Ngā tukanga whakamahana tuhinga: Isothermal Adiabatic Isochoric Isobaric
E whā ngā tukanga thermodynamic, arā, ko te isothermal, te isochoric, te isobaric me te adiabatic.
Tukanga Isothermal (pāmahana pumau)
I roto i tētahi tukanga isothermal, ka mau tonu te pāmahana o te pūnaha. I roto i te ariā, he hau pai te pūnaha kua tātarihia. He rite tonu te pāmahana hau pai ki te pūngao hau ā-roto pai (U = 3/2 n RT). Kāore a T e rerekē, nō reira kāore hoki a U e rerekē. Nō reira, ki te whakamahia ki te tukanga isothermal, ka noho te ture tuatahi o te whārite thermodynamic:
Δ U = Q – W
Kāore te pūngao ā-roto e rerekē, nō reira Δ U = 0.
0 = Q – W
Q = W
I runga i tēnei whārite, i roto i te tukanga isothermal (pāmahana pumau), ka whakamahia e te pūnaha te wera (Q) i tāpirihia ki te pūnaha hei mahi i te mahi (W).
E whakaatuhia ana te panonitanga o te pēhanga me te rōrahi o te pūnaha i roto i te tukanga isothermal e te kauwhata i raro nei:
Te rōrahi pūnaha tuatahi = V1 (rahi iti) me te pēhanga pūnaha = P1 (pēhanga nui). Kia pumau tonu te pāmahana o te pūnaha, i muri i te tāpiritanga o te wera ki te pūnaha, ka whānui te pūnaha, ka mahi ki te taiao. I muri i te mahi a te pūnaha ki te taiao, ka huri te rōrahi o te pūnaha ki te V2 (ka piki te rōrahi pūnaha) me te hurihanga o te pēhanga pūnaha ki te P2 (te hekenga o te pēhanga pūnaha). He piko te āhua o te kauwhata nā te mea kāore te pēhanga pūnaha e rerekē i ia wā i te wā o te tukanga. Te nui o te mahi i mahia e te pūnaha = te wāhi kua atarangihia.
Tukanga Adiabatic
I roto i te tukanga adiabatic, kāore he wera e tāpirihia ana ki te pūnaha, kāore rānei e wehe atu i te pūnaha (Q = 0). Ka taea e ngā tukanga adiabatic te puta i roto i ngā pūnaha kati kua wehea pai. Mō tētahi pūnaha kati kua āraia pai, kāore he wera e rere ana ki roto i te pūnaha, e wehe atu rānei i te pūnaha. Ka taea hoki e ngā tukanga adiabatic te puta i roto i ngā pūnaha kati kāore i wehea.
I tēnei wā, me tere te mahi i te tukanga kia kore ai te wera e rere ki te pūnaha, kia kore ai hoki e puta i te pūnaha. Mēnā ka whakamahia ki tētahi tukanga adiabatic, ka rerekē te ture tuatahi o te whārite thermodynamic:
Δ U = Q – W
Kāore he wera e tomo mai ana, e puta atu ana rānei i te pūnaha, nō reira ko Q = 0.
Δ U = 0 – W
Δ U = -W
Ki te pēhia teretia te pūnaha (ka oti te mahi ki te pūnaha), ka kino te mahi. Nā te mea he kino a W, ka pai a U (ka piki te pūngao i roto i te pūnaha). I tetahi atu taha, ki te tere te whānui o te pūnaha (ka mahi te pūnaha), ka pai a W. Nā te mea he pai a W, ka kino a U (ka whakaitihia te pūngao i roto i te pūnaha). He rite te pūngao i roto i te pūnaha (hau pai) ki te pāmahana (U = 3/2 n RT), nō reira, ki te piki te pūngao i roto i te pūnaha, ka piki anō hoki te pāmahana o te pūnaha. I tetahi atu taha, ki te whakaitihia te pūngao i roto i te pūnaha, ka heke te pāmahana o te pūnaha.
Ko te panonitanga o te pēhanga me te rōrahi o te pūnaha i roto i te tukanga adiabatic e whakaatuhia ana e te kauwhata i raro nei:
He pari ake te kōpiko adiabatic i tēnei kauwhata (ngā kōpiko 1-2) i te kōpiko isothermal (ngā kōpiko 1-3). E whakaatu ana tēnei rerekētanga pari, mō te pikinga rōrahi ōrite, ka nui ake te hekenga o te pēhanga pūnaha i roto i te tukanga adiabatic i te tukanga isothermal. Ka nui ake te hekenga o te pēhanga pūnaha i roto i te tukanga adiabatic nā te mea ka puta te whānui adiabatic, ka heke hoki te pāmahana o te pūnaha. He rite te pāmahana ki te pēhanga, nō reira, ki te heke te pāmahana o te pūnaha, ka heke hoki te pēhanga o te pūnaha. He rerekē ki te tukanga isothermal, he pumau tonu te pāmahana o te pūnaha. Nō reira, i roto i te tukanga isothermal, kāore te pāmahana e pā ki te hekenga pēhanga.
Ko tētahi tauira o te tukanga adiabatic ka puta i roto i te miihini mura ā-roto, pērā i te miihini tīhiera me te miihini penehīni. I roto i ngā miihini tīhiera, ka whakaurua te hau ki roto i te rango, ā, ka pēhia teretia te hau i roto i te rango mā te whakamahi i te piston (ka mahia te mahi ki te hau). Ko te tukanga kōpeketanga adiabatic (te whakaiti i te rōrahi pūnaha) e whakaaturia ana e te pihi 2-1. Nā te tere o te pēhanga adiabatic, ka tere te piki o te pāmahana. I taua wā anō, ka rehuhia te tīhiera ki roto i te rango mā te werowero, ā, ka whakaoho tonutia te ranunga. I roto i te miihini penehīni, ka whakaurua he ranunga o te hau me te penehīni ki roto i te rango, kātahi ka pēhia teretia mā te whakamahi i te piston. Nā te tere o te pana adiabatic, ka tere te piki o te pāmahana. I taua wā anō, ka mura ngā puru mura kia puta ai te tukanga tahu.
Tukanga Isochoric (rōrahi pumau)
I roto i te tukanga Isochoric, ka mau tonu te rōrahi pūnaha. Nā te mea he pumau tonu te rōrahi pūnaha, kāore e taea e te pūnaha te mahi i runga i te taiao. Kāore hoki e taea e te taiao te mahi i runga i te pūnaha. Ki te whakamahia ki te tukanga isochoric, ka huri te ture tuatahi o te whārite thermodynamic ki:
Δ U = Q – W
Kāore te pūnaha e mahi i runga i te taiao, nō reira ko W = 0
Δ U = Q – 0
Δ U = Q
Mai i tēnei hua, ka taea e tātou te whakatau i roto i te tukanga isochoric (rōrahi pumau), ka whakamahia te wera (Q) e tāpirihia ana ki te pūnaha hei whakanui ake i te pūngao i roto i te pūnaha. Ko ngā huringa o te pēhanga me te rōrahi o te pūnaha i roto i te tukanga isochoric e whakaatuhia ana e te kauwhata i raro nei:
I te tīmatanga, ko te pēhanga pūnaha = p 1 (pēhanga iti). Mā te wera tāpiri o te pūnaha ka piki ake te pūngao i roto i te pūnaha. I te pikinga ake o te pūngao i roto i te pūnaha, ka piki ake te pāmahana o te pūnaha (hau pai) (U = 3/2 n RT). He rite tonu te pāmahana ki te pēhanga. Nō reira, ki te piki ake te pāmahana o te pūnaha, ka piki ake te pēhanga o te pūnaha (p 2 ). Nā te pumau o te rōrahi o te pūnaha, kāore he mahi e mahia ana (kāore he wāhi atarangi).
I roto i te tukanga isochoric, kāore e taea e te pūnaha te mahi i runga i te taiao. Waihoki, kāore e taea e te taiao te mahi i runga i te pūnaha. Nā te mea, i roto i te tukanga isochoric, he pumau tonu te rōrahi o te pūnaha. He momo mahi ētahi kāore e uru ki ngā huringa rōrahi. Nō reira, ahakoa kāore te rōrahi o te pūnaha e rerekē, ka taea tonu te mahi i runga i te pūnaha. Hei tauira, kei roto i te ipu kati he pā hau me te pākahiko. Ka taea e te pā hau te huri mā te whakamahi i te kaha o te pākahiko. I tēnei wā, ka kiia ngā pā hau, ngā pākahiko, me te hau i roto i te ipu he pūnaha.
Ina huri te pā, ka mahi te pā, kei roto i te ipu. I taua wā anō, ka huri te kaha nekeneke o te pā hei kaha i te rangi. Ko te kaha hiko i roto i te pākahiko, kua heke iho nā te mea kua huri tōna āhua hei kaha i te rangi. E whakaatu ana tēnei tauira i roto i te tukanga isochoric (he pumau tonu te rōrahi), ka taea tonu te mahi i runga i te pūnaha (he mahi kāore e uru ki ngā huringa rōrahi).
Tukanga Isobaric (pēhanga pumau)
I roto i tētahi tukanga isobaric, ka mau tonu te pēhanga o te pūnaha. Nā te mea he pumau te pēhanga, kāore te huringa pūngao ā-roto ( ΔU ), te wera (Q) me te mahi (W) i roto i te tukanga isobaric i te kore. Nō reira, kāore te tātai thermodynamics ture tuatahi i rerekē.
ΔU = Q − W
Ko ngā panonitanga o te pēhanga me te rōrahi hau i roto i te tukanga isobaric e whakaatuhia ana e te kauwhata i raro nei:
Tuatahi, te rōrahi pūnaha = V1 (rahi iti). Nā te mea he pumau tonu te pēhanga, nō reira, i muri i te tāpiritanga o te wera ki te pūnaha, ka whānui te pūnaha, ā, ka mahi ki te taiao. I muri i te mahi ki te taiao, ka huri te rahinga o te pūnaha ki te V2 (te pikinga o te rōrahi pūnaha). Te nui o te mahi (W) i oti i te pūnaha = te wāhi kua whakamarumaruhia.
Pātai 1:
E whakaatu ana ngā kōpiko 1-2 i roto i ngā hoahoa e rua i raro nei i te whakawhanuitanga hau (te pikinga o te rōrahi hau) e puta ana i te taha adiabatic me te taha isothermal. I roto i tēhea tukanga, he iti ake te mahi e mahia ana e te hau?
He iti iho te mahi a ngā hau i roto i te tukanga adiabatic i te mahi a ngā hau i roto i te tukanga isothermal. Ko te horahanga atarangi = te mahi i mahia e te hau i te wā o te tukanga whakawhanui (te pikinga o te rōrahi hau). He iti iho te horahanga atarangi i roto i te tukanga adiabatic i te horahanga atarangi o te tukanga isothermal.
Pātai 2:
Kei te hoahoa i raro nei ngā tukanga whakamahana. Ko ngā kōpiko ab me dc = ngā tukanga isochoric (rōrahi pumau). Ko te kōpiko bc me ad = tukanga isobaric (pēhanga pumau). I roto i te tukanga ab, ka tāpirihia te wera (Q) 600 Joules ki te pūnaha. I roto i te tukanga bc, ka tāpirihia te wera (Q) 800 Joules ki te pūnaha.
a) Ngā panonitanga pūngao i roto i te tukanga ab
b) Ngā panonitanga pūngao i roto i te tukanga abc
c) Te wera katoa i tāpirihia ki te tukanga ADC
P 1 = 2 x 10 5 Pa = 2 x 10 5 N / m 2
P 2 = 4 x 10 5 Pa = 4 x 10 5 N / m 2
V 1 = 2 rita = 2 dm 3 = 2 x 10 -3 m 3
V 2 = 4 rita = 2 dm 3 = 4 x 10 -3 m 3
otinga
a) Ngā panonitanga pūngao ā-roto i roto i te tukanga ab
I roto i te tukanga ab, ka tāpirihia te wera 600 J ki te pūnaha. Tukanga ab = tukanga isochoric (rōrahi pumau). I roto i te tukanga isochoric, ko te tāpiri o te wera ki te pūnaha ka whakanui noa i te pūngao i roto i te pūnaha. Nō reira, ka huri te pūngao i roto i te pūnaha i muri i te whiwhinga wera:
ΔU = Q
ΔU = 600 J
b) Ngā panonitanga pūngao i roto i te tukanga abc
Tukanga ab = tukanga isochoric (rōrahi pumau). I roto i te tukanga ab, ka tāpirihia te wera 600 J ki te pūnaha. Nā te rōrahi pumau, kāore he mahi e mahia ana e te pūnaha.
Tukanga bc = tukanga isobaric (pēhanga pumau). I roto i te tukanga bc, ka tāpirihia te wera (Q) 800 Joules ki te pūnaha. I roto i te tukanga isobaric, ka taea e te pūnaha te mahi. Ko te nui o te mahi i mahia e te pūnaha i roto i te tukanga bc (tukanga isobaric) ko:
W = P (V 2 – V 1 ) — pēhanga pumau
W = P 2 (V 2 – V 1 )
W = 4 x 10 5 N /m² ( 4 x 10 -3 m³ – 2 x 10 -3 m³ )
W = 4 x 105 N / m2 ( 2 x 10 -3 m3 )
W = 8 x 10 2 Joule
W = 800 Joule
Ko te wera katoa i tāpirihia ki te pūnaha i roto i te tukanga abc ko:
Q katoa = Q ab + Q bc
Q katoa = 600 J + 800 J
Q katoa = 1400 Joules
Ko te mahi katoa i mahia e te pūnaha i roto i te tukanga abc ko:
W katoa = W ab + W bc
W katoa = 0 + W bc
W katoa = 0 + 800 Joule
W katoa = 800 Joule
Ngā panonitanga pūngao ā-roto i roto i te tukanga abc = 600 J
c) Te wera katoa i tāpirihia ki te tukanga ADC
Ka taea te tatau i te wera katoa i tāpirihia ki te pūnaha mā te whārite i raro nei:
ΔU = Q – W
Q = ΔU + W
Te wera katoa i tāpirihia ki te tukanga adc = ngā huringa pūngao ā-roto i roto i te adc + mahi i roto i te tukanga adc.
Kei roto i te whakawhiti pūngao te wera me te mahi i waenga i ngā pūnaha me te taiao, ko ngā huringa pūngao ā-roto ia he hua o te whakawhiti pūngao i waenga i te pūnaha me te taiao. Nō reira, kāore te huringa o te pūngao e whakawhirinaki ki te tukanga whakawhiti pūngao. I tētahi atu taha, ko te wera me te mahi e whakawhirinaki ana ki te tukanga. I roto i te tukanga isochoric (pūnaha rōrahi pumau), ko te whakawhiti pūngao kei roto i te āhua o te wera anake, engari kāore te mahi. I roto i te tukanga isobaric (pēhanga pumau), ko te whakawhiti pūngao e uru ana ki te wera me te mahi. Ahakoa kāore e whakawhirinaki ki te tukanga, ka rerekē te pūngao i runga i te āhua tīmatanga me te āhua o te pūnaha mutunga. Mena he rite ngā āhua tīmatanga me te āhua whakamutunga, he rite tonu ngā huringa o te pūngao, ahakoa he rerekē te tukanga.
Ko ngā āhua tīmatanga me ngā āhua whakamutunga mō te tukanga abc i te kauwhata i runga ake nei = ngā āhua tīmatanga me ngā āhua whakamutunga o te tukanga adc. Nō reira, ko ngā huringa pūngao ā-roto i roto i te tukanga o te adc = 600 J.
Te mahi katoa (W) i mahia ki te adc = W tukanga ki te ad + W ki te tukanga dc.
He tukanga isobaric (pēhanga pumau) te tukanga ad, ko te tukanga dc he tukanga isochoric (rōrahi pumau). Nā te rōrahi pumau, kāore he mahi e mahia ana i runga i te tukanga dc. Tuatahi, ka tatauhia e mātou te mahi e mahia ana i runga i te tukanga ad.
W ad = P (V 2 ‐ V 1 )
W ad = P 1 (V 2 ‐ V 1 )
W ad = 2 x 10⁻5 N / m² ( 4 x 10‐3 m3‐2 x 10‐3 m3 )
W ad = 2 x 10‐3 m ‐ 3 )
W ad = 4 x 10 2 Joule
W ad = 400 Joule
W katoa = W i roto i te tukanga a-d + W i roto i te tukanga d-c
W katoa = 400 Joules + 0
W katoa = 400 Joule
Nō reira, ko te nui o te wera i tāpirihia ki te tukanga ADC ko:
Q = ΔU + W
Q = 600 J + 400 J
Q = 1000 J
Pātai 3:
Ka huri te 1 rita wai ki te 1671 rita o te mamaoa ina kohuatia i te pēhanga 1 atm. Tātaihia te huringa o te pūngao ā-roto me te mahi e mahia ana e te wai ina mimiti … (Te wera mimiti mō te wai = L V = 22.6 x 10 5 J/Kg)
otinga
Te mātotoru o te wai = 1000 kg/ m3
Te wera o te mimiti mō te wai (L V ) = 22.6 x 105 J / Kg
P = 1 atm = 1.013 x 105 Pa = 1.013 x 105 N/ m2
V 1 = 1 rita = 1 dm 3 = 1 x 10 -3 m 3 (Rōrahi wai)
V 2 = 1671 rita = 1671 dm 3 = 1671 x 10 -3 m 3 (Rōrahi o te mamaoa)
a) Ngā panonitanga o te pūngao ā-roto
Ngā panonitanga o te pūngao ā-roto = Te wera i tāpirihia ki te wai tangohia te mahi i mahia e te wai ina mimiti. Te tatau tuatahi Te wera (Q) i tāpirihia ki te wai …
Q = m L V
Te mātotoru o te wai = te papatipu wai / te rahinga o te wai
Papatipu wai (m) = kiato wai x rōrahi wai
Papatipu wai (m) = (1000 kg/m³ ) ( 1 x 10 -3 m³ )
Papatipu wai (m) = (1000 kg/m 3 ) (0.001 m 3 )
Papatipu wai (m) = 1 kg
Q = (1 kg) (22.6 x 105 J / kg)
Q = 22.6 x 10 5 J
Tātaihia te mahi (W) e mahia ana e te wai ina mimiti. Ka puta te kohua o te wai i te pēhanga pumau (tukanga isobaric).
W = p (V 2 – V 1 )
W = 1.013 x 105 N /m2 ( 1671 x 10 -3 m3 – 1 x 10 -3 m3 )
W = 1.013 x 105 N / m2 ( 1670 x 10 -3 m3 )
W = 1691.71 x 10 2 Joule
W = 1.7 x 105 Joules
Ngā panonitanga o te pūngao ā-roto o te wai:
ΔU = Q – W
ΔU = 22.6 x 10 5 J – 1.7 x 10 5 J
ΔU = 20.9 x 10 5 J
ΔU = 21 x 10 5 J
Ko te wera 21 x 10 5 Joule e tāpirihia ana ki te wai ka whakamahia hei whakanui ake i te pūngao ā-roto (te wikitoria i ngā kaha kume i waenga i ngā ngota e pupuri ana i te wai kia rere). Arā, ka whakamahia te 21 x 10 5 J hei huri i te wai hei mamaoa. Ina huri te wai hei mamaoa, ka whakamahia te toenga 1.7 x 10 5 J hei mahi.
Pātai 4:
Ka tere te whakawhanui a te 1 mole o te hau i roto i te rango, he āhua ā-ā-pā. I te tīmatanga, ko te pāmahana o te hau = 1000 K. I muri i te whakawhanui, ka heke te pāmahana o te hau ki te 500 K. Tātaihia te mahi i mahia e te hau …
otinga
Ka puta te whānui haere o te hau mā te ara adiabatic. I roto i te tukanga adiabatic, kāore he wera e tomo, e puta rānei i te pūnaha. Nō reira, ko te mahi e mahia ana i roto i te hau = te hurihanga o te pūngao i roto i te hau.
ΔU = Q – W, W = Q – ΔU rānei → Q = 0
W = 0 – ΔU
W = – ΔU
Ka taea e tātou te tatau i ngā panonitanga pūngao i roto i te hau mā te whakamahi i te whārite pūngao i roto i te hau tino pai:
ΔU = 3/2 (1 mol) (8.315 J / mol. K) (500 K – 1000 K)
ΔU = 3/2 (1 mol) (8.315 J / mol. K) (- 500 K)
ΔU = -6236.25 J
Nō reira, ko te nui o te mahi e mahia ana e te hau ko:
W = – ΔU
W = – (- 6236.25 J)
W = 6236.25 J
