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Principle of maximum work

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chemical actions under ordinary conditions, it is subject to numerous exceptions, and cannot therefore be taken (as its authors originally intended) as a secure basis for theoretical reasoning on the connection between thermal effect and chemical affinity. The existence of reactions which are reversible on slight alteration of conditions at once invalidates the principle, for if the action proceeding in one direction evolves heat, it must absorb heat when proceeding in the reverse direction. As the principle was abandoned even by its authors, it is now only of historical importance, although for many years it exerted considerable influence on thermochemical research.
197: 158:: “as motion was explained by the Newtonian concept of force, chemists wanted a similar concept of ‘driving force’ for chemical change? Why do chemical reactions occur, and why do they stop at certain points? Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked a clear definition. 68:
Berthelot independently enunciated a generalization (commonly known as Berthelot's Third Principle, or Principle of Maximum Work), which may be briefly stated as: every pure chemical reaction is accompanied by evolution of heat. Whilst this principle is undoubtedly applicable to the great majority of
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and does not suffer dissipation due to friction or heat exchanges. A simple example would be a frictionless spring, or a weight on a pulley in a gravitational field. Suppose further, that we thermally connect the primary system to a third system, a "reversible heat source". A reversible heat source
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unified all of this in his 300-page "On the Equilibrium of Heterogeneous Substances". Suppose, for example, we have a general thermodynamic system, called the "primary" system and that we mechanically connect it to a "reversible work source". A reversible work source is a system which, when it does
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may be thought of as a heat source in which all transformations are reversible. For such a source, the heat energy δQ added will be equal to the temperature of the source (T) times the increase in its entropy. (If it were an irreversible heat source, the entropy increase would be larger than δQ/T)
184:. In 1875, after quantifying the heats of reaction for a large number of compounds, Berthelot proposed the “principle of maximum work” in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of a system of bodies which liberate 165:, called the “Newtonian hypothesis”, which stated that light and heat are forms of matter attracted or repelled by other forms of matter, with forces analogous to gravitation or to chemical affinity. 52:, in a more accurate form. Berthelot's version was essentially: "every pure chemical reaction is accompanied by evolution of heat." (and that this yields the maximum amount of work). The effects of 574: 506: 815: 666: 200:
Thermodynamic systems in the maximum work theorem. dU is the energy lost to the reversible heat system as heat energy δQ and to the reversible work system as work δW.
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is essentially the energy of a chemical reaction "free" or available to do external work. Historically, the "free energy" is a more advanced and accurate replacement for the
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When the primary system is reversible, the equality will hold and the amount of work delivered will be a maximum. Note that this will hold for
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in the 1850s and 60s, heats of reaction and the work associated with these processes were given a more accurate mathematical basis. In 1876,
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and others to follow, the work principle was found to be a particular case of a more general statement:
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During the entire 18th century, the dominant view in regard to heat and light was that put forward by
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produced there from. The principle was developed in approximate form in 1875 by French chemist
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The principle of work was a precursor to the development of the thermodynamic concept of
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between the same initial and final state, the delivery of work is a maximum for a
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work, or has work done to it, does not change its entropy. It is therefore not a
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will tend to yield the maximum amount of chemical energy in the form of
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The gain in internal energy of the reversible heat source
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The gain in internal energy of the reversible work source
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According to Nobelist and chemical engineering professor
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was a postulate concerning the relationship between
809: 753: 723: 700: 660: 611: 568: 500: 438: 421:The gain in entropy of the reversible heat source 411: 374: 354:The gain in entropy of the reversible work source 344: 307: 277: 257:The loss of internal energy by the primary system 247: 72:Thus, to summarize, in 1875 by the French chemist 147:. The term dates back to at least the time of 94: 448:The temperature of the reversible heat source 8: 287:The gain in entropy of the primary system 769: 745: 736: 713: 692: 683: 657: 651: 630: 608: 596: 587: 565: 553: 537: 519: 497: 468: 456:We may now make the following statements 435: 430: 408: 402: 393: 371: 363: 341: 335: 326: 304: 296: 274: 266: 244: 233: 569:{\displaystyle dS+dS_{h}+dS_{w}\geq 0\,} 168:In the 19th century, the French chemist 882:Source: Ilya Prigogine's 1998 textbook 863: 501:{\displaystyle -dU=\delta Q+\delta W\,} 87:In 1876, however, through the works of 810:{\displaystyle \delta W\leq -(dU-TdS)} 204:With the development of the first two 7: 661:{\displaystyle \delta Q=TdS_{h}\,} 14: 578:(Second law of thermodynamics) 804: 783: 761:gives the following equation: 510:(First law of thermodynamics) 1: 32:evolution, and the potential 84:as the reaction progresses. 847:Thomsen-Berthelot principle 918: 612:{\displaystyle dS_{w}=0\,} 375:{\displaystyle \delta Q\,} 308:{\displaystyle \delta W\,} 176:had attempted to quantify 670:(Reversible heat source) 621:(Reversible work source) 22:principle of maximum work 724:{\displaystyle \delta Q} 412:{\displaystyle dS_{h}\,} 345:{\displaystyle dS_{w}\,} 871:Encyclopædia Britannica 842:Chemical thermodynamics 172:and the Danish chemist 98:thermodynamic processes 811: 755: 754:{\displaystyle dS_{h}} 725: 702: 701:{\displaystyle dS_{w}} 662: 613: 570: 502: 440: 413: 376: 346: 309: 279: 249: 206:laws of thermodynamics 201: 108: 884:Modern Thermodynamics 812: 756: 726: 703: 663: 614: 571: 503: 441: 414: 377: 347: 310: 280: 250: 248:{\displaystyle -dU\,} 199: 133:Helmholtz free energy 768: 735: 712: 682: 629: 586: 518: 467: 429: 392: 362: 325: 295: 278:{\displaystyle dS\,} 265: 232: 439:{\displaystyle T\,} 170:Marcellin Berthelot 74:Marcellin Berthelot 38:Marcellin Berthelot 807: 751: 721: 698: 658: 609: 566: 498: 436: 409: 372: 342: 305: 275: 245: 202: 145:chemical reactions 78:chemical reactions 76:which stated that 48:, in the field of 40:, in the field of 26:chemical reactions 18:history of science 674: 673: 452: 451: 182:heats of reaction 178:chemical affinity 129:Gibbs free energy 909: 886: 880: 874: 868: 816: 814: 813: 808: 760: 758: 757: 752: 750: 749: 730: 728: 727: 722: 707: 705: 704: 699: 697: 696: 667: 665: 664: 659: 656: 655: 618: 616: 615: 610: 601: 600: 575: 573: 572: 567: 558: 557: 542: 541: 507: 505: 504: 499: 461: 460: 445: 443: 442: 437: 418: 416: 415: 410: 407: 406: 381: 379: 378: 373: 351: 349: 348: 343: 340: 339: 314: 312: 311: 306: 284: 282: 281: 276: 254: 252: 251: 246: 226: 225: 917: 916: 912: 911: 910: 908: 907: 906: 902:Thermochemistry 892: 891: 890: 889: 881: 877: 869: 865: 860: 852:Thermochemistry 838: 766: 765: 741: 733: 732: 710: 709: 688: 680: 679: 647: 627: 626: 592: 584: 583: 549: 533: 516: 515: 465: 464: 427: 426: 398: 390: 389: 360: 359: 331: 323: 322: 293: 292: 263: 262: 230: 229: 194: 149:Albertus Magnus 137:thermochemistry 121: 119:Thermochemistry 109: 66: 54:irreversibility 42:thermochemistry 12: 11: 5: 915: 913: 905: 904: 894: 893: 888: 887: 875: 862: 861: 859: 856: 855: 854: 849: 844: 837: 834: 818: 817: 806: 803: 800: 797: 794: 791: 788: 785: 782: 779: 776: 773: 748: 744: 740: 720: 717: 695: 691: 687: 676: 675: 672: 671: 668: 654: 650: 646: 643: 640: 637: 634: 623: 622: 619: 607: 604: 599: 595: 591: 580: 579: 576: 564: 561: 556: 552: 548: 545: 540: 536: 532: 529: 526: 523: 512: 511: 508: 496: 493: 490: 487: 484: 481: 478: 475: 472: 454: 453: 450: 449: 446: 434: 423: 422: 419: 405: 401: 397: 386: 385: 382: 370: 367: 356: 355: 352: 338: 334: 330: 319: 318: 315: 303: 300: 289: 288: 285: 273: 270: 259: 258: 255: 243: 240: 237: 193: 192:Thermodynamics 190: 174:Julius Thomsen 156:Ilya Prigogine 125:thermodynamics 120: 117: 93: 65: 62: 50:thermodynamics 13: 10: 9: 6: 4: 3: 2: 914: 903: 900: 899: 897: 885: 879: 876: 872: 867: 864: 857: 853: 850: 848: 845: 843: 840: 839: 835: 833: 831: 827: 823: 801: 798: 795: 792: 789: 786: 780: 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103:reversible 793:− 781:− 778:≤ 772:δ 716:δ 633:δ 560:≥ 492:δ 483:δ 471:− 366:δ 299:δ 236:− 151:in 1250. 896:Category 836:See also 832: . 221:Define: 141:affinity 106:process. 96:For all 64:Overview 58:entropy 16:In the 731:, and 180:using 139:term “ 127:, the 20:, the 873:1911 186:heat 82:work 34:work 30:heat 822:any 131:or 123:In 898:: 830:dS 826:dU 708:, 188:. 115:. 60:. 28:, 805:) 802:S 799:d 796:T 790:U 787:d 784:( 775:W 747:h 743:S 739:d 719:Q 694:w 690:S 686:d 653:h 649:S 645:d 642:T 639:= 636:Q 606:0 603:= 598:w 594:S 590:d 563:0 555:w 551:S 547:d 544:+ 539:h 535:S 531:d 528:+ 525:S 522:d 495:W 489:+ 486:Q 480:= 477:U 474:d 433:T 404:h 400:S 396:d 369:Q 337:w 333:S 329:d 302:W 272:S 269:d 242:U 239:d

Index

history of science
chemical reactions
heat
work
Marcellin Berthelot
thermochemistry
Willard Gibbs
thermodynamics
irreversibility
entropy
Marcellin Berthelot
chemical reactions
work
Willard Gibbs
thermodynamic processes
reversible
free energy
thermodynamics
Gibbs free energy
Helmholtz free energy
thermochemistry
affinity
chemical reactions
Albertus Magnus
Ilya Prigogine
Isaac Newton
Marcellin Berthelot
Julius Thomsen
chemical affinity
heats of reaction

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