708:, has nearly 59% more specific heat capacity on a mass basis. In other words; even though an ingot of arsenic is only about 17% larger than an antimony one of the same mass, it absorbs about 59% more heat for a given temperature rise. The heat capacity ratios of the two substances closely follows the ratios of their molar volumes (the ratios of numbers of atoms in the same volume of each substance); the departure from the correlation to simple volumes in this case is due to lighter arsenic atoms being significantly more closely packed than antimony atoms, instead of similar size. In other words, similar-sized atoms would cause a mole of arsenic to be 63% larger than a mole of antimony, with a correspondingly lower density, allowing its volume to more closely mirror its heat capacity behavior.
588:). This fact gives each gas molecule the same effective "volume" in all ideal gases (although this volume/molecule in gases is far larger than molecules occupy on average in solids or liquids). Thus, in the limit of ideal gas behavior (which many gases approximate except at low temperatures and/or extremes of pressure) this property reduces differences in gas volumetric heat capacity to simple differences in the heat capacities of individual molecules. As noted, these differ by a factor depending on the degrees of freedom available to particles within the molecules.
732:. The phenomenon exists because of a body's ability to both store and transport heat relative to its environment. Since the configuration of system components and mix of heat transfer mechanisms (e.g. conduction, convection, radiation, phase change) varies substantially between instances, there is no generally applicable mathematical definition for thermal inertia. The phenomenon occurs in conjunction with a material's or a transport medium's
740:
629:
filled by the atomic volumes of the atoms in the gas. Since the molar volume of gases is very roughly 1000 times that of solids and liquids, this results in a factor of about 1000 loss in volumetric heat capacity for gases, as compared with liquids and solids. Monatomic gas heat capacities per atom (not per molecule) are decreased by a factor of 2 with regard to solids, due to loss of half of the potential
515:) would be constant for all solids. This amounted to a prediction that volumetric heat capacity in solids would be constant. In 1819 they found that volumetric heat capacities were not quite constant, but that the most constant quantity was the heat capacity of solids adjusted by the presumed weight of the atoms of the substance, as defined by Dalton (the
634:
the discussed factor of 2) increase heat capacity per atom in polyatomic gases, as compared with monatomic gases. Volumetric heat capacities in polyatomic gases vary widely, however, since they are dependent largely on the number of atoms per molecule in the gas, which in turn determines the total number of atoms per volume in the gas.
780:. Thermal inertia is less directly comparable to the mass-and-velocity term used in mechanics, where inertia restricts the acceleration of an object. In a similar way, thermal inertia is a measure of the thermal mass and the velocity of the thermal wave which controls the surface temperature of a material.
691:
of solid elements is very roughly constant, and (even more reliably) so also is the molar heat capacity for most solid substances. These two factors determine the volumetric heat capacity, which as a bulk property may be striking in consistency. For example, the element uranium is a metal which has a
628:
and T is temperature). As noted, the much lower values for gas heat capacity in terms of volume as compared with solids (although more comparable per mole, see below) results mostly from the fact that gases under standard conditions consist of mostly empty space (about 99.9% of volume), which is not
550:
the same size, molar and volumetric heat capacity would be proportional and differ by only a single constant reflecting ratios of the atomic molar volume of materials (their atomic density). An additional factor for all types of specific heat capacities (including molar specific heats) then further
495:
This quantity is used almost exclusively for liquids and solids, since for gases it may be confused with the "specific heat capacity at constant volume", which generally has very different values. International standards now recommend that "specific heat capacity" always refer to capacity per unit
633:
per atom for storing energy in a monatomic gas, as compared with regard to an ideal solid. There is some difference in the heat capacity of monatomic vs. polyatomic gasses, and also gas heat capacity is temperature-dependent in many ranges for polyatomic gases; these factors act to modestly (up to
751:
system behavior. Steady-state calculations, many of which produce valid estimates of equilibrium heat flows and temperatures without an accounting for thermal inertia, nevertheless yield no information on the pace of changes between equilibrium states. Response times for complex systems can be
681:
per mole, as noted above), there exists noticeable inverse correlation between a solid's density and its specific heat capacity on a per-mass basis. This is due to a very approximate tendency of atoms of most elements to be about the same size, despite much wider variations in density and atomic
546:) to 3.4 MJ⋅K⋅m (for example iron). This is mostly due to differences in the physical size of atoms. Atoms vary greatly in density, with the heaviest often being more dense, and thus are closer to taking up the same average volume in solids than their mass alone would predict. If all atoms
716:
The volumetric heat capacity of liquids could be measured from the thermal conductivity and thermal diffusivity correlation. The volumetric heat capacity of liquids could be directly obtained during thermal conductivity analysis using thermal conductivity analyzers that use techniques like the
981:, which is always larger due to the pressure–volume work done as a gas expands during heating at constant pressure (thus absorbing heat which is converted to work). The distinctions between constant-volume and constant-pressure heat capacities are also made in various types of
699:
Since the volume-specific corollary of the Dulong–Petit specific heat capacity relationship requires that atoms of all elements take up (on average) the same volume in solids, there are many departures from it, with most of these due to variations in atomic size. For instance,
271:
1359:
767:
Analogies of thermal inertia to the inertial behaviors observed in other disciplines of engineering and physics can sometimes be used with caution. In building design, thermal inertia is also known as the thermal flywheel effect, and a
600:
are very similar to those of liquids and solids, again differing by less than a factor of two per mole of atoms. This factor of two represents vibrational degrees of freedom available in solids vs. gas molecules of various complexities.
686:
of any given solid chemical element and its total heat capacity. Another way of stating this, is that the volume-specific heat capacity (volumetric heat capacity) of solid elements is roughly a constant. The
409:
Since both the heat capacity of an object and its volume may vary with temperature, in unrelated ways, the volumetric heat capacity is usually a function of temperature too. It is equal to the specific heat
794:
For a semi-infinite rigid body where heat transfer is dominated by the diffusive process of conduction only, the thermal inertia response at a surface can be approximated from the material's
534:
Eventually it became clear that heat capacities per particle for all substances in all states are the same, to within a factor of two, so long as temperatures are not in the cryogenic range.
604:
In monatomic gases (like argon) at room temperature and constant volume, volumetric heat capacities are all very close to 0.5 kJ⋅K⋅m, which is the same as the theoretical value of
576:
For gases at room temperature, the range of volumetric heat capacities per atom (not per molecule) only varies between different gases by a small factor less than two, because every
140:
853:
355:
404:
470:
898:
437:
303:
107:
The volumetric heat capacity of a substance, especially a gas, may be significantly higher when it is allowed to expand as it is heated (volumetric heat capacity
920:
876:
490:
375:
323:
1088:
1056:
U.S. Army Corps of
Engineers Technical Manual: Arctic and Subarctic Construction: Calculation Methods for Determination of Depths of Freeze and Thaw in Soils
747:
A system containing one or more components with large volumetric heat capacity indicates that dynamic, or transient, effects must be considered when
1342:
1270:
1111:
682:
weight. These two factors (constancy of atomic volume and constancy of mole-specific heat capacity) result in a good correlation between the
1234:
Keshavarz, P.; Taheri, M. (2007). "An improved lumped analysis for transient heat conduction by using the polynomial approximation method".
1160:
Sreekumar, Sreehari.; Ganguly, Abhijit.; Khalil, Sameh.; Chakrabarti, Supriya.; Hewitt, Neil.; Mondol, Jayanta.; Shah, Nikhilkumar. (2023).
1053:
977:
For gases it is necessary to distinguish between volumetric heat capacity at constant volume and volumetric heat capacity at constant
542:
The volumetric heat capacity of solid materials at room temperatures and above varies widely, from about 1.2 MJ⋅K⋅m (for example
1425:
1210:
1105:
20:
1147:
630:
88:
This quantity may be convenient for materials that are commonly measured by volume rather than mass, as is often the case in
51:
596:
Large complex gas molecules may have high heat capacities per mole (of molecules), but their heat capacities per mole of
1430:
92:
and other technical disciplines. The volumetric heat capacity often varies with temperature, and is different for each
508:
928:
761:
733:
584:. Thus, each gas molecule occupies the same mean volume in all ideal gases, regardless of the type of gas (see
266:{\displaystyle s(T)={\frac {C(T)}{V(T)}}={\frac {1}{V(T)}}\lim _{\Delta T\to 0}{\frac {\Delta Q(T)}{\Delta T}}}
562:
at 1.9. This reflects the modest loss of degrees of freedom for particles in liquids as compared with solids.
1014:
585:
1162:"Thermo-optical characterization of novel MXene/Carbon-dot hybrid nanofluid for heat transfer applications"
1440:
999:
982:
813:
757:
101:
62:
822:
753:
516:
805:
654:
551:
reflects degrees of freedom available to the atoms composing the substance, at various temperatures.
776:
heat flow and temperature which is similar to the delay between current and voltage in an AC-driven
760:. A higher value of volumetric heat capacity generally means a longer time for the system to reach
504:
123:
1134:
1092:
1216:
1064:
1009:
796:
789:
328:
743:
The thermal wave induced by a stepped heat source illustrates the phenomenon of thermal inertia.
728:
is a term commonly used to describe the observed delays in a body's temperature response during
380:
1261:
Gerald R. North (1988). "Lessons from energy balance models". In
Michael E. Schlesinger (ed.).
1338:
1266:
1206:
1101:
446:
511:
predicted in 1818 that the product of solid substance density and specific heat capacity (ρc
1401:
1374:
1313:
1243:
1198:
1173:
748:
736:. A larger thermal storage capacity typically yields a more sluggish temperature response.
97:
883:
111:) than when is heated in a closed vessel that prevents expansion (volumetric heat capacity
1435:
1287:
413:
279:
93:
1392:
Bunn, J.P. (1983). "The thermal response of a homogeneous slab to a constant heat flux".
1317:
1202:
905:
861:
739:
475:
360:
308:
34:
of a sample of the substance divided by the volume of the sample. It is the amount of
1419:
1405:
1220:
994:
773:
729:
520:
104:, because the heat goes into changing its state rather than raising its temperature.
31:
1034:
941:
Non-SI units of kieffers: Cal⋅cm⋅K⋅s, are also used informally in older references.
769:
688:
674:
625:
581:
496:
of mass. Therefore, the word "volumetric" should always be used for this quantity.
1178:
1161:
677:
of a solid chemical element is strongly related to its molar mass (usually about 3
1332:
1265:(NATO Advanced Study Institute on Physical-Based Modelling ed.). Springer.
1004:
646:
357:
is the amount of heat energy needed to raise the temperature of the sample from
119:
89:
55:
47:
1378:
1247:
777:
662:
658:
524:
82:
577:
804:). It is defined as the square root of the product of the material's bulk
985:(the latter meaning either mass-specific or mole-specific heat capacity).
100:, such as melting or boiling, its volumetric heat capacity is technically
978:
705:
531:(not per unit of volume) which is closest to being a constant in solids.
66:
1263:
Physically-based
Modelling and Simulation of Climate and Climatic Change
554:
For most liquids, the volumetric heat capacity is narrower, for example
809:
701:
570:
559:
543:
440:
70:
650:
555:
43:
35:
569:
has a very high volumetric heat capacity, at 4.18 MJ⋅K⋅m, and
738:
642:
566:
74:
945:
When a constant flow of heat is abruptly imposed upon a surface,
808:
and volumetric heat capacity, where the latter is the product of
692:
density almost 36 times that of the metal lithium, but uranium's
46:
of the material in order to cause an increase of one unit in its
122:
in the sample (as is sometimes done in chemistry), one gets the
78:
39:
949:
performs nearly the same role in limiting the surfaces initial
406:. This parameter is an intensive property of the substance.
492:. Its SI unit is joule per kelvin per cubic meter (J⋅K⋅m).
935:
638:
519:). This quantity was proportional to the heat capacity per
61:
The volumetric heat capacity can also be expressed as the
54:
unit of volumetric heat capacity is joule per kelvin per
118:
If the amount of substance is taken to be the number of
961:) as the rigid body's usual heat transfer coefficient (
696:
heat capacity is only about 20% larger than lithium's.
126:(whose SI unit is joule per kelvin per mole, J⋅K⋅mol).
1310:
Handbook of
Friction Materials and Their Applications
1058:, TM 5-852-6/AFR 88-19, Volume 6, 1988, Equation 2-1"
908:
886:
864:
825:
478:
449:
416:
383:
363:
331:
311:
282:
143:
752:evaluated with detailed numerical simulation, or a
19:For volumetric heats of particular substances, see
1288:"Mathematical Theory of Thermal Inertia Revisited"
914:
892:
870:
847:
637:The volumetric heat capacity is defined as having
484:
464:
431:
398:
369:
349:
317:
297:
265:
1360:"A New Thermal Inertia Model Based on Effusivity"
1193:Sala-Lizarraga, Jose; Picallo-Perez, Ana (2019).
653:). It can also be described in Imperial units of
1195:Exergy Analysis and Thermoeconomics of Buildings
527:), which suggested that it is the heat capacity
216:
620:RT per kelvin per mole of gas molecules (where
8:
1089:International Bureau of Weights and Measures
1295:46th Lunar and Planetary Science Conference
922:is specific heat capacity, with unit J⋅kg⋅K
305:is the volume of the sample at temperature
134:The volumetric heat capacity is defined as
1177:
907:
885:
863:
832:
824:
477:
448:
415:
382:
362:
330:
310:
281:
234:
219:
194:
159:
142:
1358:van der Maas, J.; Maldonado, E. (1997).
878:is thermal conductivity, with unit W⋅m⋅K
65:(heat capacity per unit of mass, in J⋅K⋅
1045:
1026:
1286:Veto, M.S.; Christensen, P.R. (2015).
1094:The International System of Units (SI)
704:, which is only 14.5% less dense than
573:is also fairly high: 3.3 MJ⋅K⋅m.
96:. While the substance is undergoing a
1367:International Journal of Solar Energy
973:Constant volume and constant pressure
7:
1331:Carslaw, H.S.; Jaeger, J.C. (1959).
931:multiplied by square root of time:
848:{\displaystyle e={\sqrt {k\rho c}}}
712:Volumetric heat capacity of liquids
472:, both measured at the temperature
38:that must be added, in the form of
1318:10.1016/B978-0-08-100619-1.00009-2
1203:10.1016/B978-0-12-817611-5.00004-7
927:Thermal effusivity has units of a
669:Volumetric heat capacity of solids
390:
332:
254:
237:
220:
14:
965:) plays in determining the final
592:Volumetric heat capacity of gases
21:Table of specific heat capacities
1117:from the original on 2021-06-04
717:transient plane source method.
1312:. Elsevier. pp. 123–134.
1197:. Elsevier. pp. 272–273.
459:
453:
426:
420:
344:
338:
292:
286:
249:
243:
226:
209:
203:
185:
179:
171:
165:
153:
147:
1:
1179:10.1016/j.jclepro.2023.140395
1166:Journal of Cleaner Production
953:"thermal inertia" response (
1406:10.1016/0360-1323(83)90019-7
1334:Conduction of Heat in Solids
938:units of W⋅m⋅K⋅s or J⋅m⋅K⋅s.
772:can produce a delay between
1337:. Clarendon Press, Oxford.
439:of the substance times its
350:{\displaystyle \Delta Q(T)}
1457:
1308:Dante, Roberto C. (2016).
900:is density, with unit kg⋅m
787:
399:{\displaystyle T+\Delta T}
18:
1379:10.1080/01425919708914334
1248:10.1007/s00231-006-0200-0
929:heat transfer coefficient
1426:Thermodynamic properties
1394:Building and Environment
1033:Coined by the planetary
734:heat transfer properties
465:{\displaystyle \rho (T)}
73:of the substance (in kg/
28:volumetric heat capacity
1015:Thermodynamic equations
558:at 1.64 MJ⋅K⋅m or
1236:Heat and Mass Transfer
1000:Specific heat capacity
983:specific heat capacity
916:
894:
872:
849:
814:specific heat capacity
758:lumped system analysis
744:
486:
466:
433:
400:
371:
351:
319:
299:
267:
63:specific heat capacity
969:surface temperature.
917:
895:
893:{\displaystyle \rho }
873:
850:
754:thermal time constant
742:
487:
467:
434:
401:
372:
352:
320:
300:
268:
30:of a material is the
906:
884:
862:
823:
806:thermal conductivity
476:
447:
432:{\displaystyle c(T)}
414:
381:
361:
329:
309:
298:{\displaystyle V(T)}
280:
141:
109:at constant pressure
1431:Physical quantities
1133:Based on values in
124:molar heat capacity
1010:Thermal effusivity
912:
890:
868:
845:
797:thermal effusivity
790:Thermal effusivity
784:Thermal effusivity
745:
631:degrees of freedom
482:
462:
443:(mass per volume)
429:
396:
367:
347:
315:
295:
263:
233:
113:at constant volume
1344:978-0-19-853368-9
1272:978-90-277-2789-3
1242:(11): 1151–1156.
915:{\displaystyle c}
871:{\displaystyle k}
843:
756:estimated from a
485:{\displaystyle T}
370:{\displaystyle T}
318:{\displaystyle T}
261:
215:
213:
189:
42:, to one unit of
1448:
1410:
1409:
1389:
1383:
1382:
1373:(1–3): 131–160.
1364:
1355:
1349:
1348:
1328:
1322:
1321:
1305:
1299:
1298:
1292:
1283:
1277:
1276:
1258:
1252:
1251:
1231:
1225:
1224:
1190:
1184:
1183:
1181:
1157:
1151:
1144:
1138:
1131:
1125:
1124:
1123:
1122:
1116:
1100:(8th ed.),
1099:
1085:
1079:
1078:
1076:
1075:
1069:
1063:. Archived from
1062:
1050:
1038:
1037:Hugh H. Kieffer.
1031:
921:
919:
918:
913:
899:
897:
896:
891:
877:
875:
874:
869:
854:
852:
851:
846:
844:
833:
619:
617:
616:
613:
610:
517:Dulong–Petit law
491:
489:
488:
483:
471:
469:
468:
463:
438:
436:
435:
430:
405:
403:
402:
397:
376:
374:
373:
368:
356:
354:
353:
348:
324:
322:
321:
316:
304:
302:
301:
296:
272:
270:
269:
264:
262:
260:
252:
235:
232:
214:
212:
195:
190:
188:
174:
160:
98:phase transition
1456:
1455:
1451:
1450:
1449:
1447:
1446:
1445:
1416:
1415:
1414:
1413:
1391:
1390:
1386:
1362:
1357:
1356:
1352:
1345:
1330:
1329:
1325:
1307:
1306:
1302:
1290:
1285:
1284:
1280:
1273:
1260:
1259:
1255:
1233:
1232:
1228:
1213:
1192:
1191:
1187:
1159:
1158:
1154:
1145:
1141:
1132:
1128:
1120:
1118:
1114:
1108:
1097:
1087:
1086:
1082:
1073:
1071:
1067:
1060:
1052:
1051:
1047:
1042:
1041:
1032:
1028:
1023:
991:
975:
958:
926:
904:
903:
882:
881:
860:
859:
821:
820:
792:
786:
726:Thermal inertia
723:
721:Thermal inertia
714:
671:
614:
611:
608:
607:
605:
594:
540:
514:
502:
474:
473:
445:
444:
412:
411:
379:
378:
359:
358:
327:
326:
307:
306:
278:
277:
253:
236:
199:
175:
161:
139:
138:
132:
94:state of matter
24:
17:
16:Thermal quality
12:
11:
5:
1454:
1452:
1444:
1443:
1438:
1433:
1428:
1418:
1417:
1412:
1411:
1400:(1–2): 61–64.
1384:
1350:
1343:
1323:
1300:
1278:
1271:
1253:
1226:
1211:
1185:
1172:(29): 140395.
1152:
1139:
1126:
1106:
1080:
1044:
1043:
1040:
1039:
1025:
1024:
1022:
1019:
1018:
1017:
1012:
1007:
1002:
997:
990:
987:
974:
971:
956:
943:
942:
939:
924:
923:
911:
901:
889:
879:
867:
856:
855:
842:
839:
836:
831:
828:
788:Main article:
785:
782:
730:heat transfers
722:
719:
713:
710:
670:
667:
593:
590:
586:kinetic theory
539:
538:Typical values
536:
512:
501:
498:
481:
461:
458:
455:
452:
428:
425:
422:
419:
395:
392:
389:
386:
366:
346:
343:
340:
337:
334:
314:
294:
291:
288:
285:
274:
273:
259:
256:
251:
248:
245:
242:
239:
231:
228:
225:
222:
218:
211:
208:
205:
202:
198:
193:
187:
184:
181:
178:
173:
170:
167:
164:
158:
155:
152:
149:
146:
131:
128:
15:
13:
10:
9:
6:
4:
3:
2:
1453:
1442:
1441:Heat transfer
1439:
1437:
1434:
1432:
1429:
1427:
1424:
1423:
1421:
1407:
1403:
1399:
1395:
1388:
1385:
1380:
1376:
1372:
1368:
1361:
1354:
1351:
1346:
1340:
1336:
1335:
1327:
1324:
1319:
1315:
1311:
1304:
1301:
1296:
1289:
1282:
1279:
1274:
1268:
1264:
1257:
1254:
1249:
1245:
1241:
1237:
1230:
1227:
1222:
1218:
1214:
1212:9780128176115
1208:
1204:
1200:
1196:
1189:
1186:
1180:
1175:
1171:
1167:
1163:
1156:
1153:
1149:
1143:
1140:
1136:
1130:
1127:
1113:
1109:
1107:92-822-2213-6
1103:
1096:
1095:
1090:
1084:
1081:
1070:on 2016-03-04
1066:
1059:
1057:
1049:
1046:
1036:
1030:
1027:
1020:
1016:
1013:
1011:
1008:
1006:
1003:
1001:
998:
996:
995:Heat capacity
993:
992:
988:
986:
984:
980:
972:
970:
968:
964:
960:
952:
948:
940:
937:
934:
933:
932:
930:
909:
902:
887:
880:
865:
858:
857:
840:
837:
834:
829:
826:
819:
818:
817:
815:
811:
807:
803:
799:
798:
791:
783:
781:
779:
775:
771:
765:
763:
759:
755:
750:
741:
737:
735:
731:
727:
720:
718:
711:
709:
707:
703:
697:
695:
690:
685:
680:
676:
668:
666:
664:
660:
656:
652:
648:
644:
640:
635:
632:
627:
623:
602:
599:
591:
589:
587:
583:
580:has the same
579:
574:
572:
568:
563:
561:
557:
552:
549:
545:
537:
535:
532:
530:
526:
522:
521:atomic weight
518:
510:
506:
499:
497:
493:
479:
456:
450:
442:
423:
417:
407:
393:
387:
384:
364:
341:
335:
312:
289:
283:
257:
246:
240:
229:
223:
206:
200:
196:
191:
182:
176:
168:
162:
156:
150:
144:
137:
136:
135:
129:
127:
125:
121:
116:
114:
110:
105:
103:
99:
95:
91:
86:
84:
80:
76:
72:
68:
64:
59:
57:
53:
49:
45:
41:
37:
33:
32:heat capacity
29:
22:
1397:
1393:
1387:
1370:
1366:
1353:
1333:
1326:
1309:
1303:
1294:
1281:
1262:
1256:
1239:
1235:
1229:
1194:
1188:
1169:
1165:
1155:
1150:and density.
1142:
1137:and density.
1129:
1119:, retrieved
1093:
1083:
1072:. Retrieved
1065:the original
1055:
1048:
1035:geophysicist
1029:
976:
966:
962:
954:
950:
946:
944:
925:
801:
795:
793:
770:thermal mass
766:
746:
725:
724:
715:
698:
693:
689:molar volume
683:
678:
675:bulk density
672:
636:
626:gas constant
621:
603:
597:
595:
582:molar volume
575:
564:
553:
547:
541:
533:
528:
503:
494:
408:
275:
133:
117:
112:
108:
106:
87:
69:) times the
60:
27:
25:
1005:Temperature
762:equilibrium
90:engineering
56:cubic meter
48:temperature
1420:Categories
1135:this table
1121:2021-12-16
1074:2015-05-19
1021:References
778:RC circuit
694:volumetric
673:Since the
525:molar mass
130:Definition
1221:210737476
1148:NIST data
1146:Based on
888:ρ
838:ρ
749:modelling
641:units of
578:ideal gas
565:However,
451:ρ
391:Δ
333:Δ
255:Δ
238:Δ
227:→
221:Δ
58:, J⋅K⋅m.
1112:archived
1091:(2006),
989:See also
979:pressure
959:≈ e ⋅ t
706:antimony
529:per atom
523:(or per
102:infinite
951:dynamic
810:density
774:diurnal
702:arsenic
624:is the
618:
606:
571:ammonia
560:ethanol
544:bismuth
500:History
441:density
71:density
50:. The
1436:Volume
1341:
1269:
1219:
1209:
1104:
967:static
684:volume
556:octane
505:Dulong
325:, and
276:where
44:volume
36:energy
1363:(PDF)
1291:(PDF)
1217:S2CID
1115:(PDF)
1098:(PDF)
1068:(PDF)
1061:(PDF)
598:atoms
567:water
509:Petit
120:moles
77:, or
1339:ISBN
1267:ISBN
1207:ISBN
1102:ISBN
812:and
548:were
507:and
40:heat
26:The
1402:doi
1375:doi
1314:doi
1244:doi
1199:doi
1174:doi
1170:434
957:dyn
665:).
655:BTU
377:to
217:lim
115:).
85:).
1422::
1398:18
1396:.
1371:19
1369:.
1365:.
1293:.
1240:43
1238:.
1215:.
1205:.
1168:.
1164:.
1110:,
936:SI
816::
764:.
663:°F
659:ft
657:/(
645:/(
639:SI
83:mL
67:kg
52:SI
1408:.
1404::
1381:.
1377::
1347:.
1320:.
1316::
1297:.
1275:.
1250:.
1246::
1223:.
1201::
1182:.
1176::
1077:.
1054:"
963:U
955:U
947:e
910:c
866:k
841:c
835:k
830:=
827:e
802:e
800:(
679:R
661:⋅
651:K
649:⋅
647:m
643:J
622:R
615:2
612:/
609:3
513:p
480:T
460:)
457:T
454:(
427:)
424:T
421:(
418:c
394:T
388:+
385:T
365:T
345:)
342:T
339:(
336:Q
313:T
293:)
290:T
287:(
284:V
258:T
250:)
247:T
244:(
241:Q
230:0
224:T
210:)
207:T
204:(
201:V
197:1
192:=
186:)
183:T
180:(
177:V
172:)
169:T
166:(
163:C
157:=
154:)
151:T
148:(
145:s
81:/
79:g
75:L
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.