ʻŌlelo ke kumumanaʻo kinetic ua hana ʻia kēlā me kēia mea me nā ʻātoma a i ʻole nā molekala a neʻe mau nā ʻātoma a i ʻole nā molekala me ka mālama ʻole. Hoʻohālikelike kēia manaʻo o ke kumumanaʻo kinetic i ke kūlana a me ke kūlana o ka ʻātoma a i ʻole ka molekala o ka mea hoʻohui kinoea. He nāwaliwali ka ikaika o ka huki ʻana ma waena o nā ʻātoma a i ʻole nā molekala e hana ana i ke kinoea i hiki i nā ʻātoma a i ʻole nā molekala ke neʻe manuahi.
I ka neʻe ʻana, loaʻa i nā ʻātoma a i ʻole nā molekala ka wikiwiki. Loaʻa pū kekahi nuipa i nā ʻātoma a i ʻole nā molekala. No ka mea, loaʻa iā ia ka nuipa (m) a me ka wikiwiki (v), a laila loaʻa i ka ʻātoma a i ʻole ka ikehu kinetic (KE) a me ka momentum (p). Ikehu kinetic: KE = 1/2 mv 2. ʻOiai ʻo momentum: p = m v. Ma waho aʻe o ka ikehu kinetic a me ka momentum, aia kekahi ikaika (F). Ke neʻe manuahi nei, pono e kū mai nā collisions. No laila, piʻi ka ikaika ma muli o nā loli o ka momentum ke kū mai kahi collision. ʻO ka ikehu kinetic, momentum, a me nā ikaika impulse ke kumu o kā mākou kūkākūkā ʻana i nā dynamics (nā kānāwai o ka neʻe ʻana, impulse, a me ka momentum). Hiki iā mākou ke ʻōlelo e pili ana ke kumumanaʻo kinetic o nā kinoea i ka dynamics ma ka pae atomic a molekala paha.
Manaʻo Kinoea Kūpono (ma muli o nā waiwai macroscopic o ke kinoea)
Ma ke kūkākūkā ʻana i nā kānāwai o ke kinoea, ua wehewehe ʻia e pili ana i ʻekolu mau nui e hōʻike ana i ke ʻano macroscopic o ke kinoea maoli. ʻO nā nui ʻekolu i nīnau ʻia ʻo ia ka Mahana (T), ka Leo (V) a me ke kaomi (P). Ua ʻōlelo ʻia ka pilina ma waena o kēia mau nui macroscopic ʻekolu ma ke Kānāwai o Boyle, ke kānāwai o Charles, a me ke kānāwai o Gay Lussac. E ʻoluʻolu e hoʻomaopopo he pili wale kēia mau kānāwai ʻekolu i ke kinoea maoli nona ke kaomi a me ka density (density = mass/volume) ʻaʻole nui loa. Pili wale nō kēia mau kānāwai ʻekolu i ke kinoea maoli nona ka mahana ʻaʻole kokoke i ka paila.
ʻAʻole pili ke kānāwai o Boyle, ke kānāwai o Charles, a me ke kānāwai o Gay-Lussac i nā kūlana kinoea maoli a pau i hiki ai iā mākou ke hana i kahi kumu hoʻohālike kinoea kūpono. ʻAʻole noho ke kinoea kūpono i ke ola o kēlā me kēia lā; ʻo ke kinoea kūpono wale nō ke ʻano kūpono i hana ʻia e kōkua i kā mākou loiloi, e like me nā kino paʻa a me nā kino wai kūpono. No laila, ke manaʻo nei mākou e pili ke kānāwai o Boyle, ke kānāwai o Charles a me ke kānāwai o Gay-Lussac i nā kūlana kinoea kūpono a pau. ʻO ke ola ʻana o kahi kumu hoʻohālike kinoea kūpono e kōkua iā mākou e nānā hou i ka pilina ma waena o nā nui macroscopic o ke kinoea.
Ua hōʻike ʻia ke kānāwai kinoea kūpono ma nā hoʻohālikelike ʻelua, PV = nRT (ke kānāwai kinoea kūpono i ka helu o nā mole) a me PV = NkT (ke kānāwai kinoea kūpono i ka helu o nā mole). Manaʻo mākou ua kūlike ke kinoea kūpono i kēia mau hoʻohālikelike ʻelua. I nā huaʻōlelo ʻē aʻe, pili ke kānāwai kinoea kūpono i nā kūlana kinoea kūpono āpau, inā paha he nui ke kaomi kinoea kūpono a i ʻole ka nuipa a i ʻole ke kokoke ka mahana kinoea kūpono i ka paila. I ka hoʻohālikelike ʻana, ʻaʻole pili ke kānāwai kinoea kūpono i nā kūlana kinoea maoli āpau. Pili wale ke kānāwai kinoea kūpono i ka wā ʻaʻole nui loa ke kaomi a me ka nui o ke kinoea maoli. Pili wale nō ke kānāwai kinoea kūpono i ka wā ʻaʻole kokoke ka mahana o ke kinoea maoli i ka paila. Ma muli o kēia wehewehe pōkole, hiki iā mākou ke ʻōlelo he like nā waiwai o ke kinoea maoli me ke kinoea kūpono i ka wā wale nō ka nui maoli,
a ʻaʻole nui loa ke kaomi kinoea a i ka wā ʻaʻole kokoke ka mahana kinoea maoli i kahi e paila ai.
Ua nānā hou ʻia ke kumumanaʻo o ke kinoea kūpono i wehewehe ʻia ma luna nei ma muli o nā waiwai macroscopic. ʻOiai he kumu hoʻohālike kūpono wale nō ke kinoea kūpono, ua manaʻo ʻia ke kinoea kūpono he kinoea i loaʻa nā ʻātoma a i ʻole nā mole e neʻe manuahi ana. No laila, he mea maikaʻi inā kūkākūkā pū mākou i ke kumumanaʻo kinoea kūpono mai kahi kuanaʻike microscopic.
Manaʻo Kinoea Kūpono (ma muli o nā waiwai microscopic o ke kinoea)
Eia kekahi mau wehewehe pōkole e wehewehe ana i nā kūlana microscopic o ke kinoea kūpono, i hoʻokumu ʻia ma ke Kumumanaʻo Gas Kinetic:
1. Aia kahi kinoea kūpono i nā ʻāpana, i kapa ʻia he mau molekala. Hiki i nā molekala kinoea kūpono ke hoʻokomo i hoʻokahi ʻātoma a i ʻole kekahi mau ʻātoma. Loaʻa i kēlā me kēia molekala ka nuipa (m) a neʻe ma ke ʻano hewa i kekahi ʻaoʻao ma kahi wikiwiki kikoʻī (v).
2. ʻOi aku ke kiʻekiʻe o ka mamao ma waena o kēlā me kēia molekala ma mua o ke anawaena o kēlā me kēia molekala.
3. Hoʻolohe kēia mau molekala i nā kānāwai o ka neʻe ʻana a launa pū kekahi me kekahi ke kū mai nā kuʻi ʻana.
4. ʻO nā kuʻi ʻana ma waena o nā molekala a me nā molekala a i ʻole ma waena o nā molekala me ka paia o ka ipu ka kuʻi kūpono, a hana ʻia kēlā me kēia kuʻi ʻana i kahi manawa pōkole.
I ke kuʻi kūpono, pili ke kānāwai o ka mālama ʻana i ka ikehu (ikehu ma mua o ke kuʻi = ikehu ma hope o ke kuʻi) a me ke kānāwai o ka mālama ʻana i ka momentum (momentum ma mua o ke kuʻi = momentum ma hope o ke kuʻi).
ʻO ka loiloi o ke kuʻi impulse no ke kumumanaʻo kinetic o nā kinoea
E nānā hou i ka pilina quantitative ma waena o nā nui macroscopic a me nā nui microscopic o ke kinoea. ʻO nā nui e hōʻike ana i ke ʻano macroscopic o ke kinoea, ʻo ia ka mahana (T), ka nui (V) a me ke kaomi (P). ʻOiai ʻo nā nui e hōʻike ana i ke ʻano microscopic o ke kinoea, ʻo ia ka wikiwiki a i ʻole ka wikiwiki (v), ka momentum (p), ka ikaika (F) a me ka ikehu kinetic (EK) o nā ʻātoma a i ʻole nā molekala e hana ana i ke kinoea.
Ke nānā hou nei mākou i kekahi mau molekala kinoea i loko o kahi pahu pani. ʻO ka lōʻihi o ka ʻaoʻao o ka pahu = l a me ka ʻāpana ʻoki = A.
Loaʻa i nā molekala ke kaumaha (m) a, i ka neʻe ʻana, loaʻa i ka molekala ka wikiwiki (v). No ka mea ua pani ʻia ka ipu, aia kahi hiki ke kuʻi ma waena o nā molekala a me ka paia o ka ipu hao nona ka ʻili o A.
I mea e hoʻomaʻalahi ai i ka nānā ʻana, ʻo ke kuʻi wale nō e kū nei ma ka paia hema (ka paia e kūlike ana me ka axis z). ʻO ka mea mua, kūkākūkā mākou i nā kuʻi i ʻike ʻia e hoʻokahi molekala. Kāhea iā ia he molekala 1. ʻO ka nuipa molekala = m1 a ʻo ka wikiwiki o ka neʻe ʻana = v1. Ua hoʻonohonoho ʻia ke kuhikuhi o ka neʻe ʻana i ka hema i mea maikaʻi ʻole, ʻoiai ua hoʻonohonoho ʻia ke kuhikuhi o ka neʻe ʻana i ka ʻākau i mea maikaʻi ʻole.
Hiki iā kākou ke manaʻo ma mua o ke kuʻi ʻana i ka paia o ka ipu, ua kūlike ka neʻe ʻana o ka molekala me ke axis-x a me ke kuhikuhi o ka neʻe ʻana i ka hema. No laila, aia kahi ʻāpana o ka wikiwiki ma ke axis-x he maikaʻi ʻole (-v1x). No ka mea, he nuipa kona (m1) a me ka wikiwiki (-v1x), loaʻa i ka molekala ka momentum (p1 = -m1 v1x). ʻO kēia ka momentum mua. Ke kuʻi ʻia me ka paia, hāʻawi ka molekala i kahi ikaika hana ma ka paia. No ka mea aia kahi ikaika hana, hāʻawi ka paia i kahi ikaika pane. ʻO ka ikaika pane mai ka paia ke kumu e hōʻike ʻia ai ka molekala ma ka ʻākau. Ma muli o ke kuhikuhi o ka neʻe ʻana i ka ʻākau, he maikaʻi ka ʻāpana wikiwiki molekala (v1x). ʻO ka momentum molekala ma hope o ke kuʻi ʻana he p2 = m1 v1xʻO kēia ka manawa hope loa.
ʻO ka nui o ka loli o ka momentum ma muli o nā collisions:
Ka nui o ka momentum = ka momentum hope loa—ka momentum mua
huina p = p 2 – p 1
huina p = m 1 v 1x – (-m 1 v 1x )
huina p = 2m 1 v 1x
2m 1 v 1x = ka holoʻokoʻa o ka momentum no hoʻokahi kuʻi ʻana. No ka mea, ʻo nā kuʻi molekala ka kuʻi kūpono, ʻaʻole i hoʻokahi wale nō kuʻi ʻana, akā, pinepine ʻia. I ka kuʻi kūpono, pili ke kānāwai o ka mālama ʻana i ka ikehu a me ke kānāwai o ka mālama ʻana i ka momentum. Ikehu a me ka momentum ma mua o ke kuʻi ʻana = ikehu a me ka momentum ma hope o ke kuʻi ʻana. No laila, ʻaʻole e pau ka neʻe ʻana o ka molekala (ikehu pau ʻole). ʻAʻole hoʻi e emi ka wikiwiki o ka molekala (hoʻomau i ka momentum).
Ma hope o ke kuʻi ʻana me ka paia hema, neʻe ka molekala i ka ʻākau a hiki i ka paʻi ʻana i ka paia ʻākau. Ma hope o ke kuʻi ʻana i ka paia ʻākau, neʻe hou ka molekala i ka hema a kuʻi hou i ka paia hema. No ka mea, ʻo ka lōʻihi o ka ʻaoʻao o ka pahu = l, a laila ma hope o ke kuʻi ʻana i ka paia hema no ka manawa mua, e hele ka molekala i kahi mamao o 2l ma mua o ke kuʻi ʻana i ka paia hema no ka lua o ka manawa. Ke neʻe a hiki i ka 2l, pono nā molekala e koi i kahi manawa kikoʻī ( Δt ). ʻO ka nui o ka manawa ( Δt ) e pono ai ka molekala e neʻe a hiki i ka 2l, he makemakika ia:
ʻO Δt ka manawa ma waena o kēlā me kēia kuʻi ʻana. Ke kuʻi ʻana i kahi pā, hāʻawi ka molekala i kahi ikaika hana ma ka pā. Ma muli o ka ikaika hana, hāʻawi ka pā i kahi ikaika hopena. ʻO ke ola ʻana o kēia ikaika hopena e hoʻoneʻe hou i ka molekala i ka ʻākau. I kēia hihia, loli ke kuhikuhi o ka neʻe ʻana o ka molekala. I ka wā mua, neʻe ka molekala i ka hema (-v1x), ma hope o ke kuʻi ʻana i ka pā, neʻe ka molekala i ka ʻākau (v 1x ). ʻO nā loli i ke kuhikuhi o ka neʻe ʻana ke kumu o nā loli i ka momentum (momentum hope loa - momentum mua = m 1 v 1x - (-m 1 v 1x ) = 2m 1 v 1x ). Hiki iā mākou ke ʻōlelo ua hana ʻia ka loli o ka momentum ma muli o ka ikaika holoʻokoʻa i hāʻawi ʻia e ka pā. ʻO ka nui o ka ikaika holoʻokoʻa i hāʻawi ʻia e ka pā, ma ke ʻano makemakika:
Ma ka pahu ma luna, hoʻokahi wale nō molekala i wehewehe ʻia. ʻAʻole kēia manaʻo he hoʻokahi wale nō molekala kinoea i loko o ka pahu. ʻO ka ʻoiaʻiʻo, he nui nā molekala kinoea. ʻO ka nui o ka ikaika holoʻokoʻa no nā molekala kinoea āpau i loko o ka pahu, ma ke ʻano makemakika:
F = F 1 + F 2 + F 3 + ….. + F n
F 1 = ka ikaika holoʻokoʻa no ka molekala 1
F 2 = ka ikaika holoʻokoʻa no ka molekole 2
F 3 = ka ikaika holoʻokoʻa no ka molekole 3
…… = a pēlā aku
F n = ka ikaika holoʻokoʻa no nā molekala 4
n = ka molekole hope loa.
m1 = ka nuipaʻa molekala 1, m2 = ka nuipaʻa molekala 2, m3 = ka nuipaʻa molekala 3, mn = ka nuipaʻa o ka molekala hope loa. m1 +m2 +m3 + ….. + mn = m (ke kaumaha o ke kinoea i loko o ka pahu). l = ka lōʻihi o ka ʻaoʻao o ka pahu.
ʻO v 12x = ka wikiwiki o ka molekala 1, v 22 x = ka wikiwiki o ka molekala 2, v 33 x = ka wikiwiki o ka molekala 3, v n2 x = ka wikiwiki o ka molekala hope loa. ʻOkoʻa ka wikiwiki o kēlā me kēia molekala, no laila pono mākou e helu i ka wikiwiki awelika o nā molekala āpau. No ka helu ʻana i ka wikiwiki awelika o kahi molekala, hiki iā mākou ke puʻunaue i ka wikiwiki o nā molekala āpau e ka helu o nā molekala. Ma ke kumumanaʻo kinetic o ke kinoea, hāʻawi pinepine ʻia ka helu o nā molekala i ka hōʻailona N. Ma ke ʻano makemakika, ua kākau ʻia ka wikiwiki awelika o nā molekala āpau:
Hoʻohui mākou i ka hoohalike b me ka hoohalike a:
F = ikaika, m = nuipa o nā kinoea, l = ka lōʻihi o ka ʻaoʻao o ka pahu, N = helu o nā molekala.
Ma ka wehewehe ʻana ma mua, ua manaʻo ʻia ka neʻe ʻana o nā molekala e kūlike ana me ke axis-x. Hana ʻia kēia manaʻo mua e maʻalahi ai kā mākou loiloi. ʻO ka ʻoiaʻiʻo, ʻaʻole neʻe nā molekala kinoea a pau i loko o kahi pahu i kekahi ʻaoʻao ma ke ʻano random. No ka mea, hana random ʻia ka neʻe ʻana, me ka loaʻa ʻana o kahi ʻāpana wikiwiki awelika ma ke axis-x, loaʻa pū kekahi ʻāpana wikiwiki awelika i ka molekala ma ke axis-y a i ʻole ke axis-z. No laila, ʻo ka wikiwiki awelika o kahi molekala kinoea = ka huina o nā ʻāpana o ka wikiwiki awelika ma ke axis-x, axis-y, a me ke axis-z. Ma ke ʻano makemakika:
Ma muli o ka neʻe ʻana o nā molekala ma ke ʻano hewa, ua like ka nui o nā ʻāpana wikiwiki ma ke axis-x, axis-y, a me ke axis-z. Ma ke ʻano makemakika:
Hoʻohui mākou i ka hoohalike 2 me ka hoohalike 1 :
Hoʻohui mākou i ka hoohalike 3 me ka hoohalike n c :
ʻO F = ka nui o ka ikaika i hoʻokomo ʻia e nā molekala kinoea ma ka paia o ka pahu, nona ka ʻili o A.
ʻO ka pilina ma waena o ke kaomi (P) a me ka nui microscopic
ʻO ke kaomi (P) kahi nui e hōʻike ana i ke ʻano macroscopic o ke kinoea. E nānā hou i ke kaomi ma muli o nā waiwai microscopic o ke kinoea. ʻO ka nui o ke kaomi i hāʻawi ʻia e ka mole kinoea ma ka paia nona ka ʻāpana cross-sectional A:
P = kaomi, N = helu o nā molekala kinoea, m = nuipa, v = Ka wikiwiki awelika o kahi molekala, V = ka nui o ka pahu
