Ko ngā mea totoka anake ka pāngia e te whānui rārangi; ko ngā mea katoa ka pāngia e te whānui rōrahi, te totoka, te wai, me te hau. He rite te whārite o te whānui rōrahi ki te whārite o te whānui rārangi.
Whakaahuatanga: V o = Te rōrahi tīmatanga, V = Te rōrahi whakamutunga, ΔV = V – V o = Te huringa o te rōrahi, T o = Te pāmahana tīmatanga, T = Te pāmahana whakamutunga, ΔT = T – T o = Te huringa o te pāmahana, β = te tauwehenga o te whakawhānui rōrahi. Ngā waeine o β = (C o ) -1
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Ka pā te whārite whānui rōrahi i runga ake nei ina iti iho ngā huringa o te rōrahi o ngā mea (totoka, wai, me te hau) i te rōrahi taketake o te mea. Mena he nui ake te huringa o te rōrahi o tētahi mea i te rōrahi tīmatanga o te mea, kāore te whārite o te whānui rōrahi e homai i ngā hua tika. I te nuinga o te wā, kāore i te nui rawa ngā huringa o te rōrahi e pāngia ana e ngā mea totoka. I tētahi atu taha, he nui te tauwehenga whānui rōrahi o te wai me te hau. He ngāwari hoki te whakarerekē i te tauwehenga whānui rōrahi mō ngā matū hau mena ka rerekē te pāmahana. Nō reira, ka whakamahia te tātai i runga ake nei mō te whānui o ngā mea totoka anake.
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1. I te 30 ° C, ko te rōrahi o tētahi porowhita konumohe he 30 cm³ . Ko te tauwehenga whānui rārangi he 24 x 10−6 ° C −1 . Mena ko te rōrahi whakamutunga he 30.5 cm³ , he aha te pāmahana whakamutunga o te porowhita konumohe?
Mōhiotia:
Ko te tauwehenga whānui rārangi ( α ) = 24 x 10 -6 o C -1
Ko te tauwehenga o te whakawhanuitanga rōrahi ( β ) = 3 α = 3 x 24 x 10 -6 o C -1 = 72 x 10 -6 o C -1
Ko te pāmahana tīmatanga (T 1 ) = 30 ° C
Ko te rōrahi tīmatanga (V 1 ) = 30 cm 3
Ko te rōrahi whakamutunga (V 2 ) = 30.5 cm 3
Ko te panonitanga o te rōrahi ( Δ V) = 30.5 cm 3 – 30 cm 3 = 0.5 cm 3
E hiahiatia ana: Te pāmahana whakamutunga (T 2 )
Rongoā:
ΔV = β (V1 ) ( ΔT )
Δ V = β (V 1 )(T 2 – T 1 )
0.5 cm3 = ((72 x 10-6 o te ataC-1)(30cm3)(T2 - 30oC)
0.5 = (2160 x 10 -6 ) (T 2 – 30 )
0.5 = (2.160 x 10 -3 ) (T 2 – 30 )
0.5 = (2.160 x 10 -3 ) (T 2 – 30 )
0.5 / (2.160 x 10 -3 ) = T 2 – 30
0.23 x 10 3 = T 2 – 30
0.23 x 1000 = T 2 – 30
230 = T 2 – 30
230 + 30 = T 2
T 2 = 260 ° C
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2. Ko te tauwehenga whānui rārangi o tētahi porowhita whakarewa he 9 x 10 -6 o C -1 . Ko te whānui o roto o te porowhita whakarewa i te 20 o C he 2.2 cm. Mena ko te whānui whakamutunga he 2.8 cm, he aha te pāmahana whakamutunga!
Mōhiotia:
Ko te tauwehenga whānui rārangi ( α ) = 9 x 10 -6 o C -1
Ko te tauwehenga o te whakawhanuitanga rōrahi ( β) = 3 α = 3 x 9 x 10 -6 o C -1 = 27 x 10 -6 o C -1
Ko te pāmahana tīmatanga (T 1 ) = 20 ° C
Ko te whānui tīmatanga (D 1 ) = 2.2 cm
Ko te whānui whakamutunga (D 2 ) = 2.8 cm
Ko te pūtoro tīmatanga (r 1 ) = D 1 / 2 = 2.2 cm 3 / 2 = 1.1 cm 3
Ko te pūtoro whakamutunga (r 2 ) = D 2 / 2 = 2.8 cm 3 / 2 = 1.4 cm 3
Ko te rōrahi tīmatanga (V 1 ) = 4/3 π r 1 3 = (4/3)(3.14)(1.1 cm) 3 = (4/3)(3.14)(1.331 cm 3 ) = 5.57 cm 3
Ko te rōrahi whakamutunga (V 2 ) = 4/3 π r 2 3 = (4/3)(3.14)(1.4 cm) 3 = (4/3)(3.14)(2.744 cm 3 ) = 11.48 cm 3
Ko te panonitanga o te rōrahi ( Δ V) = 11.48 cm³ – 5.57 cm³ = 5.91 cm³
E hiahiatia ana: Te pāmahana whakamutunga ( T2 )
Rongoā:
ΔV = β (V1 ) ( ΔT )
5.91 cm3 = ((27 x 10-6 o te ataC-1)(5.57 cm3)(T2 - 20oC)
5.91 = (150.39 x 10 -6 ) (T 2 – 20)
5.91 / 150.39 x 10 -6 = T 2 – 20
0.039 x 10 6 = T 2 – 20
39 x 10 3 = T 2 – 20
39,000 = T 2 – 20
39,000 + 20 = T 2
T 2 = 39,020 ° C
3. He 2000-cm3 ipu konumohe, kī tonu i te wai i te 0oC. Kātahi ka whakamahanatia ki te 90oC. Mena ko te tauwehenga whānui rārangi mō te konumohe he 24 x 10-6 (oC)-1 ā, ko te tauwehenga whakawhanui rōrahi mō te wai he 6.3 x 10-4 (oC)-1, whakatau i te rahinga o te wai i maringi.
Mōhiotia:
Ko te rōrahi tīmatanga o te ipu konumohe me te wai (V o ) = 2000 cm 3 = 2 x 10 3 cm 3
Ko te pāmahana tīmatanga o te ipu konumohe me te wai (T 1 ) = 0 ° C
Ko te pāmahana whakamutunga o te ipu konumohe me te wai (T 2 ) = 90 ° C
Ko te tauwehenga whānui rārangi mō te konumohe (α) = 24 x 10 -6 ( o C ) -1
Ko te tauwehenga whakawhanui rōrahi mō te konumohe (γ) = 3α = 3 (24 x 10 -6 ( o C ) -1 ) = 72 x 10 -6 o C -1
Ko te tauwehenga whānui o te rōrahi mō te wai (γ) = 6.3 x 10 -4 ( o C ) -1
E hiahiatia ana: Te rahinga 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
Tātaihia te huringa o te rōrahi o te ipu konumohe:
ΔV = γ V o ΔT = (72 x 10 -6 )(2 x 10 3 )(90) = 12960 x 10 -3 = 12.960 cm 3
Tātaihia te huringa o te rōrahi o te wai:
ΔV = γ V o ΔT = (6.3 x 10 -4 )(2 x 10 3 )(90) = 1134 x 10 -1 = 113.4 cm 3
He nui ake te panonitanga o te rōrahi o te wai i te ipu konumohe, nō reira i maringi ai ētahi wai.
Tātaihia te nui o te wai i maringi:
113.4 henimita 3 – 12.960 henimita 3 = 100.44 henimita 3
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- Te huri i ngā tauine pāmahana
- Whānuitanga rārangi
- Te whakawhānui ake i te rohe
- Whakawhanuitanga rōrahi
- Heat
- Te ōrite ā-pūkaha o te wera
- Te wera motuhake me te kaha wera
- Te wera huna, te wera o te hanumi, te wera o te mimiti
- Te tiaki pūngao mō te whakawhiti wera
