Te Tātari Hau Pai i roto i ngā Pūnaha Mīhini Wera
Pendahuluan
He taputapu te miihini wera e huri ana i te pūngao wera hei mahi miihini. Ko te tauira tino noa ko te te miihini mura o roto e whakakā ana ngā waka, ngā tāpine mamaoa i roto i ngā tipu hiko, me ngā mīhini whakamatao (e mahi "whakamuri" ana mā te whakawhiti wera mā te whakamahi i te mahi). mārama Hei whakamārama ariā me te rahinga i te mahi a ēnei miihini, i whakaurua mai e te ahupūngao te tauira hau pai rawa atu—he huarahi e whakangawari ana i te whanonga o ngā hau kia taea ai te tātari pāngarau i ngā whanaungatanga i waenga i te pēhanga, te rōrahi, me te pāmahana. Ahakoa kāore ngā hau tūturu i te pai i ngā wā katoa, he tino whai hua tēnei tauira hei pūtake mō te mārama ki ngā huringa thermodynamic, te whai huatanga, me ngā huringa pūngao i roto i ngā pūnaha miihini wera.
Ariā Hau Pai
Ko te hau pai rawa atu he hau e whakaarohia ana ko ōna matūriki: (1) he tino iti ki te rahinga o te ipu, (2) kāore e taunekeneke tetahi ki tetahi engari i ngā wā e tukinga ana te rapa, me te (3) whai i ngā whanaungatanga māmā i waenga i ngā taurangi makroskopi. Ka whakarapopototia tōna whanonga ki te whārite hau pai rawa atu o te āhua:
\[
PV = nRT
\]
me te pēhanga \(P\), te rōrahi \(V\), te maha o ngā ira \(n\), te pūmau hau whānui \(R\), me te pāmahana tino \(T\) (Kelvin). Ko tēnei whārite te wāhi tomo mō te tātari i ngā tukanga thermodynamic pērā i te whakawhānui, te kōpeketanga, te whakamahana, me te whakamatao e puta ana i roto i ngā miihini wera.
I roto i te miihini wera, ka pāngia te hau (te wai mahi rānei) e ngā huringa āhua maha i roto i te huringa. I roto i te huringa, ka mimiti te pūnaha i te wera mai i te pūtake wera, ka mahi, ā, ka panaia ētahi o te wera ki te taiao, ki te puna pāmahana iti iho rānei. Mā te tauira hau pai ka taea e tātou te hono i ēnei huringa āhua ki ngā rahinga pūngao: te wera \(Q\), te mahi \(W\), me te huringa o te pūngao ā-roto \(\Delta U\).
Te Ture Tuatahi o te Thermodynamics me te Pūngao Ā-roto
Ko te kaupapa o te tātaritanga miihini wera ko te Ture Tuatahi o te Thermodynamics:
\[
\Delta U = Q – W
\]
ko \(\Delta U\) te huringa o te pūngao i roto i te hau, \(Q\) te wera e tomo ana ki te pūnaha, me \(W\) te mahi i mahia e te pūnaha ki te taiao. I roto i te huringa katoa o te miihini wera, he rite tonu ngā āhua tīmatanga me ngā āhua whakamutunga, arā, \(\Delta U = 0\). Ko te tikanga o tēnei ko te wera kupenga katoa i riro mai he ōrite ki te mahi kupenga i puta:
\[
W_{\text{net}} = Q_{\text{in}} – Q_{\text{out}}
\]
Mō te hau pai rawa atu, ko te pūngao ā-roto e whakawhirinaki ana ki te pāmahana anake . Mō te hau pai kotahi-atomika, hei tauira:
\[
U = \frac{3}{2}nRT
\]
Mō ngā hau rua-atomic i runga i tētahi awhe pāmahana motuhake, he rerekē ngā tauwehenga nā te mea he nui ake ngā nekehanga herekoretanga. He mea nui tēnei whanaungatanga nā te mea he maha ngā tukanga miihini wera e uru ana ki ngā huringa pāmahana, ā, mai i tēnei, ka taea e tātou te whakatau tata i te huringa o te pūngao ā-roto.
Ngā Tukanga Termodynamic Matua i roto i ngā Hau Pai
He maha ngā tukanga pai o te huringa miihini wera. E whā te tukanga e whakamahia nuitia ana i roto i te tātaritanga ko:
1. Isothermal (T pumau)
I roto i tētahi tukanga isothermal o tētahi hau pai, kāore te pūngao ā-roto e rerekē (\(\Delta U = 0\)) nā te mea kei te mau tonu te pāmahana. Nō reira \(Q = W\). Te mahi isothermal mō tētahi hau pai:
\[
W = nRT \ln \left(\frac{V_2}{V_1}\right)
\]
He mea nui tēnei tukanga i roto i te matapakinga o te huringa Carnot nā te mea ka whakaratohia te whai huatanga ariā mōrahi.
2. Isobaric (P pumau)
I roto i tētahi tukanga pēhanga pumau, he māmā noa te tatau i te mahi:
\[
W = P(V_2 – V_1)
\]
Ka hurihia tetahi wāhanga o te wera e haere mai ana hei mahi, ā, ko ētahi ka whakanui ake i te pūngao i roto i
3. Isochoric (pūmau V)
Nā te mea he pumau te rōrahi, kāore he mahi:
\[
W = 0
\]
Nō reira, ko te wera e uru katoa ana ka whakanui i te pūngao o roto:
\[
Q = \Delta U
\]
4. Adiabatic (Q = 0)
Kāore he whakawhiti wera ki te taiao. Mēnā ka horapa te hau i roto i te āhua ā-ā-pāpā, ka mahi te hau, ā, ka heke te pāmahana. Ko te whanaungatanga ā-ā-pāpā noa mō te hau pai:
\[
PV^\gamma = \text{pūmau}
\]
me \(\gamma = \frac{C_p}{C_v}\). He mea tino nui ngā tukanga adiabatic i roto i te huringa Otto rāua ko Diesel e whakatauira ana i te tukanga o te pēhitanga me te whakawhanuitanga tere.
Kauwhata P–V me te Tikanga o te Horahanga o te Huringa
He maha ngā wā ka whakaatuhia te tātaritanga miihini wera mā te hoahoa pēhanga-rōrahi (P–V). I roto i tēnei hoahoa, ka whakaaturia ia tukanga hei kōpiko. He mea nui: ko te mahi kupenga i mahia i roto i te huringa kotahi he ōrite ki te horahanga e karapotia ana e te kōpiko huringa i runga i te hoahoa P–V. Ko te nui ake o te horahanga, ko te nui ake o te mahi kupenga i mahia mō ia huringa.
Ki te rere te huringa i te taha matau, ka puta he mahi kupenga (mīhini wera) i te mīhini. Ki te rere i te taha maui, me mahi te pūnaha i waho (pouaka whakamātao, papu wera rānei).
Te Whai Hua o te Mīhini Wera me te Tūranga o ngā Hau Pai
Ka inehia te mahi a te miihini wera mā te whai huatanga wera o tōna whakamahinga:
\[
\eta = \frac{W_{\text{net}}}{Q_{\text{in}}} = 1 – \frac{Q_{\text{out}}}{Q_{\text{in}}}
\]
Mā te tauira hau tino pai ka āwhina i te tatau i \(Q_{\text{in}}\), \(Q_{\text{out}}\), me \(W_{\text{net}}\) mō ētahi tukanga.
Huringa Carnot: Te Herenga Whai Hua Tino Pai
E rua ngā tukanga isothermal me ngā tukanga adiabatic e rua kei roto i te huringa Carnot. Ko te whai huatanga o Carnot ka whakawhirinaki noa ki ngā pāmahana o te puna wera (\(T_H\)) me te puna matao (\(T_C\)):
\[
\eta_{\text{Carnot}} = 1 – \frac{T_C}{T_H}
\]
He rohe taketake tēnei: kāore e taea e tētahi mīhini wera e mahi ana i waenga i ngā pāmahana e rua kua tohua te neke atu i te whai huatanga o Carnot. Ka whakamahia he hau pai hei wai mahi hei whakahaere i te whakaputanga o tēnei tātai, hei mārama hoki he aha i tino pāngia ai te whai huatanga e ngā rerekētanga pāmahana.
Pahikara Otto (Mīhini Penehīni)
Ko te huringa Otto tino pai ko ngā tukanga adiabatic e rua (te pēhi me te whakawhanui) me ngā tukanga isochoric e rua (te whakauru wera me te whakakore i te rōrahi pumau). Ko te whai huatanga o te huringa Otto tino pai ko:
\[
\eta_{\text{Otto}} = 1 – \frac{1}{r^{\gamma-1}}
\]
ko \(r\) te ōwehenga kōpeketanga. E hiahiatia ana he hau tino pai hei hono i ngā huringa o te pēhanga, te rōrahi, me te pāmahana i te wā kōpeketanga/whānuitanga adiabatic.
Huringa Tīhiera (Mīhini Tīhiera)
He rite te huringa Tīhiera ki te huringa Otto, engari ka puta te wera i te pēhanga pumau (isobaric). He uaua ake te tātari, engari ko te huringa hau pai tonu te pūtake mō ngā tataunga. te pāmahana me te pēhanga i ia pūwāhi o te huringa, ā, whakatauhia tōna whai huatanga hei pānga o te ōwehenga kōpeketanga me te ōwehenga tapahi.
Ngā Here o te Tauira Hau Pai i roto i ngā Mīhini Tuturu
Ahakoa he tino whai hua, he whakamāmā noa iho te tauira hau pai. I roto i ngā miihini tūturu, kei reira ngā āhuatanga e rerekē ai ngā hua tatau pai mai i te mea tūturu:
1. Ka whakaitihia te mahi kupenga e te waku me te mararatanga o te pūngao i roto i ngā wāhanga mīhini.
2. Kāore te whakawhiti wera i te tino whakahaeretia, he maha ngā tukanga kāore i te tino adiabatic.
3. Mā ngā panonitanga o te hanganga hau (hei tauira, te mura) ka kore te wai mahi e waiho hei hau pai noa iho me te \(n\ pumau.
4. Ka rerekē ngā hau tūturu mai i te pai i te pēhanga teitei, pāmahana rānei iti; ka nui haere te hiranga o ngā taunekeneke i waenga i ngā ngota ngota.
5. Ka taea e ngā tukanga kore-pūmau (tino tere) te whakararu i te taurite ā-rohe, ka kore ai e tino tika te tātaritanga pai.
Heoi, ahakoa ōna herenga, he anga tīmatanga kaha tonu te tātari hau pai mō te hoahoa, te whakatairite, me te mārama ki ngā au o te mahi a ngā miihini wera.
Whakamutunga
Mā te tātari hau pai i roto i te pūnaha miihini wera ka whakaratohia he pūtake ariā me te pāngarau hei mārama ki te hurihanga o te wera hei mahi mā te huringa thermodynamic. Mā te whārite (PV = nRT), Ture Tuatahi o te Thermodynamics, me te whakatauira i ngā tukanga isothermal, isobaric, isochoric, me te adiabatic, ka taea e tātou te tatau i te mahi, te wera, me te whai huatanga o tētahi mīhini i roto i tētahi huarahi hanganga. Mā te tūtohi P–V e mārama ai ko te mahi kupenga he ōrite ki te horahanga huringa, ko te whai huatanga e whakaatu ana i ngā herenga taketake e whakanuia ana e te huringa Carnot. Ahakoa e pāngia ana ngā mīhini tūturu e ngā mate me ngā peka ke mai i te whanonga pai, he mea nui tonu te tauira hau pai hei pūtake matua mō te tātari me te ako i ngā mīhini wera.
Ki te hiahia koe, ka taea e au te tāpiri i ngā tauira o ngā tātaitanga tau (hei tauira , te tātai i te whai huatanga o Otto mō tētahi ōwehenga kōpeketanga kua hoatu) te whakaatu rānei i tētahi putanga o te tuhinga me tētahi hanganga pūtaiao katoa (whakarāpopototanga, arotake ariā, tikanga, matapakinga, me te rārangi pukapuka).
