:
679:
675:
671:
663:
658:
652:
645:
633:
628:
626:
621:
619:
614:
613:
611:
610:
602:
599:
597:
594:
592:
589:
587:
584:
582:
579:
577:
574:
572:
569:
567:
564:
562:
559:
557:
554:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
528:
521:
520:
509:
506:
504:
501:
499:
496:
495:
494:
493:
490:
487:
486:
481:
478:
476:
473:
471:
468:
467:
466:
465:
460:
455:
454:
445:
442:
441:
435:
432:
430:
427:
425:
422:
420:
417:
415:
414:Charles's law
412:
410:
407:
405:
402:
401:
399:
398:
395:
392:
391:
385:
382:
380:
377:
375:
372:
370:
367:
365:
362:
361:
359:
358:
355:
352:
351:
345:
342:
338:
335:
331:
328:
323:
322:non-Newtonian
320:
316:
312:
311:
310:
307:
305:
302:
298:
295:
293:
290:
288:
285:
281:
278:
276:
273:
269:
266:
265:
263:
262:
259:
256:
255:
250:
245:
244:
236:
233:
231:
228:
224:
221:
220:
219:
216:
214:
211:
209:
208:Compatibility
206:
202:
199:
197:
196:Finite strain
194:
193:
192:
189:
187:
184:
182:
179:
177:
174:
170:
167:
166:
165:
162:
160:
157:
156:
152:
147:
146:
135:
132:
131:
130:
129:
125:
124:
119:
116:
114:
111:
109:
106:
105:
104:
103:
100:Conservations
99:
98:
90:
89:
85:
66:
63:
58:
55:
49:
46:
43:
40:
33:
32:
29:
26:
25:
21:
20:
2718:
2717:Drago, R.S.
2713:
2694:
2688:
2673:
2670:Peter Atkins
2650:. Retrieved
2645:
2636:
2627:
2615:
2599:
2569:Knudsen cell
2566:
2563:Knudsen cell
2558:
2497:
2409:
2405:Graham's law
2397:
2394:
2304:
2203:
2050:
1988:gas constant
1891:
1808:
1757:). The rate
1452:
1337:
1329:
1249:
1246:
1110:
1107:
1103:gas constant
1002:
848:
825:
818:
753:
742:
730:
696:
694:
690:Sampson flow
682:
677:
669:
667:
489:Smart fluids
434:Graham's law
340:
333:
318:
304:Pascal's law
300:
283:
271:
126:Inequalities
2577:sublimation
882:impingement
766:impingement
717:pericardial
508:Ferrofluids
409:Boyle's law
181:Hooke's law
159:Deformation
2739:Categories
2591:References
1786:molar mass
1025:molar mass
705:loculation
561:Gay-Lussac
524:Scientists
424:Fick's law
404:Atmosphere
223:frictional
176:Plasticity
164:Elasticity
2314:Φ
2272:π
2231:Δ
2216:Φ
2164:π
2123:Δ
2108:Φ
2066:≪
2060:Δ
1900:Δ
1862:π
1838:Δ
1823:Φ
1766:Φ
1721:≈
1687:π
1617:≈
1591:π
1284:×
1278:¯
1201:π
1185:¯
1158:¯
1134:¯
973:π
917:π
887:×
821:ideal gas
783:π
727:Etymology
662:diffusion
601:Truesdell
531:Bernoulli
480:Rheometer
475:Rheometry
315:Newtonian
309:Viscosity
59:φ
47:−
1293:effusion
865:effusion
709:subdural
697:effusion
670:effusion
644:Affusion
459:Rheology
364:Adhesion
344:Pressure
330:Buoyancy
275:Dynamics
113:Momentum
2652:6 April
2010:is the
1986:is the
1962:is the
1541:is the
1508:is the
1101:is the
1054:is the
1023:is the
713:mastoid
678:pinhole
546:Charles
354:Liquids
268:Statics
213:Bending
2725:
2701:
2680:
2607:
2498:where
2398:number
2305:where
1809:number
1727:
1700:
1623:
1596:
1453:where
1342:, the
1058:, and
1003:where
596:Stokes
591:Pascal
581:Navier
576:Newton
566:Graham
541:Cauchy
444:Plasma
339:
337:Mixing
332:
317:
299:
282:
270:
258:Fluids
191:Strain
186:Stress
169:linear
118:Energy
2750:Gases
2624:(PDF)
1892:Here
1724:1.085
1620:0.921
733:Latin
692:law.
571:Hooke
551:Euler
536:Boyle
394:Gases
2723:ISBN
2699:ISBN
2678:ISBN
2654:2021
2605:ISBN
2567:The
2525:and
2051:i.e.
1990:and
719:and
586:Noll
556:Fick
108:Mass
93:Laws
2204:or
1549:as
1366:is
2741::
2662:^
2644:.
2626:.
2587:.
2556:.
2283:32
2182:32
1966:,
1105:.
1027:,
823:.
723:.
715:,
711:,
2707:.
2656:.
2630:.
2538:2
2534:M
2511:1
2507:M
2478:1
2474:M
2468:2
2464:M
2457:=
2450:2
2436:1
2375:d
2352:g
2349:v
2346:a
2341:P
2318:V
2286:M
2278:T
2275:R
2260:g
2257:v
2254:a
2249:P
2242:2
2238:d
2234:P
2225:=
2220:V
2185:m
2177:T
2172:B
2168:k
2152:g
2149:v
2146:a
2141:P
2134:2
2130:d
2126:P
2117:=
2112:V
2081:g
2078:v
2075:a
2070:P
2063:P
2034:g
2031:v
2028:a
2023:P
1998:T
1974:R
1948:A
1944:N
1923:A
1903:P
1877:.
1871:T
1868:R
1865:M
1859:2
1852:A
1848:N
1844:A
1841:P
1832:=
1827:N
1795:M
1770:N
1742:g
1739:v
1736:a
1731:v
1715:g
1712:v
1709:a
1704:v
1695:8
1691:/
1684:3
1679:=
1673:s
1670:m
1667:r
1662:v
1638:s
1635:m
1632:r
1627:v
1611:s
1608:m
1605:r
1600:v
1588:3
1584:/
1580:8
1575:=
1569:g
1566:v
1563:a
1558:v
1526:B
1521:k
1493:s
1490:m
1487:r
1482:v
1461:m
1438:T
1432:B
1427:k
1421:2
1418:3
1413:=
1408:2
1402:s
1399:m
1396:r
1391:v
1387:m
1382:2
1379:1
1354:T
1316:.
1311:2
1307:A
1304:P
1298:=
1289:Q
1273:z
1269:v
1263:m
1260:=
1257:F
1229:.
1222:m
1219:2
1214:T
1209:B
1205:k
1194:=
1180:z
1176:v
1166:0
1163:=
1153:y
1149:v
1143:=
1129:x
1125:v
1087:B
1083:k
1077:A
1073:N
1069:=
1066:R
1040:A
1036:N
1011:M
982:T
979:R
976:M
970:2
963:A
959:N
955:A
952:P
946:=
933:T
928:B
924:k
920:m
914:2
909:A
906:P
900:=
890:A
878:J
874:=
861:Q
834:A
805:.
799:T
794:B
790:k
786:m
780:2
776:P
771:=
762:J
653:.
646:.
631:e
624:t
617:v
341:·
334:·
324:)
319:·
313:(
301:·
284:·
272:·
67:x
64:d
56:d
50:D
44:=
41:J
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