I-theorem ye-energy equipmentpartition yatholwa ngokwethiyori nguClerk Maxwell esebenzisa i-statistical mechanics. Ibizwa ngokuthi i-theorem ngoba abukho ubufakazi obutholakala ngokuhlola. Ukuhlukaniswa kwamandla kusho ukusatshalaliswa kwamandla okulinganayo.
I-KE = amandla ajwayelekile e-kinetic okuhumusha ama-molecule egesi (i-Joule)
k = okungaguquki kukaBoltzmann = 1.38 x 10 -23 J/K
T = izinga lokushisa eliphelele le-molecule yegesi efanele (uKelvin)
Amandla e-kinetic okuhumusha atholakala ekunyakazeni kokuhumusha okunezingxenye ezintathu zejubane, okungukuthi ingxenye yejubane ku-x-axis, i-y-axis, kanye ne-z-axis. Kunezingxenye ezintathu zalesi sivinini, lapho kukhona inombolo 3 ku-equation engenhla. Ingxenye ngayinye yejubane ibizwa ngokuthi izinga lenkululeko. Ngenxa yokuthi inezingxenye ezintathu zejubane, amandla e-kinetic okuhumusha anamazinga amathathu enkululeko.
Ithiyori ye-equipment equipment ithi amandla angempela kumele ahlukaniswe ngokulinganayo kuzo zonke amazinga enkululeko. Ngakho-ke, amandla ajwayelekile ezinga ngalinye lenkululeko yi-1/2 kT.
Ama-molecule egesi e-Monatomic
Ama-molecule egesi ye-monatomic enza ukunyakaza kokuhumusha kuphela ukuze ama-molecule egesi ye-monatomic abe nama-degree amathathu enkululeko.
Amandla ajwayelekile e-kinetic e-molecule ngayinye yegesi ye-monatomic yile:
3 (1/2 kT) = 3/2 kT = 3/2 nRT.
Umthamo wokushisa wama-molecule egesi e-monatomic:
C = 3/2 R = 3/2 (8.315 J / mol. K) = 12.47 J/Kg. K
Ama-molecule egesi e-diatomic
Ngaphezu kokunyakaza kokuhumusha, ama-molecule egesi e-diatomic nawo enza ukujikeleza nokudlidliza. Inani lamadigri enkululeko yokunyakaza kokuhumusha = 3. Liyini izinga lenkululeko yokunyakaza kokujikeleza nokudlidliza?
Kunezingqimba ezintathu zokujikeleza, okungukuthi ama-x, y, kanye nama-Z-axis. Ukunyakaza kokujikeleza ku-x-axis akubalwa ngoba ama-athomu amabili ahambisana ne-axis yokujikeleza. Uma kuhambisana ne-x-axis, umzuzu we-inertia wama-athomu amabili = 0. Ngakho-ke, inani lamadigri enkululeko yokunyakaza kokujikeleza = 2.
Amandla ajwayelekile e-molecule ngayinye yegesi ye-diatomic yile:
3 (1/2 kT) + 2 (1/2 kT) = 5/2 kT = 5/2 n R T.
Umthamo wokushisa wama-molecule egesi e-diatomic:
C = 5/2 R = 5/2 (8.315 J / mol. K) = 20.79 J / Kg. K
Umthamo wokushisa wama-molecule otholwe ngokwethiyori mkhulu kunomthamo wokushisa wama-molecule egesi e-diatomic atholwe ngokuhlolwa.
Uma kwenziwa ukunyakaza kokudlidliza, ama-molecule egesi e-diatomic anezinhlobo ezimbili zamandla, okungukuthi amandla e-kinetic kanye namandla e-elastic potential. Ngakho-ke, inani lamadigri enkululeko yokunyakaza kokudlidliza = 2.
Amandla ajwayelekile e-molecule ngayinye yegesi ye-diatomic yile:
3 (1/2 kT) + 2 (1/2 kT) + 2 (1/2 kT) = 7/2 kT = 7/2 n R T.
Umthamo wokushisa wama-molecule egesi e-diatomic:
C = 7/2 R = 7/2 (8,315 J / mol. K) = 29.1 J / Kg. K
Umphumela wokunyakaza kokudlidliza enanini lomthamo wokushisa wama-molecule egesi e-diatomic uncike nasebangeni lokushisa (T). Ukuhlolwa okwenziwe ngaphambili kwenzeka ebangeni lokushisa elingelikhulu kakhulu. Ukuhlolwa kwamuva nje okwenziwe ebangeni lokushisa elibanzi kubonisa ukuthi inani lomthamo wokushisa wama-molecule egesi lincike nasebangeni lokushisa. Ukuze siqonde kangcono le nkinga, ake sibukeze ukuhlukahluka komthamo wokushisa wama-molecule egesi e-hydrogen emazingeni okushisa ahlukene.
I-Hydrogen (H₂)) ifaka igesi ye-diatomic. Isithombe esiseceleni sibonisa ukwehluka kwamandla okushisa kwama-molecule egesi ye-hydrogen emazingeni okushisa ahlukene. Inani lamandla okushisa kwama-molecule lingu-5/2 R = 20.79 J/Kg. I-K isebangeni lokushisa eliphakathi kuka-250 K kuya ku-750 K. Ngaphansi kuka-250 K, amandla okushisa ama-molecule egesi ye-hydrogen ancipha njalo aze afike ku-3/2 R = 12.47 J/Kg. K. Ngokuphambene nalokho, ngaphezu kuka-750 K, amandla okushisa ama-molecule egesi ayanda ngezikhathi ezithile aze afike ku-7/2 R = 29.1 J/Kg. K.
Ngokusekelwe kuleli qiniso, singasho ukuthi emazingeni okushisa aphansi, ama-molecule egesi enza ukunyakaza kokuhumusha kuphela. Ngemva kokwenyuka kwezinga lokushisa, ama-molecule amasha egesi enza ukunyakaza kokujikeleza. Emazingeni okushisa aphezulu, ama-molecule egesi ashayisana ukuze ama-athomu adlidlize. Ngakho-ke, lezi zinhlobo ezintathu zokunyakaza zenziwa ngezigaba, okokuqala ukunyakaza kokuhumusha kuphela (izinga lokushisa eliphansi), ngemva kwalokho ukuhumusha + ukujikeleza (izinga lokushisa eliphakathi) kanye nokuguqulwa kokugcina + ukujikeleza + ukudlidliza (izinga lokushisa eliphezulu). Ukunyakaza kokudlidliza kwenzeka kuphela uma ama-molecule egesi eshayisana.
Izimo ezinjengalezi azenzeki nje kuphela kugesi we-hydrogen, kodwa nakwamanye amagesi. Kusukela ekuhlolweni okwenziwa ososayensi, amandla okushisa ama-molecule egesi nawo avame ukushintsha ngokushisa. Izinguquko ezenzekayo zifana nalezo ezitholwa yigesi we-hydrogen, kodwa ngenxa yokuthi isakhiwo kugesi ngayinye sihlukile (inani nohlobo lwama-athomu kuhlukile), izinguquko emandleni okushisa nazo zenzeka emazingeni okushisa ahlukene.
Ithiyori ye-energy equipment ithi amandla aphelele kumele ahlukaniswe ngokulinganayo ngesilinganiso ngasinye senkululeko. Amandla engeziwe atholakala ngama-molecule egesi awasatshalaliswa ngokulinganayo ngesilinganiso ngasinye senkululeko kodwa ahlukaniswa kancane kancane. Ngaphezu kwalokho, i-equation yamandla okushisa kwama-molecule egesi esiwathole ngokwethiyori ngokusekelwe ku-kinetic theory yegesi,
ithi amandla okushisa e-molecule ancike kuphela ku-R (1/2 R ngezinga ngalinye lenkululeko). Amandla okushisa e-molecule nawo athintwa yizinga lokushisa (T).
Okokuqala, kungaphethwa ngokuthi i-equipartition theorem isuselwa ku-classical statistical mechanics, esekelwe emithethweni ye-Newtonian mechanics. Okwesibili, i-kinetic theory yegesi esiyisebenzisayo ekuchazeni ukunyakaza kwama-molecule egesi nayo isekelwe emithethweni ye-Newtonian mechanics. Ngenxa yokuthi i-energy equipartition theorem kanye ne-kinetic theory yamagesi kuphuliwe, kungaphethwa ngokuthi imithetho kaNewton ye-mechanics ayikwazi ukuchaza ukunyakaza okwenzeka ezingeni le-athomu noma lama-molecule. Ngamanye amazwi, i-Newtonian mechanics noma i-classical mechanics ingachaza kuphela ukunyakaza kwezinto ezinkulu.
