Te whakawhānui wera - ngā raruraru me ngā otinga
1. Ko te rahi o tētahi rau maitai i te 20 ° C e rite ana ki te pikitia i raro nei. Mena ko te tauwehenga whānui rārangi mō te maitai he 10 -5 ° C -1 , he aha te huringa o te horahanga i te 60 ° C?
Mōhiotia:
Te roa o te maitai = 40 cm 
Whānui o te maitai = 20 cm
Ko te tīmatanga o te horahanga o te maitai (A o ) = (40)(20) = 800 cm 2
Ko te tauwehenga whānui rārangi (α) = 10 -5 o C -1
Ko te tauwehenga whānui o te horahanga (β) = 2 x tauwehenga whānui raina (2α) = 2 x 10 -5 o C -1
Ko te huringa o te pāmahana (ΔT) = 60 ° C – 20 ° C = 40 ° C
E hiahiatia ana: Te panonitanga o te horahanga o te maitai i te 60 ° C
Rongoā:
Whārite o te whakawhānui horahanga:
ΔA = βA o ΔT
ΔA = te pikinga o te horahanga o te maitai, β = Te tauwehenga o te whakawhānui horahanga, A o = te horahanga tīmatanga, ΔT = te huringa o te pāmahana = te pāmahana whakamutunga – te pāmahana tīmatanga
Te pikinga o te horahanga o te maitai:
ΔA = βA o ΔT
ΔA = (2 x 10 -5 )(800)(40) = 0.64 cm
2. Kua whakaaturia tētahi pereti rino i te 20 ° C i te pikitia i raro nei. Mēnā ka whakanuia te pāmahana ki te 100 ° C, ā, ko te tauwehenga whānui o te rino he 1.1 x 10⁻¹ -7 ° C -1 , he aha te horahanga whakamutunga o te pereti?
Mōhiotia:
Te roa o te pereti = 2 m 
Whānui o te pereti = 2 m
Ko te horahanga tīmatanga o te rino (A o ) = (2)(2) = 4 m2
Ko te tauwehenga whānui rārangi mō te rino (α) = 1.1 x 10 -7 o C -1
Ko te tauwehenga whānui mō te rino (β) = 2 x te tauwehenga whānui rārangi mō te rino (2α) = 2.2 x 10 -7 o C -1
Ko te huringa o te pāmahana (ΔT) = 100 ° C – 20 ° C = 80 ° C
E hiahiatia ana : Te horahanga o te rino i te 100 ° C
Rongoā:
Te pikinga o te roa:
ΔA = βA o ΔT
ΔA = (2.2 x 10 -7 )(4)(80) = 704 x 10 -7 = 0,0000704 m²
Te horahanga o te rino:
Horahanga o te rino = te horahanga tīmatanga + te pikinga o te horahanga
Te horahanga o te rino = 4 m² + 0.0000704 m²
Te horahanga o te rino = 4.0000704 m²
3. He pereti parahi, ko te tauwehenga whānui rārangi α = 18.10 -6 o C -1 i te 0 o C, he rite te rahi ki te pikitia i raro nei. Mēnā ka whakamahanahia te pereti i te 80 o C, he aha te pikinga o te horahanga o te pereti?
Mōhiotia:
Te roa o te parahi = 40 cm = 0.4 mita
Whānui o te parahi = 20 cm = 0.2 mita
Te horahanga tuatahi o te parahi (A o ) = (0.4)(0.2) = 0.08 m²
Ko te tauwehenga whānui rārangi mō te parahi (α) = 18 x 10 -6 o C -1
Ko te tauwehenga whānui mō te parahi (β) = 2 x Ko te tauwehenga whānui rārangi (2α) = 36 x 10 -6 o C -1
Ko te huringa o te pāmahana (ΔT) = 80 ° C – 0 ° C = 80 ° C
E hiahiatia ana: Te whakanui ake i te horahanga mō te parahi i te 80 ° C
Rongoā:
Te pikinga ake o te horahanga mō te parahi:
ΔA = βA o ΔT
ΔA = (36 x 10 -6 ) (0.08)(80) = 230.4 x 10 -6 = 2.304 x 10 -4 m²
4. He ipu karāhe he 4 rita te rahinga, kī tonu i te wai, kātahi ka whakamahanatia kia piki ake te pāmahana ki te 20 ° C. I maringi ētahi wai. Ko te tauwehenga whānui rārangi mō te karāhe = 9 x 10 -6 ° C -1 ; ko te tauwehenga whānui rōrahi mō te wai = 2.1 x 10 -4 ° C -1 . Tātaihia te rōrahi o te wai i maringi.
Mōhiotia:
Ko te rōrahi tīmatanga o te hau me te wai (V o ) = 4 rita
Ko te pikinga o te pāmahana o te karāhe me te wai (ΔT) = 20 ° C
Ko te tauwehenga whānui rārangi mō te karāhe (α) = 9 x 10 -6 o C -1
Ko te tauwehenga whakawhanui rōrahi mō te karāhe (γ) = 3α = 3 (9 x 10 -6 o C -1 ) = 27 x 10 -6 o C -1
Ko te tauwehenga o te whakawhanuitanga rōrahi mō te wai (γ) = 2.1 x 10 -4 o C -1
E hiahiatia ana: Te nui o te wai i maringi
Rongoā:
Ko te whārite o te whakawhanuitanga rōrahi:
V = V o + γ V o ΔT
V – V o = γ V o ΔT
ΔV = γV o ΔT
V = rōrahi whakamutunga , V o = rōrahi tīmatanga , ΔV = te huringa o te rōrahi , γ = te tauwehenga o te whakawhānui rōrahi , ΔT = te huringa o te pāmahana.
Te panonitanga o te rōrahi o te ipu karāhe:
ΔV = γ V o ΔT = (27 x 10 -6 )(4)(20) = 2160 x 10 -6 = 2.160 x 10 -3 = 0.002160 rita
Te huringa o te rahinga o te wai:
ΔV = γ V o ΔT = (2.1 x 10 -4 )(4)(20) = 168 x 10 -4 = 0.0168 rita
He nui ake te panonitanga o te rōrahi o te wai i te ipu karāhe, nō reira ka maringi ētahi wai.
Te nui o te wai i maringi:
0.0168 rita – 0.002160 rita = 0.01464 rita = 0.015 rita
5. He ipu maitai (ko te tauwehenga whānui rārangi = 10 -5 o C -1 ) he 6 rita te rōrahi e kī ana i te acetone (ko te tauwehenga whānui rōrahi = 1.5 x 10 -3 o C -1 ). Mena ka whakamahanahia te ipu me te acetone mai i te 0 o C ki te 40 o C, he aha te rōrahi o te acetone i maringi?
Mōhiotia:
Ko te rōrahi tīmatanga o te ipu me te acetone (V o ) = 6 rita
Ko te huringa o te pāmahana o te ipu me te acetone (ΔT) = 40 ° C
Ko te tauwehenga whānui rārangi mō te maitai (α) = 10 -5 o C -1
Ko te tauwehenga whakawhanui rōrahi mō te maitai (γ) = 3α = 3 (10 -5 o C -1 ) = 3 x 10 -5 o C -1
Ko te tauwehenga o te whakawhanuitanga rōrahi mō te acetone (γ) = 1.5 x 10 -3 o C -1
E hiahiatia ana: Te rahinga o te acetone i maringi
Rongoā:
Te whārite o te whakawhanuitanga rōrahi:
ΔV = γV o ΔT
ΔV = te huringa o te rōrahi , γ = te tauwehenga o te whakawhānui rōrahi , Vo = te rōrahi tīmatanga , ΔT = te huringa o te pāmahana.
Te panonitanga o te rōrahi o te ipu maitai:
ΔV = γ V o ΔT = (3 x 10 -5 )(6)(40) = 720 x 10 -5 = 0.00720 rita
Te huringa o te rahinga o te acetone:
ΔV = γ V o ΔT = (1.5 x 10 -3 )(6)(40) = 360 x 10 -3 = 0.360 rita
He nui ake te panonitanga o te rōrahi o te acetone i te ipu maitai , nō reira ka whakamahia ētahi pire acetone.
Te nui o te acetone i maringi:
0.360 rita – 0.00720 rita = 0.3528 rita = 0.35 rita
- He aha te whakawhānui wera?
- whakahoki: Ko te whānui wera e pā ana ki te ia o te matū ki te whakarerekē i tōna rahinga hei urupare ki te huringa o te pāmahana.
- He pēhea te pānga o te whānui wera ki te mātotoru o tētahi matū?
- whakahoki: I te whakawhānuitanga wera o tētahi matū, ka piki ake tōna rōrahi, ka heke iho tōna mātotoru, ki te mea ka noho pūmau tonu tōna papatipu.
- He aha i puta ai ngā āputa i waenganui i ngā wāhanga o ngā piriti me ngā ara rerewē?
- whakahoki: Ko ēnei āputa, e kiia ana ko ngā hononga whakawhānui, he mea hanga hei whakauru i te whakawhānui me te whakaheke o te rauemi nā ngā huringa pāmahana, hei ārai i te āhua o te whakarerekētanga, te kino rānei.
- He aha te rerekētanga i waenga i te whakawhānui raina, te whakawhānui rōrahi, me te whakawhānui horahanga?
- whakahoki: Ko te whānui rārangi e pā ana ki te huringa o te taha kotahi (pērā i te roa o te tokotoko); ko te whānui horahanga e pā ana ki te huringa o ngā taha e rua (pērā i te horahanga mata o te rau); ā, ko te whānui rōrahi e pā ana ki te huringa o ngā taha e toru (pērā i te rōrahi o te wai).
- Me pēhea te whakatau i te tauwehenga whānui rārangi?
- whakahoki: Ko te tikanga, ko te huringa roa ā-wāhanga mō ia nekehanga, ia huringa pāmahana i te pēhanga pumau. Mō tētahi matū, ko te huringa roa (∆L) nā te huringa pāmahana (∆T) ka hoatuhia e , i reira ko te roa tīmatanga me ko te tauwehenga whānui rārangi.
- He aha i piko ai ngā rīpene bimetallic ina werahia, ina whakamataohia rānei?
- whakahoki: He rīpene whakarewa-rua he mea hanga mai i ngā konganuku rerekē e rua e honoa ana tetahi ki tetahi. Nā te mea he rerekē te tauwehenga o te whānui wera o ia konganuku, ka whānui, ka whakawhāiti rānei i ngā tere rerekē ina rerekē te pāmahana. Nā tēnei whānui rerekē ka piko te rīpene.
- He aha te hononga o te āhuatanga o te whānui wera ki te pikinga o ngā taumata o te moana?
- whakahoki: Ko tētahi wāhanga o te pikinga o ngā taumata o te moana ka taea te kī ko te whānui haere o te wai moana. I te pikinga ake o te pāmahana o te Ao, ka mahana haere ngā moana, ka whānui haere te wai, ā, ka piki ake ngā taumata o te moana.
- He aha te mea ka tupu i roto i te "whanuitanga rerekē o te wai"?
- whakahoki: He rerekē tēnei āhuatanga i te nuinga o ngā matū, ka whakawhanui te wai ina whakamatao mai i te 4°C ki te 0°C, kātahi ka whakawhāiti ina tio. Ko te tikanga o tēnei āhuatanga rerekē ko te 4°C te matotoru mōrahi o te wai. Koia te take e mānu ai te hukapapa (he iti ake te matotoru i te wai wai) i runga i te wai.
- He aha te hiranga o te whakawhānui wera i roto i te hangarau me te hanga?
- whakahoki: Ka whānui, ka whakawhāiti rānei ngā rauemi i te huringa o te pāmahana. Ki te kore e whakaarohia te whānui o te wera, ka pāngia pea ngā hanganga e te ahotea nui, te whakarerekētanga, te hinga rānei. Ka whakauruhia e ngā miihini me ngā kaihoahoa ngā āhuatanga hoahoa hei whakahaere haumaru i ēnei huringa.
- Ka taea te whakakore i te whānui wera?
- whakahoki: Āe, i te nuinga o te wā ka whakamataohia he rauemi, ka pāngia e te whakawhāititanga wera, he rerekē tēnei i te whakawhāititanga wera. Ko te nui me te āhua o tēnei whakawhāititanga ka whakawhirinaki ki te rauemi me ngā āhuatanga.
