I ahu mai te ariā wehewehenga ōrite o te pūngao i roto i te ariā e Clerk Maxwell mā te whakamahi i ngā tikanga tatauranga. Ka kiia he ariā nā te mea kāore he taunakitanga whakamātautau. Ko te tikanga o te wehewehenga ōrite o te pūngao ko te tohatoha ōrite o te pūngao.
I ahu mai te pūngao nekeneke whakawhiti i te nekehanga whakawhiti, e toru ngā wāhanga tere: te tuaka-x, te tuaka-y, me te tuaka-z. Ko ēnei wāhanga tere e toru te take i puta ai te tau 3 i roto i te whārite i runga ake nei. Ka kiia ia wāhanga tere he tohu herekore. Nā te mea e toru ngā wāhanga tere, e toru ngā tohu herekore o te pūngao nekeneke whakawhiti.
E ai ki te ariā wehewehenga ōrite o te pūngao me tohatoha ōrite te pūngao ki ngā nekehanga herekore katoa. Nō reira, ko te pūngao toharite mō ia nekehanga herekore he 1⁄2 kT.
Ngā ngota hau monoatomic
Ka mahi noa ngā ngota hau monoatomic i te nekehanga whakawhiti, kia 3 ngā nekehanga herekore o ngā ngota hau monoatomic.
Ko te pūngao nekeneke toharite mō ia ngota ngota o te hau monoatomic ko:
3 (1⁄2 kT) = 3/2 kT = 3/2 nRT.
Te kaha wera o ngā ngota hau monoatomic:
C = 3/2 R = 3/2 (8,315 J/mol.K) = 12,47 J/Kg.K
Ngā ngota hau rua-atomika
Haunga te nekehanga whakawhiti, ka mahi anō hoki ngā ngota hau rua-atomic i ngā nekehanga hurihuri me te wiri. Ko te maha o ngā nekehanga herekore mō te nekehanga whakawhiti = 3. E hia ngā nekehanga herekore mō te nekehanga hurihuri me te wiri?
E toru ngā tuaka hurihuri, arā, ko ngā tuaka x, y me z. Kāore te nekehanga hurihuri huri noa i te tuaka-x e whakaurua ki te tatau nā te mea e ōrite ana ngā ngota e rua e hanga ana i te ngota ki te tuaka hurihuri. Ina ōrite rāua ki te tuaka-x, ko te wā o te korekore o ngā ngota e rua = 0. Nō reira, ko te maha o ngā nekehanga herekore mō te nekehanga hurihuri = 2.
Ko te pūngao toharite mō ia ngota hau rua-atomika ko:
3(1⁄2 kT) + 2(1⁄2 kT) = 5/2 kT = 5/2 nRT.
Te kaha wera o ngā ngota hau rua-atomic:
C = 5/2 R = 5/2 (8,315 J/mol.K) = 20,79 J/Kg.K
He nui ake te kaha wera ngota i whiwhihia e ai ki te ariā i te kaha wera tuturu. 
ngā ngota hau rua-atomika i whiwhihia mā roto i ngā whakamātautau.
I te wā e wiri ana, e rua ngā momo pūngao o ngā ngota hau rua-atomika: te pūngao nekeneke me te pūngao pūmanawa pīngore. Nō reira, ko te maha o ngā nekehanga herekore mō te nekehanga wiri he 2.
Ko te pūngao toharite mō ia ngota hau rua-atomika ko:
3(1⁄2 kT) + 2(1⁄2 kT) + 2(1⁄2 kT) = 7/2 kT = 7/2 nRT.
Te kaha wera o ngā ngota hau rua-atomic:
C = 7/2 R = 7/2 (8,315 J/mol.K) = 29,1 J/Kg.K
Tena koa whakatairitea tēnei hua ki te kaha wera o ngā ngota hau rua-atomic i whiwhihia mā te whakamātautau. He nui te rerekētanga. E 7 ngā nekehanga herekore o ngā ngota hau rua-atomic (te nekehanga whakawhiti, te hurihanga, me te wiri), nō reira ko te kaha wera o ngā ngota hau rua-atomic i whiwhihia mā te whakamātautau me tata ki te 29,1 J/Kg.J.
Ko te pānga o te nekehanga wiri ki te kaha wera o ngā ngota hau rua-atomic ka whakawhirinaki anō ki te awhe pāmahana (T). I whakahaerehia ngā whakamātautau o mua i runga i te awhe pāmahana whaiti. Kua whakaatuhia e ngā whakamātautau tata nei i whakahaerehia i runga i te awhe pāmahana whānui ko te kaha wera o ngā ngota hau ka whakawhirinaki anō ki te awhe pāmahana. Hei mārama ake i tēnei take, me tirotiro tātou i te rerekētanga o te kaha wera o ngā ngota hau hauwai i ngā pāmahana rerekē.
Te rerekētanga o te kaha wera o ngā ngota hau hauwai i ngā pāmahana rerekē.
Hauwai (H2) tae atu ki ngā hau rua-atomika. E whakaatu ana te ahua i te taha i te rerekētanga o te kaha wera o ngā ngota hau hauwai i ngā pāmahana rerekē. Ko te uara kaha wera ngota o te 5/2 R = 20,79 J/Kg.K kei roto noa i te awhe pāmahana o te 250 K ki te 750 K. I raro iho i te 250 K, ka heke haere te kaha wera ngota o te hau hauwai tae noa ki te tae ki te 3/2 R = 12,47 J/Kg.K. I tetahi atu taha, i runga ake i te 750 K, ka piki haere te kaha wera ngota o te hau tae noa ki te tae ki te 7/2 R = 29,1 J/Kg.K.
I runga i tēnei meka, ka taea e tātou te kī i ngā pāmahana iti, ko te nekehanga whakawhiti anake te mahi a ngā ngota hau. Kia piki ake te pāmahana, ko te nekehanga hurihuri anake te mahi a ngā ngota hau. I ngā pāmahana teitei, ka tukinga ngā ngota hau tetahi ki tetahi, ka meinga ngā ngota e hanga ana i ngā ngota kia mahi i te nekehanga wiri. Nō reira, ka puta ēnei momo nekehanga e toru i ngā wāhanga, ko te nekehanga whakawhiti anake (ngā pāmahana iti), kātahi ko te whakawhiti + te hurihanga (ngā pāmahana waenga), ā, i te mutunga ko te whakawhiti + te hurihanga + te wiri (ngā pāmahana teitei). Ka puta noa te nekehanga wiri ina tukinga ngā ngota hau tetahi ki tetahi.
Ehara i te mea he hau hauwai anake tēnei, engari e pā ana hoki ki ētahi atu hau. Kua kitea e ngā kaipūtaiao ka rerekē anō te kaha wera o ngā ngota hau i te pāmahana. He rite ngā huringa ki ērā e pā ana ki te hau hauwai, engari nā te mea he rerekē te hanganga o ia hau (te maha me ngā momo ngota kei roto), ka puta anō hoki ngā huringa o te kaha wera i ngā awhe pāmahana rerekē.
E kī ana te ariā wehewehenga ōrite o te pūngao me tohatoha ōrite te pūngao katoa puta noa i ia tohu herekoretanga. Ko te mea pono, ko te pūngao tāpiri e whiwhihia ana e ngā ngota hau kāore i tohatoha ōrite puta noa i ia tohu herekoretanga, engari ka tohatoha haere. Hei tāpiri, ko te whārite mō te kaha wera ngota o te hau, i ahu mai i runga i te ariā nekeneke o ngā hau, e kī ana ko te kaha wera ngota e whakawhirinaki ana ki a R anake (1/2 R mō ia tohu herekoretanga). Ko te mea pono, ka pāngia hoki te kaha wera ngota e te pāmahana (T).
He maha ngā whakatau ka taea te whakatau. Tuatahi, ko te ariā wehewehenga ōrite o te pūngao i ahu mai i te miihini tatauranga tawhito, e ahu mai ana i ngā ture miihini a Newton. Tuarua, ko te ariā nekeneke o ngā hau, e whakamahia ana e tātou hei whakamārama i te nekehanga o ngā ngota hau, e ahu mai ana hoki i ngā ture miihini a Newton. Nā te mea kua takahia te ariā wehewehenga ōrite o te pūngao me te ariā nekeneke o ngā hau, ka taea te whakatau kāore e taea e ngā ture miihini a Newton te whakamārama i te nekehanga e puta ana i te taumata ngota ngota, i te taumata ngota rānei. Arā, ko te miihini Newtonian, ko te miihini tawhito rānei, ka taea anake te whakamārama i te nekehanga o te mea i ngā tauine nui.
