Te ariā nekeneke o ngā hau

E ai ki te ariā nekeneke o ngā hau, he mea tito ia matū i ngā ngota, i ngā ngota rānei, ā, kei roto ēnei ngota, ngā ngota rānei i te nekehanga matapōkere tonu. E ōrite ana tēnei ariā nekeneke ki te āhuatanga me ngā tikanga o ngā ngota, ngā ngota rānei e hanga ana i te hau. He tino ngoikore ngā kaha kukume i waenganui i ngā ngota, ngā ngota rānei e hanga ana i te hau, e āhei ai ngā ngota, ngā ngota rānei ki te neke noa.

I te nekehanga, he tere tō ngā ngota, ngā ngota rānei. He papatipu anō hoki tō ngā ngota, ngā ngota rānei. Nā te mea he papatipu (m) me te tere (v), he pūngao nekeneke (EK) me te nekehanga (p) tō ngā ngota, ngā ngota rānei. Pūngao nekeneke : EK = 1⁄2 mv² ^. Ko te nekehanga : p = mv. Haunga te pūngao nekeneke me te nekehanga, kei reira anō te kaha (F). Ina neke noa, ka tino puta ngā tukinga. Nō reira ka puta te kaha nā te huringa o te nekehanga ina puta he tukinga. Kia mahara anō ki te kōrero mō te nekehanga me te nekehanga. Ko te pūngao nekeneke, te nekehanga me te kaha nekehanga te kaupapa matua o tā tātou kōrero i roto i te rauemi o te hihiri (ngā ture a Newton, te nekehanga me te nekehanga). Ka taea e tātou te kī ko te ariā nekeneke o ngā hau e whakamahi ana i te pūtaiao o te hihiri i te taumata o ngā ngota, ngā ngota rānei e hanga ana i ngā matū hau.

Ariā Hau Pai (i runga i ngā āhuatanga makaro o ngā hau)

I roto i te kōrero mō ngā ture hau, e toru ngā rahinga i whakamāramahia e whakaahua ana i ngā āhuatanga makaro o ngā hau tūturu. Ko ēnei rahinga e toru ko te Pāmahana (T), te Rōrahi (V), me te Pēhanga (P). Ko te whanaungatanga i waenga i ēnei rahinga makaro e toru e whakaatuhia ana i roto i te Ture a Boyle, te Ture a Charles, me te Ture a Gay-Lussac. Me mōhio ko ēnei ture e toru ka pā anake ki ngā hau tūturu he iti te pēhanga me te mātotoru (mātotoru = papatipu / rōrahi). Ka pā anake hoki ēnei ture e toru ki ngā hau tūturu kāore ō rātou pāmahana e tata ki tō rātou pūwāhi kohua.

Kāore te ture a Boyle, te ture a Charles, me te ture a Gay-Lussac e pā ki ngā āhuatanga hau tūturu katoa, nō reira ka taea e tātou te waihanga i tētahi tauira hau pai. Kāore ngā hau pai e noho ana i te ao o ia rā; he āhua tino tika noa iho ēnei i hangaia hei āwhina i tā tātou tātaritanga, he rite ki ngā tinana pakari me ngā wai pai. Nō reira, e whakaaro ana tātou ka pā te ture a Boyle, te ture a Charles, me te ture a Gay-Lussac ki ngā āhuatanga hau pai katoa. Mā te noho o tētahi tauira hau pai ka āwhina i a tātou ki te tirotiro i te whanaungatanga i waenga i ngā rahinga hau matawhānui.

E whakaatuhia ana te ture hau pai i roto i ngā whārite e rua, arā, ko PV = nRT (te ture hau pai i roto i ngā mole) me PV = NkT (te ture hau pai i roto i ngā ngota). E whakaaro ana tātou ka tutuki i tētahi hau pai ēnei whārite e rua. Arā, ka pā te ture hau pai ki ngā āhuatanga hau pai katoa, ina tino nui te pēhanga, te mātotoru rānei o te hau pai, me te mea hoki e tata ana te pāmahana o te hau pai ki te pūwāhi koropupū. I tetahi atu taha, kāore te ture hau pai e pā ki ngā āhuatanga hau tūturu katoa. Ka pā anake te ture hau pai ina kāore i te tino nui te pēhanga me te mātotoru o te hau tūturu. Ka pā anake hoki te ture hau pai ina kāore te pāmahana o te hau tūturu i te tata ki te pūwāhi koropupū. I runga i tēnei whakaahuatanga poto, ka taea e tātou te kī he rite ngā āhuatanga o ngā hau tūturu ki ngā hau pai ina kāore i te tino nui te mātotoru me te pēhanga o te hau tūturu, ā, ina kāore te pāmahana o te hau tūturu i te tata ki te pūwāhi koropupū.

Ko te ariā hau pai kua whakamāramahia i runga ake nei ka tirohia mai i te tirohanga whānui. Ahakoa he tauira pai noa iho te hau pai, e kiia tonu ana he hau i titoa mai i ngā ngota, i ngā ngota rānei e nekeneke noa ana. Nō reira, he mea pai kia matapakihia hoki te ariā hau pai mai i te tirohanga mōkitokito.

Ariā Hau Pai (e ahu mai ana i ngā āhuatanga moroiti o ngā hau)

Anei tētahi whakamārama poto e whakaahua ana i ngā āhuatanga moroiti o tētahi hau pai, e ahu mai ana i te Ariā Kinetic o ngā Hau:

1. He matūriki te hau pai, e kiia nei ko ngā ngota. He tino nui te maha o ngā ngota. Ka taea e ngā ngota hau pai te tito i te kotahi ngota, i ētahi ngota rānei. He papatipu (m) tō ia ngota, ā, ka neke matapōkeretia ki ngā ahunga katoa i tētahi tere (v).

2. He nui ake te tawhiti i waenganui i ia ngota i te whānui o ia ngota.

3. Ka whakarongo ēnei ngota ki ngā ture o te nekehanga, ā, ka taunekeneke tetahi ki tetahi ina puta he tukinga.

4. He tukinga tino pīngore ngā tukinga i waenga i ngā ngota, i waenga rānei i ngā ngota me ngā pakitara o te ipu, ā, he poto noa te wā e puta ai ia tukinga.

I roto i te tukinga tino pīataata, ka pā te ture tiaki pūngao (pūngao i mua i te tukinga = pūngao i muri i te tukinga) me te ture tiaki o te nekehanga (nekehanga i mua i te tukinga = nekehanga i muri i te tukinga).

Arotake i te Tukinga-Whakaoho mō te Ariā Kinetic o ngā Hau

Arotakehia te whanaungatanga tauanga i waenga i ngā rahinga makaro me ngā rahinga moroiti o te hau. Ko ngā rahinga e whakaahua ana i ngā āhuatanga makaro o te hau ko te pāmahana (T), te rōrahi (V), me te pēhanga (P). I taua wā, ko ngā rahinga e whakaahua ana i ngā āhuatanga moroiti o te hau ko te tere, te tere rānei (v), te nekehanga (p), te kaha (F), me te pūngao nekeneke (EK) o ngā ngota, o ngā ngota rānei e hanga ana i te hau.

Hei āwhina i te whakatau i tēnei whanaungatanga, me whakaaro tātou ki ētahi ngota hau i roto i tētahi ipu kua kati. Ko te roa o te taha o te pouaka he l, ā, ko tōna horahanga whakawhiti he A.

He papatipu (m) tō ngā ngota ngota, ā, he tere (v) tō rātou ina neke. Nā te mea kua kati te ipu, tera pea ka tukinga ngā ngota ngota me ngā pakitara o te ipu, ko te horahanga mata he A.

Hei whakangawari i te tātari, ka whakaarohia noa e tātou te tukinga e puta ana i te pakitara maui (te pakitara e whakarara ana ki te tuaka-z). Tuatahi, me whakaaro tātou ki te tukinga e pā ana ki tētahi ngota kotahi. Me kī ko te ngota 1. Ko tōna papatipu he m1 _{, ā,} ko tōna tere he v1 _. Ko te ahunga nekehanga ki te taha maui kua whakatakotoria ki te kino, ko te ahunga nekehanga ki te taha matau kua whakatakotoria ki te pai.

Ka taea e tātou te whakaaro i mua i te pānga ki te pakitara o te ipu, he whakarara te nekehanga o te ngota ngota ki te tuaka-x, ā, ko tōna ahunga nekehanga kei te taha maui. Nō reira, he wāhanga tere kei runga i te tuaka-x he uara kino (-v_1x Nā te mea he papatipu tōna (m₁) me te tere (-v_1x), kātahi ka whai nekehanga te ngota ngota (p₁ = ‐m₁ v_1x). Koinei te nekehanga tīmatanga. Ina pā te ngota ki te pakitara, ka whakamahia he kaha mahi ki te pakitara. Nā te mea he kaha mahi, ka whakamahia e te pakitara he kaha tauhohenga. Mā te kaha tauhohenga mai i te pakitara ka peke te ngota ki te taha matau. Nā te mea kei te taha matau te ahunga o te nekehanga, he pai te wāhanga tere o te ngota (v_1xKo te nekehanga o te ngota i muri i te tukinga ko: p₂ = m₁ v_1xKoinei te nekehanga whakamutunga.

Ko te rahi o te huringa o te nekehanga nā te tukinga ko:

Te nekehanga katoa = te nekehanga whakamutunga – te nekehanga tīmatanga

p katoa = p ₂ – p ₁

p katoa = m ₁ v _1x ‐ (‐m ₁ v _1x )

p katoa = 2m ₁ v _1x

2m ₁ v _1x = te katoa o te nekehanga mō te tukinga kotahi. Nā te mea he tino pīngore ngā tukinga ngota, kāore i te kotahi noa te wā e puta ai engari he maha tonu. I roto i ngā tukinga tino pīngore, ka pā ngā ture tiaki pūngao me te ture tiaki nekehanga. Ko te pūngao me te nekehanga i mua i te tukinga = te pūngao me te nekehanga i muri i te tukinga. Nō reira, e kore rawa ngā ngota e mutu te neke (ka tiakina te pūngao). Kāore hoki te tere o ngā ngota e heke (ka tiakina te nekehanga).

I muri i te tukinga ki te pakitara maui, ka neke te ngota ki te taha matau tae noa ki te tukinga ki te pakitara matau. I muri i te tukinga ki te pakitara matau, ka hoki te ngota ki te taha maui ki te tukinga anō ki te pakitara maui. Nā te mea ko te roa o te taha o te pouaka = l, kātahi i muri i te tukinga ki te pakitara maui mō te wā tuatahi, ka haere te ngota i te tawhiti o te 2l i mua i te tukinga ki te pakitara maui mō te wā tuarua (2l = tawhiti haere hoki). Ina nekehia te tawhiti o te 2l, me tino hiahia te ngota ki tētahi wā motuhake (me kī tātou ko te delta t). Ko te nui o te wā (delta t) e hiahiatia ana kia neke te ngota i te tawhiti o te 2l, ka tuhia penei i te pāngarau:

Ko te Delta t te wā i waenganui i ia tukinga. Ina pā te ngota ki te pakitara, ka whakamahia he kaha mahi ki te pakitara. Nā te mea ka whiwhi i te kaha mahi, ka whakamahia e te pakitara he kaha tauhohenga. Mā te noho mai o tēnei kaha tauhohenga ka neke anō te ngota ki te taha matau. I tēnei wā, ka rerekē te ahunga o te nekehanga o te ngota. I te tīmatanga, ka neke te ngota ki te taha maui (-v _1x ), i muri i te pā ki te pakitara, ka neke te ngota ki te taha matau (v _1x ). Mā te huringa o te ahunga nekehanga ka puta he huringa o te nekehanga (nekehanga whakamutunga - nekehanga tīmatanga = m1 v1x - (-m1 v1x) = 2m1 v1x). Ka taea e tātou te kī ko te huringa o te nekehanga ka puta nā te kaha katoa i whakamahia e te pakitara. Ko te rahi o te kaha katoa i whakamahia e te pakitara, i runga i te pāngarau:

Kotahi anake te ngota e whakaatuhia ana i te pouaka i runga ake nei. Ehara i te mea kotahi anake te ngota hau i roto i te pouaka. Inaa, he maha ngā ngota hau. Ko te rahi o te kaha katoa i runga i ngā ngota hau katoa i roto i te pouaka koia tēnei:

F = F1 + F2 + F3 +….. + Fn

F1 = te kaha katoa mō te ngota 1

F2 = te kaha katoa mō te ngota 2

F3 = te kaha katoa mō te ngota 3

…… = me ērā atu anō

Fn = te kaha katoa mō te ngota ngota 4

He tino nui te maha o ngā ngota, nō reira ka tuhia noa e mātou te tohu n. n = te ngota whakamutunga.

m1 = te papatipu o te ngota 1, m2 = te papatipu o te ngota 2, m3 = te papatipu o te ngota 3, mn = te papatipu o te ngota whakamutunga. m1 + m2 + m3 + ….. + mn = m (te papatipu o te hau i roto i te pouaka). l = te roa o te taha o te pouaka. Me haere ngā ngota katoa i te l kotahi.

v _12x = te tere o te ngota 1, v _{22 x} = te tere o te ngota 2, v _{33 x} = te tere o te ngota 3, v _{n2 x} = te tere o te ngota whakamutunga. He rerekē te tere o ia ngota, nō reira me tatau te tere toharite o ngā ngota katoa. Hei tatau i te tere toharite o ngā ngota, ka taea e tātou te wehewehe i te tere o ngā ngota katoa mā te maha o ngā ngota. I roto i te ariā nekeneke o ngā hau, ko te maha o ngā ngota ka hoatu ki te tohu N. Mā te pāngarau, ka tuhia te tere toharite o ngā ngota katoa penei:

I te whakamārama o mua, i whakaarohia ka neke ngā ngota i te taha whakarara o te tuaka-x. I hangaia tēnei whakaaro hei whakahaere noa i te tātari. Ko te mea pono, kāore ngā ngota hau katoa i roto i te pouaka e neke matapōkere ana i ngā taha katoa. Nā te mea ka puta matapōkere tā rātou nekehanga, me te whai i te wāhanga tere toharite i te tuaka-x, he wāhanga tere toharite anō hoki kei ngā ngota i te tuaka-y, i te tuaka-z rānei. Nō reira, ko te tere toharite o ngā ngota hau = te tapeke o ngā wāhanga tere toharite i te tuaka-x, te tuaka-y, me te tuaka-z. I roto i te pāngarau, ka tuhia penei:

Nā te mea ka neke matapōkere ngā ngota, he rite tonu te rahi o ngā wāhanga tere i runga i te tuaka-x, te tuaka-y, me te tuaka-z. Mā te pāngarau, ka tuhia tēnei penei:

F = te rahi o te kaha e pā ana ki ngā ngota hau i runga i ngā pakitara o tētahi ipu he A te horahanga mata.

Te Hononga i waenga i te Pēhanga (P) me ngā Rahinga Makariri

Ko te pēhanga (P) he rahinga e tohu ana i ngā āhuatanga makaro o te hau. Whakaarohia te pēhanga i runga i ngā āhuatanga makaro o te hau. Ko te rahi o te pēhanga e tukuna ana e ngā ngota hau ki runga i te pakitara he horahanga whakawhiti A ko:

Ngā Mōhiohio:

P = Pēhanga

N = Te maha o ngā ngota hau

m = papatipu

v = Te tere toharite o ngā ngota ngota

V = te rōrahi o te ipu