ʻŌlelo ke kumumanaʻo kinetic o nā kinoea ua haku ʻia kēlā me kēia mea me nā ʻātoma a i ʻole nā molekala, a aia kēia mau ʻātoma a i ʻole nā molekala i ka neʻe mau ʻana, ka neʻe kaulele. Kūpono kēia kuhiakau kumumanaʻo kinetic i ke kūlana a me nā kūlana o nā ʻātoma a i ʻole nā molekala e hana ana i kahi kinoea. He nāwaliwali loa nā mana hoʻowalewale ma waena o nā ʻātoma a i ʻole nā molekala e hana ana i kahi kinoea, e ʻae ana i nā ʻātoma a i ʻole nā molekala e 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 he nuipa (m) a me ka wikiwiki (v), loaʻa i nā ʻātoma a i ʻole nā molekala ka ikehu kinetic (EK) a me ka momentum (p). Ikehu kinetic : EK = 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, e kū pono ana nā collisions. No laila, kū mai ka ikaika ma muli o ka loli o ka momentum ke hana ʻia kahi collision. E hoʻomanaʻo hou i ke kūkākūkā e pili ana i ka impulse a me ka momentum. ʻO ka ikehu kinetic, ka momentum a me ka ikaika impulse ke kumu o kā mākou kūkākūkā ʻana ma nā mea o ka dynamics (nā kānāwai o Newton, impulse a me ka momentum). Hiki iā mākou ke ʻōlelo ʻo ke kumumanaʻo kinetic o nā kinoea e hoʻopili maoli i ka ʻepekema o ka dynamics ma ka pae o nā ʻātoma a i ʻole nā molekala e hana ana i nā mea kinoea.
Manaʻo Kinoea Kūpono (ma muli o nā waiwai macroscopic o nā kinoea)
Ma ke kūkākūkā ʻana i nā kānāwai kinoea, ua wehewehe ʻia ʻekolu mau nui e wehewehe ana i nā waiwai macroscopic o nā kinoea maoli. ʻO kēia mau nui ʻekolu ʻo ia ka Mahana (T), ka Leo (V), a me ke Kaomi (P). Ua hōʻike 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. Pono e hoʻomaopopo ʻia e pili wale ana kēia mau kānāwai ʻekolu i nā kinoea maoli nona ke kaomi haʻahaʻa a me ka density (density = mass / volume). Pili wale nō kēia mau kānāwai ʻekolu i nā kinoea maoli nona nā mahana ʻaʻole i hoʻokokoke i ko lākou kiko 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, no laila hiki iā mākou ke hana i kahi kumu hoʻohālike kinoea kūpono. ʻAʻole noho nā kinoea kūpono i ke ola o kēlā me kēia lā; he mau ʻano kūpono wale nō lākou i hana ʻia e kōkua i kā mākou loiloi, e like me nā kino paʻa a me nā 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 i ka pilina ma waena o nā nui kinoea macroscopic.
Ua hōʻike ʻia ke kānāwai kinoea kūpono ma nā hoʻohālikelike ʻelua, ʻo ia hoʻi ʻo PV = nRT (ke kānāwai kinoea kūpono i nā mole) a me PV = NkT (ke kānāwai kinoea kūpono i nā mole). Manaʻo mākou e hoʻokō ana kahi kinoea kūpono i kēia mau hoʻohālikelike ʻelua. I nā huaʻōlelo ʻē aʻe, pili ke kānāwai kinoea kūpono i nā kūlana kinoea kūpono āpau, i ka wā e nui loa ai ke kaomi a i ʻole ka nui o ke kinoea kūpono a i ka wā e kokoke ana ka mahana o ke kinoea kūpono i ka pae paila. I ka ʻaoʻao ʻē aʻe, 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 pae paila. Ma muli o kēia wehewehe pōkole, hiki iā mākou ke ʻōlelo he like nā waiwai o nā kinoea maoli me nā kinoea kūpono i ka wā ʻaʻole nui loa ka nui a me ke kaomi o ke kinoea maoli a i ka wā ʻaʻole kokoke ka mahana o ke kinoea maoli i ka pae paila.
Ua nānā ʻia ke kumumanaʻo kinoea kūpono i wehewehe ʻia ma luna mai kahi kuanaʻike macroscopic. ʻOiai he kumu hoʻohālike kūpono wale nō ke kinoea kūpono, ua manaʻo ʻia nō ia he kinoea i haku ʻia me nā ʻātoma a i ʻole nā molekala e neʻe manuahi ana. No laila, he mea pono ke kūkākūkā pū i ke kumumanaʻo kinoea kūpono mai kahi kuanaʻike microscopic.
Manaʻo Kinoea Kūpono (ma muli o nā ʻano microscopic o nā kinoea)
Eia ka wehewehe pōkole e wehewehe ana i nā kūlana microscopic o kahi kinoea kūpono, i hoʻokumu ʻia ma ke Kinetic Theory of Gases:
1. Aia ke kinoea kūpono i nā ʻāpana, i kapa ʻia he mau molekala. He nui loa ka helu o nā molekala. Hiki i nā molekala kinoea kūpono ke loaʻa i hoʻokahi ʻātoma a i ʻole kekahi mau ʻātoma. Loaʻa i kēlā me kēia molekala kahi nuipa (m) a neʻe ma ke ʻano hewa i nā ʻaoʻao āpau ma kahi wikiwiki (v).
2. ʻOi aku 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 i ʻole ma waena o nā molekala a me nā paia o ka pahu he mau kuʻi elastic kūpono a hana ʻia kēlā me kēia kuʻi ʻana i loko o ka manawa pōkole loa.
I loko o kahi kuʻi elastic 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).
Loiloi Impulse-Collision no ke Kumumanaʻo Kinetic o nā Kinoea
E nānā hou i ka pilina quantitative ma waena o nā nui macroscopic a me microscopic o ke kinoea. ʻO nā nui e wehewehe ana i nā waiwai macroscopic o ke kinoea, ʻo ia ka mahana (T), ka nui (V), a me ke kaomi (P). I kēia manawa, ʻo nā nui e wehewehe ana i nā waiwai microscopic o ke kinoea, ʻo ia ka wikiwiki a i ʻole ka velocity (v), momentum (p), force (F), a me ka ikehu kinetic (EK) o nā ʻātoma a i ʻole nā molecule e hana ana i ke kinoea.
I mea e kōkua ai i ka loaʻa ʻana o kēia pilina, e noʻonoʻo kākou i kekahi mau molekala kinoea i loko o kahi pahu pani. ʻO ka lōʻihi o ka ʻaoʻao o ka pahu he l a ʻo kona wahi ʻāpana kea he A.
He nuipa ko nā molekala (m) a ke neʻe lākou he wikiwiki ko lākou (v). No ka mea ua pani ʻia ka ipu, aia kahi hiki ke kuʻi ma waena o nā molekala a me nā paia o ka ipu nona ka ʻilikai A.
I mea e hoʻomaʻalahi ai i ka nānā ʻana, e noʻonoʻo wale kākou i ke kuʻi ʻana e kū nei ma ka paia hema (ka paia e kūlike ana me ke axis z). E noʻonoʻo mua kākou i ke kuʻi ʻana i ʻike ʻia e kahi molekala hoʻokahi. E kapa kākou iā ia he molekala 1. ʻO kona nuipa he m1 a ʻo kona wikiwiki he v1 . Ua hoʻonohonoho ʻia ke kuhikuhi o ka neʻe ʻana i ka hema i ka maikaʻi ʻole, ʻoiai ua hoʻonohonoho ʻia ke kuhikuhi o ka neʻe ʻana i ka ʻākau i ka maikaʻi.
Hiki iā kākou ke manaʻo ma mua o ke kuʻi ʻana i ka paia o ka pahu, ua kūlike ka neʻe ʻana o ka molekala me ke axis-x a ʻo kona kuhikuhi o ka neʻe ʻana ma ka hema. No laila, aia kahi ʻāpana wikiwiki ma ke axis-x nona ka waiwai maikaʻi ʻole (-v1x ). No ka mea, he nuipa kona (m1) a me ka wikiwiki (-v1x), a laila loaʻa i ka molekala ka momentum (p1 = ‐m1 v1x). ʻO kēia ka momentum mua. Ke kuʻi ka molekala i ka paia, hoʻopuka ia i kahi ikaika hana ma ka paia. No ka mea aia kahi ikaika hana, hoʻopuka ka paia i kahi ikaika pane. ʻO ka ikaika pane mai ka paia ke kumu e lele ai ka molekala i ka ʻākau. No ka mea aia ke kuhikuhi o ka neʻe ʻana i ka ʻākau, he maikaʻi ka ʻāpana wikiwiki o ka molekala (v1x). ʻO ke momentum o ka molekala ma hope o ke kuʻi ʻana: p2 = m1 v1xʻO kēia ka momentum hope loa.
ʻO ka nui o ka loli o ka momentum ma muli o ke kuʻi ʻana:
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 nui o ka momentum no hoʻokahi kuʻi ʻana. No ka mea, he elastic kūpono nā kuʻi ʻana o nā molekala, ʻaʻole lākou e hana hoʻokahi wale nō akā hana hou ʻia. I nā kuʻi ʻana elastic kūpono, pili nā 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 nā molekala (mālama ʻia ka ikehu). ʻAʻole hoʻi e emi iho ka wikiwiki o nā molekala (mālama ʻia ka momentum).
Ma hope o ke kuʻi ʻana me ka paia hema, neʻe ka molekala i ka ʻākau a hiki i kona kuʻi ʻana me ka paia ʻākau. Ma hope o ke kuʻi ʻana me ka paia ʻākau, neʻe hou ka molekala i ka hema e kuʻi hou me ka paia hema. ʻOiai ʻo ka lōʻihi o ka ʻaoʻao o ka pahu = l, a laila ma hope o ke kuʻi ʻana me ka paia hema no ka manawa mua, e hele ka molekala i kahi mamao o 2l ma mua o ke kuʻi ʻana me ka paia hema no ka lua o ka manawa (2l = ka mamao hele a puni). Ke neʻe nei i kahi mamao o 2l, pono maoli ka molekala i kahi manawa kikoʻī (e kapa kākou iā ia he delta t). ʻO ka nui o ka manawa (delta t) e pono ai no ka molekala e neʻe i kahi mamao o 2l, ua kākau ʻia ma ke ʻano makemakika penei:
ʻO Delta t ka manawa ma waena o kēlā me kēia kuʻi ʻana. Ke kuʻi ka molekala i ka paia, hoʻopuka ia i kahi ikaika hana ma ka paia. No ka mea, loaʻa iā ia kahi ikaika hana, hoʻopuka ka paia i kahi ikaika hopena. ʻO ke alo 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 (-v 1x ), ma hope o ke kuʻi ʻana i ka paia, neʻe ka molekala i ka ʻākau (v 1x ). ʻO ka loli i ke kuhikuhi o ka neʻe ʻana ke kumu o ka loli o ka momentum (momentum hope loa - momentum mua = m1 v1x - (-m1 v1x) = 2m1 v1x). Hiki iā mākou ke ʻōlelo ua hana ʻia ka loli o ka momentum ma muli o ka ikaika holoʻokoʻa i hoʻopuka ʻia e ka paia. ʻO ka nui o ka ikaika holoʻokoʻa i hoʻopuka ʻia e ka paia, ma ke ʻano makemakika:
Hōʻike ka pahu ma luna i hoʻokahi wale nō molekala. 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 ma luna o nā molekala kinoea a pau i loko o ka pahu ma ke ʻano makemakika:
F = F1 + F2 + F3 +….. + Fn
F1 = ka ikaika holoʻokoʻa no ka molekala 1
F2 = ka ikaika holoʻokoʻa no ka molekala 2
F3 = ka ikaika holoʻokoʻa no ka molekala 3
…… = a pēlā aku
Fn = ka ikaika holoʻokoʻa no ka molekole 4
He nui loa ka helu o nā molekala, no laila kākau wale mākou i ka hōʻailona n. n = ka molekala hope loa.
m1 = ke kaumaha o ka molekala 1, m2 = ke kaumaha o ka molekala 2, m3 = ke kaumaha o ka molekala 3, mn = ke kaumaha 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. Pono nā molekala a pau e hele i ka l like.
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. He 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 nā molekala, hiki iā mākou ke puʻunaue i ka wikiwiki o nā molekala āpau e ka helu o nā molekala. Ma ke kumumanaʻo kinetic o nā 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 penei:
Ma ka wehewehe ʻana ma mua, ua manaʻo ʻia e neʻe like ana nā molekala me ke axis-x. Ua hana ʻia kēia kuhiakau e hoʻomaʻalahi i ka nānā ʻana wale nō. ʻO ka ʻoiaʻiʻo, ʻaʻole neʻe nā molekala kinoea a pau i loko o ka pahu i nā ʻaoʻao a pau me ka manaʻo ʻole. No ka mea, neʻe wale nō kā lākou neʻe ʻana, me ka loaʻa ʻana o kahi ʻāpana wikiwiki awelika ma ke axis-x, loaʻa pū kekahi ʻāpana wikiwiki awelika i nā molekala ma ke axis-y a i ʻole ke axis-z. No laila, ʻo ka wikiwiki awelika o nā molekala kinoea = ka huina o nā ʻāpana wikiwiki awelika ma ke axis-x, ke axis-y, a me ke axis-z. Ma ke ʻano makemakika, ua kākau ʻia penei:
Ma muli o ka neʻe ʻana o nā molekala me ka manaʻo ʻole, ua like ka nui o nā ʻāpana wikiwiki ma ke axis-x, axis-y, a me ke axis-z. Ma ke ʻano makemakika, ua kākau ʻia kēia penei:
ʻO F = ka nui o ka ikaika i hoʻokau ʻia e nā molekala kinoea ma nā paia o kahi pahu nona ka ʻilikai A.
Ka pilina ma waena o ke kaomi (P) a me nā nui microscopic
ʻO ke kaomi (P) kahi nui e hōʻike ana i nā waiwai macroscopic o ke kinoea. E noʻonoʻo i ke kaomi e pili ana i nā waiwai microscopic o ke kinoea. ʻO ka nui o ke kaomi i hoʻokau ʻia e nā molekala kinoea ma kahi paia me kahi ʻāpana kea A:
ʻIkepili:
P = Kaomi
N = Helu o nā molekole kinoea
m = ka nuipa
v = Ka wikiwiki awelika o nā molekala
V = ka nui o ka ipu
