Ua loaʻa mai ke kumumanaʻo equipartition ikehu e Clerk Maxwell me ka hoʻohana ʻana i ka mechanics helu. Ua kapa ʻia ʻo ia he theorem no ka mea ʻaʻohe hōʻoia ma o ka hoʻokolohua ʻana. ʻO ke ʻano o ka māhele ikehu he like ka hoʻokaʻawale ʻana o ka ikehu.
KE = ka ikehu kinetic unuhi awelika o nā molekala kinoea (Joule)
k = ke kūpaʻa o Boltzmann = 1.38 x 10-23 J/K
T = ka mahana paʻa o ka molekole kinoea kūpono (Kelvin)
Loaʻa ka ikehu kinetic Translational mai ka neʻe ʻana o ka translational nona nā ʻāpana wikiwiki ʻekolu, ʻo ia hoʻi ka ʻāpana wikiwiki ma ke axis-x, ke axis-y, a me ke axis-z. ʻEkolu mau ʻāpana o kēia wikiwiki, ma ia hihia aia kahi helu 3 ma ka hoohalike ma luna. Ua kapa ʻia kēlā me kēia ʻāpana o ka wikiwiki ʻo ke kekelē o ke kūʻokoʻa. No ka mea he ʻekolu mau ʻāpana o ka wikiwiki, he 3 kekelē o ke kūʻokoʻa ka ikehu kinetic translational.
ʻŌlelo ke kumumanaʻo equipartition ikehu e pono e puʻunaue like ʻia ka ikehu maoli ma nā kekelē āpau o ke kūʻokoʻa. No laila, ʻo ka ikehu awelika no kēlā me kēia kekelē o ke kūʻokoʻa he 1/2 kT.
Nā molekala kinoea monatomic
Hana nā molekula kinoea monatomic i ka neʻe unuhi wale nō i loaʻa i nā molekula kinoea monatomic he 3 degere o ke kūʻokoʻa.
ʻO ka ikehu kinetic awelika no kēlā me kēia mole kinoea monatomic:
3 (1/2 kT) = 3/2 kT = 3/2 nRT.
Ka mana wela o nā molekala kinoea monatomic:
C = 3/2 R = 3/2 (8.315 J / mol. K) = 12.47 J/Kg. K
Nā molekala kinoea diatomic
Ma waho aʻe o ka neʻe ʻana o ka unuhi, hana pū nā molekala kinoea diatomic i ka wili a me ka haʻalulu. ʻO ka helu o nā kekelē o ke kūʻokoʻa no ka neʻe ʻana o ka unuhi = 3. He aha ke kekelē o ke kūʻokoʻa no ka neʻe ʻana o ka wili a me ka haʻalulu?
ʻEkolu mau koʻi wili, ʻo ia hoʻi nā koʻi x, y, a me Z. ʻAʻole helu ʻia ka neʻe wili ma ke koʻi x no ka mea e kūlike ana nā ʻātoma ʻelua me ke koʻi o ka wili. Ke kūlike me ke koʻi x, ʻo ka manawa o ka inertia o nā ʻātoma ʻelua = 0. No laila, ʻo ka helu o nā kekelē o ke kūʻokoʻa no ka neʻe wili = 2.
ʻO ka ikehu awelika no kēlā me kēia molekala kinoea diatomic:
3 (1/2 kT) + 2 (1/2 kT) = 5/2 kT = 5/2 n R T.
Ka mana wela o nā molekala kinoea diatomic:
C = 5/2 R = 5/2 (8.315 J / mol. K) = 20.79 J / Kg. K
ʻOi aku ka nui o ka mana wela molekala i loaʻa ma ke kumumanaʻo ma mua o ka mana wela o nā molekala kinoea diatomic i loaʻa ma o nā hoʻokolohua.
I ka hana ʻana i ka neʻe haʻalulu, loaʻa i nā molekala kinoea diatomic ʻelua ʻano ikehu, ʻo ia hoʻi ka ikehu kinetic a me ka ikehu hiki ke elastic. No laila, ʻo ka helu o nā kekelē o ke kūʻokoʻa no ka neʻe haʻalulu = 2.
ʻO ka ikehu awelika no kēlā me kēia molekala kinoea diatomic:
3 (1/2 kT) + 2 (1/2 kT) + 2 (1/2 kT) = 7/2 kT = 7/2 n R T.
Ka mana wela o nā molekala kinoea diatomic:
C = 7/2 R = 7/2 (8,315 J / mol. K) = 29.1 J / Kg. K
ʻO ka hopena o ka neʻe haʻalulu ma ka waiwai o ka hiki ke wela o nā molekala kinoea diatomic e pili pū ana i ka pae mahana (T). ʻO nā hoʻokolohua i hana ʻia ma mua e hana ʻia ma kahi pae mahana ʻaʻole ākea loa. Hōʻike nā hoʻokolohua hou i hana ʻia ma kahi pae mahana ākea e pili pū ana ka waiwai o ka hiki ke wela o ka molekala kinoea i ka pae mahana. No ka hoʻomaopopo maikaʻi ʻana i kēia pilikia, e nānā hou kākou i ka ʻokoʻa o ka hiki ke wela o nā molekala kinoea hydrogen ma nā mahana like ʻole.
ʻO ka hydrogen (H₂) hoʻokomo pū ʻia ke kinoea diatomic. Hōʻike ke kiʻi ma ka ʻaoʻao i ka ʻokoʻa o ka hiki ke wela o nā molekala kinoea hydrogen ma nā mahana like ʻole. ʻO ka waiwai o ka hiki ke wela molekala he 5/2 R = 20.79 J/Kg. Aia ʻo K ma ka pae mahana ma kahi o 250 K a i 750 K. Ma lalo o 250 K, emi mau ka hiki ke wela o nā molekala kinoea hydrogen a hiki i ka hiki ʻana i 3/2 R = 12.47 J/Kg. K. I ka hoʻohālikelike ʻana, ma luna o 750 K, piʻi mau ka hiki ke wela o nā molekala kinoea a hiki i ka hiki ʻana i 7/2 R = 29.1 J/Kg. K.
Ma muli o kēia ʻoiaʻiʻo, hiki iā mākou ke ʻōlelo i nā mahana haʻahaʻa, hana wale nā mole kinoea i kahi neʻe unuhi. Ma hope o ka piʻi ʻana o ka mahana, hana nā mole kinoea hou i kahi neʻe wili. I nā mahana kiʻekiʻe, kuʻi nā mole kinoea kekahi i kekahi i mea e haʻalulu ai nā ʻātoma. No laila, hana ʻia kēia mau ʻano neʻe ʻekolu i nā pae, ʻo ka neʻe unuhi mua wale nō (mahana haʻahaʻa), ma hope o kēlā unuhi + wili (mahana waena) a ʻo ka hope unuhi + wili + haʻalulu (mahana kiʻekiʻe). Hana wale ʻia ka neʻe haʻalulu inā kuʻi nā mole kinoea kekahi i kekahi.
ʻAʻole wale nā hihia e like me kēia e hana ʻia i ke kinoea hydrogen, akā i nā kinoea ʻē aʻe pū kekahi. Mai nā hoʻokolohua i hana ʻia e nā kānaka ʻepekema, ʻo ka hiki ke wela o nā molekala kinoea e loli pū kekahi me ka mahana. Ua like nā loli e hana ʻia me nā mea i ʻike ʻia e ke kinoea hydrogen, akā no ka mea he ʻokoʻa ke ʻano o kēlā me kēia kinoea (ʻokoʻa ka helu a me ke ʻano o nā ʻātoma), hana pū nā loli i ka hiki ke wela ma nā pae mahana like ʻole.
ʻŌlelo ke kumumanaʻo equipartition ikehu e pono e puʻunaue like ʻia ka ikehu holoʻokoʻa no kēlā me kēia kekelē o ke kūʻokoʻa. ʻAʻole i puʻunaue like ʻia ka ikehu hou i loaʻa e nā molekala kinoea no kēlā me kēia kekelē o ke kūʻokoʻa akā ua puʻunaue mālie ʻia. Eia kekahi, ʻo ka hoohalike o ka hiki ke wela molekala o ke kinoea a mākou i loaʻa ai ma ke kumumanaʻo e pili ana i ke kumumanaʻo kinetic o ke kinoea,
ʻōlelo ʻia e hilinaʻi wale ana ka mana wela o ka molekala iā R (1/2 R no kēlā me kēia kekelē o ke kūʻokoʻa). Hoʻopilikia pū ʻia ka mana wela molekala e ka mahana (T).
Hiki ke hoʻoholo ʻia, ʻo ka mea mua, ua loaʻa ka theorem equipartition mai ka mechanics helu kuʻuna, kahi i hoʻokumu ʻia ma nā kānāwai o ka mechanics Newtonian. ʻO ka lua, ʻo ke kumumanaʻo kinetic o ke kinoea a mākou e hoʻohana ai i ka wehewehe ʻana i ka neʻe ʻana o nā molekala kinoea ua hoʻokumu pū ʻia ma nā kānāwai o ka mechanics Newtonian. Ma muli o ka uhaki ʻia ʻana o ka theorem equipartition ikehu a me ke kumumanaʻo kinetic o nā kinoea, hiki ke hoʻoholo ʻia ʻaʻole hiki i nā kānāwai mechanics o Newton ke wehewehe i nā neʻe e hana ʻia ma ka pae atomika a molekala paha. I nā huaʻōlelo ʻē aʻe, hiki i ka mechanics Newtonian a i ʻole ka mechanics kuʻuna ke wehewehe wale i ka neʻe ʻana o nā mea nui.
