412:
201:
789:
141:. These contributions to the entropy are always present, because crystals always grow at a finite rate and at temperature. However, the residual entropy is often quite negligible and can be accounted for when it occurs using
937:
1068:
537:
193:
576:
407:{\displaystyle S^{\circ }=\sum _{k=1}^{N}\Delta S_{k}=\sum _{k=1}^{N}{\frac {dQ_{k}}{T}}\rightarrow \int _{0}^{T_{2}}{\frac {dS}{dT}}dT=\int _{0}^{T_{2}}{\frac {C_{p_{k}}}{T}}dT}
498:. The molar heat capacity is not constant during the experiment because it changes depending on the (increasing) temperature of the substance. Therefore, a table of values for
451:
485:
71:
668:
808:
582:. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.
492:
1049:
1020:
591:
40:
1088:
90:
802:, a spontaneous reaction always results in an increase in total entropy of the system and its surroundings:
501:
1083:
1041:
799:
942:
Molar entropy is not the same for all gases. Under identical conditions, it is greater for a heavier gas.
172:
976:
632:
542:
118:
1093:
39:
of pressure and any temperature of interest. These are often (but not necessarily) chosen to be the
420:
130:
456:
966:
618:
142:
49:
8:
795:
659:
488:
137:, and/or incomplete rotational quenching within the solid, as originally pointed out by
97:
is absolute. That is, an element in its standard state has a definite, nonzero value of
651:
647:
794:
The standard entropy of reaction helps determine whether the reaction will take place
784:{\displaystyle {\Delta S^{\circ }}_{rxn}=S_{products}^{\circ }-S_{reactants}^{\circ }}
1045:
1036:
Chang, Raymond; Cruickshank, Brandon (2005). "Entropy, Free Energy and
Equilibrium".
1016:
961:
643:
611:
126:
102:
932:{\displaystyle (\Delta S_{total}=\Delta S_{system}+\Delta S_{surroundings})>0}
122:
578:
represents the ratio of a very small exchange of heat energy to the temperature
971:
36:
165:
K without melting, its absolute molar entropy would be the sum of a series of
1077:
625:
607:
599:
138:
134:
16:
Standard entropy content of one mole of a substance under a standard state
154:
106:
82:
32:
638:
The heat capacity of the gas from the boiling point to room temperature.
655:
20:
1069:
Table of
Standard Thermodynamic Properties for Selected Substances
169:
stepwise and reversible entropy changes. The limit of this sum as
951:
28:
86:
624:
The heat capacity of the liquid from the melting point to the
78:
161:
K, then if the solid is warmed by its surroundings to 298.15
956:
610:(including heat absorbed in any changes between different
539:
is required to find the total molar entropy. The quantity
157:
of a solid substance is a perfectly ordered solid at 0
1000:(3rd ed.). Ithaca, NY: Cornell University Press.
811:
671:
545:
504:
459:
423:
204:
175:
52:
121:. However, this assumes that the material forms a '
931:
783:
570:
531:
479:
445:
406:
187:
65:
1075:
1035:
1011:Kosanke, K. (2004). "Chemical Thermodynamics".
491:at a constant pressure of the substance in the
662:to find the standard entropy of reaction:
654:make use of the standard molar entropy of
46:The standard molar entropy at pressure =
1015:. Journal of Pyrotechnics. p. 29.
1010:
995:
642:Changes in entropy are associated with
590:The standard molar entropy of a gas at
1076:
532:{\displaystyle {\frac {C_{p_{k}}}{T}}}
188:{\displaystyle N\rightarrow \infty }
571:{\displaystyle {\frac {dQ_{k}}{T}}}
13:
874:
843:
815:
674:
239:
182:
14:
1105:
1062:
148:
41:standard temperature and pressure
91:standard enthalpies of formation
998:The Nature of the Chemical Bond
602:of one mole of the solid from 0
1029:
1004:
989:
920:
812:
298:
179:
1:
982:
594:includes contributions from:
446:{\displaystyle T_{2}=298.15K}
1042:McGraw-Hill Higher Education
800:second law of thermodynamics
585:
73:is usually given the symbol
7:
977:Third law of thermodynamics
945:
633:latent heat of vaporization
119:third law of thermodynamics
10:
1110:
480:{\displaystyle C_{p_{k}}}
131:crystallographic defects
105:. The entropy of a pure
996:Pauling, Linus (1960).
35:of pure substance at a
933:
785:
572:
533:
481:
447:
408:
275:
238:
189:
67:
25:standard molar entropy
1089:Thermodynamic entropy
1013:Pyrotechnic chemistry
967:Helmholtz free energy
934:
786:
619:latent heat of fusion
573:
534:
482:
448:
409:
255:
218:
195:becomes an integral:
190:
143:statistical mechanics
129:. This can be due to
68:
66:{\displaystyle P^{0}}
809:
669:
543:
502:
457:
421:
202:
173:
117:K, according to the
50:
1084:Chemical properties
798:. According to the
780:
738:
489:molar heat capacity
373:
322:
77:, and has units of
929:
781:
742:
703:
652:Chemical equations
648:chemical reactions
612:crystal structures
568:
529:
493:reversible process
477:
443:
404:
352:
301:
185:
109:structure can be 0
89:(J⋅mol⋅K). Unlike
63:
962:Gibbs free energy
644:phase transitions
566:
527:
417:In this example,
396:
341:
296:
113:J⋅mol⋅K only at 0
1101:
1094:Molar quantities
1056:
1055:
1033:
1027:
1026:
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993:
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251:
250:
237:
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214:
213:
194:
192:
191:
186:
168:
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127:residual entropy
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112:
103:room temperature
100:
96:
76:
72:
70:
69:
64:
62:
61:
1109:
1108:
1104:
1103:
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1100:
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1044:. p. 765.
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31:content of one
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1063:External links
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149:Thermodynamics
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125:' without any
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1022:1-889526-15-0
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796:spontaneously
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626:boiling point
623:
621:of the solid.
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608:melting point
601:
600:heat capacity
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991:
941:
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416:
152:
135:dislocations
45:
24:
18:
107:crystalline
1078:Categories
983:References
1038:Chemistry
875:Δ
844:Δ
816:Δ
777:∘
740:−
735:∘
683:∘
675:Δ
656:reactants
606:K to the
586:Chemistry
354:∫
303:∫
299:→
257:∑
240:Δ
220:∑
211:∘
183:∞
180:→
21:chemistry
946:See also
660:products
952:Entropy
487:is the
29:entropy
27:is the
1048:
1019:
604:
438:298.15
163:
159:
115:
111:
87:kelvin
79:joules
23:, the
153:If a
1046:ISBN
1017:ISBN
957:Heat
924:>
658:and
646:and
631:The
617:The
598:The
453:and
155:mole
85:per
83:mole
81:per
33:mole
592:STP
145:.
101:at
19:In
1080::
1040:.
650:.
614:).
133:,
95:S°
75:S°
43:.
1054:.
1025:.
927:0
921:)
916:s
913:g
910:n
907:i
904:d
901:n
898:u
895:o
892:r
889:r
886:u
883:s
879:S
872:+
867:m
864:e
861:t
858:s
855:y
852:s
848:S
841:=
836:l
833:a
830:t
827:o
824:t
820:S
813:(
772:s
769:t
766:n
763:a
760:t
757:c
754:a
751:e
748:r
744:S
730:s
727:t
724:c
721:u
718:d
715:o
712:r
709:p
705:S
701:=
696:n
693:x
690:r
679:S
628:.
580:T
564:T
558:k
554:Q
550:d
525:T
518:k
514:p
509:C
496:k
471:k
467:p
462:C
441:K
435:=
430:2
426:T
402:T
399:d
394:T
387:k
383:p
378:C
368:2
364:T
358:0
350:=
347:T
344:d
338:T
335:d
330:S
327:d
317:2
313:T
307:0
294:T
288:k
284:Q
280:d
272:N
267:1
264:=
261:k
253:=
248:k
244:S
235:N
230:1
227:=
224:k
216:=
207:S
177:N
167:N
99:S
59:0
55:P
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