1. I te 20 ° C, ko te roa o tētahi rau maitai he 50 cm, ā, ko te whānui he 30 cm. Mena ko te tauwehenga whānui rārangi mō te maitai he 10 -5 ° C -1 , tātaihia te huringa horahanga me te horahanga whakamutunga i te 60 ° C.
Mōhiotia:
Ko te pāmahana tīmatanga (T 1 ) = 20 ° C
Ko te pāmahana whakamutunga (T 2 ) = 60 ° C
Ko te huringa o te pāmahana ( ΔT ) = 60 ° C – 20 ° C = 40 ° C
Ko te horahanga tīmatanga (A 1 ) = te roa x te whānui = 50 cm x 30 cm = 1500 cm 2
Ko te tauwehenga whānui rārangi mō te maitai ( α) = 10 -5 o C -1
Ko te tauwehenga whānui o te horahanga mō te maitai ( β) = 2α = 2 x 10 -5 o C -1
E hiahiatia ana: Te huringa o te horahanga ( ΔA )
Rongoā:
Te huringa o te horahanga ( ΔA ):
ΔA = βA 1 ΔT
ΔA = ( 2 x 10 -5 o C -1 )(1500 cm 2 )(40 o C)
ΔA = (80 x 10 -5 )(1500 cm 2 )
ΔA = 1 20,000 x 10 -5 cm 2
ΔA = 1. 2 x 10 5 x 10 -5 cm 2
ΔA = 1.2 cm²
Ko te horahanga whakamutunga ( A 2 ):
A 2 = A 1 + ΔA
A 2 = 1500 cm 2 + 1. 2 cm 2
A 2 = 1501. 2 cm 2
[irp]
2. I te 30 ° C, ko te horahanga o tētahi rau konumohe he 40 cm² , ā, ko te tauwehenga whānui rārangi he 24 x 10⁻¹ -6 / ⁻¹ . Tātaihia te pāmahana whakamutunga mēnā ko te horahanga whakamutunga he 40.2 cm².
Mōhiotia:
Ko te pāmahana tīmatanga (T 1 ) = 30 ° C
Ko te tauwehenga whānui rārangi ( α) = 24 x 10 -6 o C -1
Ko te tauwehenga whānui o te horahanga ( β) = 2a = 2 x 24 x 10 -6 o C -1 = 48 x 10 -6 o C -1
Ko te horahanga tīmatanga (A 1 ) = 40 cm 2
Ko te horahanga whakamutunga (A 2 ) = 40.2 cm 2
Ko te panonitanga o te horahanga ( ΔA) = 40.2 cm² – 40 cm² = 0.2 cm²
E hiahiatia ana: Whakatauhia te pāmahana whakamutunga (T 2 )
Rongoā:
Te tātai o te huringa horahanga ( ΔA) :
ΔA = βA 1 ΔT
Te pāmahana whakamutunga (T 2 ):
ΔA = βA1 ( T2 – T1 )
0.2 cm2 = (48 x 10-6 oC-1)(40 henimita2)(T2 - 30oC)
0.2 = (1920 x 10 -6 ) (T 2 – 30 )
0.2 = (1.920 x 10 -3 ) (T 2 – 30)
0.2 = (2 x 10 -3 ) (T 2 – 30)
0.2 / (2 x 10 -3 ) = T 2 – 30
0.1 x 10 3 = T 2 – 30
1 x 10 2 = T 2 – 30
100 = T 2 – 30
100 + 30 = T 2
T2 = 130
Ko te pāmahana whakamutunga = 130 ° C
[irp]
3. Ko te radius o te mowhiti i te 20 ° C he 20 cm. Mena ko te radius whakamutunga i te 100 ° C he 20.5 cm, tautuhia te tauwehenga whānui o te horahanga me te tauwehenga whānui rārangi…
Mōhiotia:
Ko te pāmahana tīmatanga (T 1 ) = 30 ° C
Ko te pāmahana whakamutunga (T 2 ) = 100 ° C
Ko te huringa o te pāmahana ( ΔT ) = 100 ° C – 30 ° C = 70 ° C
Ko te pūtoro tīmatanga (r 1 ) = 20 cm
Ko te radius whakamutunga (r 2 ) = 20.5 cm
E hiahiatia ana: Te tauwehenga whānui o te horahanga ( β )
Rongoā:
Ko te horahanga tīmatanga (A 1 ) = π r 1 2 = (3.14)(20 cm) 2 = (3.14)(400 cm 2 ) = 1256 cm 2
Ko te horahanga whakamutunga (A 2 ) = π r 2 2 = (3.14)(20.5 cm) 2 = (3.14)(420.25 cm 2 ) = 1319.585 cm 2
Ko te panonitanga o te horahanga ( ΔA) = 1319.585 cm² – 1256 cm² = 63.585 cm²
Te tātai o te huringa horahanga ( ΔA) :
ΔA = βA 1 ΔT
Te tauwehenga o te whakawhānui rohe:
ΔA = βA 1 ΔT
63.585 henimita 2 = b (1 256 henimita 2 )(70 o C)
63.585 = b ( 87,920 ° C)
β = 63.585 / 87,920 ° C
β = 0.00072 / o C
β = 7.2 x 10 -4 / o C
β = 7.2 x 10 -4 o C -1
Te tauwehenga o te whakawhānui raina ( α ):
β = 2 α
α = β / 2
α = (7.2 x 1 0 -4 ) / 2
α = 3.6 x 10 -4 o C -1
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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
