5 ngā tauira o ngā pātai whakawhanui rōrahi
1. He pōro totoka he mea hanga ki te konumohe, ā, ko te tauwehenga whānui rārangi he 24 x 10 -6° C -1 . Mena he 30 cm³ te rōrahi o te pōro i te pāmahana 30 ° C , me whakamahana te pōro ki te pāmahana o….. ° C kia piki ake ai te rōrahi o te pōro ki te 30,5 cm³.
Kōrero
E mōhiotia ana:
Tauwehenga o te whakawhanuitanga rārangi (α ) = 24 x 10 -6 o C -1
Tauwehenga whānui rōrahi (γ ) = 3 a = 3 x 24 x 10 -6 o C -1 = 72 x 10 -6 o C -1
Te pāmahana tīmatanga (T 1 ) = 30 ° C
Te rōrahi tīmatanga (V 1 ) = 30 cm 3
Te rōrahi whakamutunga (V 2 ) = 30,5 cm 3
Huringa rōrahi (Δ V) = 30,5 cm 3 – 30 cm 3 = 0,5 cm 3
Pātai: Te pāmahana whakamutunga (T 2 )
Whakautu:
ΔV = g (V 1 )( ΔT )
ΔV = g (V1 ) ( T2 – T1 )
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
2. He pōro tuwhera he mea hanga ki te karāhe, ko te tauwehenga whānui rārangi he 9 x 10 -6° C -1 . I te pāmahana 20 ° C, ko te whānui o roto o te porowhita he 2,2 cm. Mena ka piki te whānui o roto o te pōro ki te 2,8, ko te pāmahana whakamutunga ko...
Kōrero
E mōhiotia ana:
Tauwehenga o te whakawhanuitanga rārangi (α ) = 9 x 10 -6 o C -1
Tauwehenga o te whakawhanuitanga rōrahi (γ ) = 3 α = 3 x 9 x 10 -6 o C -1 = 27 x 10 -6 o C -1
Te pāmahana tīmatanga (T 1 ) = 20 ° C
Te whānui tīmatanga (D 1 ) = 2,2 cm
Te whānui whakamutunga (D 2 ) = 2,8 cm
Te pūtoro tīmatanga (r 1 ) = D 1 / 2 = 2,2 cm 3 / 2 = 1,1 cm 3
Te pūtoro whakamutunga (r 2 ) = D 2 / 2 = 2,8 cm 3 / 2 = 1,4 cm 3
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
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
Huringa rōrahi (Δ V) = 11,48 cm 3 – 5,57 cm 3 = 5,91 cm 3
Pātai: Te pāmahana whakamutunga ( T 2 )
Whakautu:
ΔV = g (V 1 )( 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
39000 = T 2 – 20
39000 + 20 = T 2
T 2 = 39020 ° C
3. Ina werahia te hau, ka rite te pikinga o te rōrahi ki...
A. Te pāmahana tīmatanga
B. Te pāmahana whakamutunga
C. Te pikinga o te pāmahana
D. Te rōrahi tīmatanga
E. Te rōrahi whakamutunga
Kōrero:
He rite tonu te pikinga o te rōrahi hau ki te pikinga o te pāmahana, ki te panoni rānei o te pāmahana. Ka nui ake te pikinga o te pāmahana, ka nui ake te pikinga o te rōrahi.
4. Ka whakakīia tētahi oko karāhe 4 rita ki te wai, kātahi ka whakamahanatia kia piki ake te pāmahana mā te 20 ° C. Ka puta ko ētahi o ngā wai ka maringi. E mōhiotia ana ko te tauwehenga whānui raina o te karāhe = 9 x 10 -6 ° C -1 ; ko te tauwehenga whānui rōrahi o te wai = 2,1 x 10 -4 ° C -1 , kātahi ko te nui o te wai e maringi ana ko...
A. 0,015 rita
B. 0,018 rita
C. 0,020 rita
D. 0,021 rita
E. 0,025 rita
Kōrero
E mōhiotia ana:
Te rōrahi tīmatanga o te ipu karāhe me te wai (V o ) = 4 rita
Te huringa o te pāmahana o te karāhe me te wai ( ΔT) = 20 ° C
Ko te tauwehenga whānui rārangi o te karāhe (α) = 9 x 10 -6 o C -1
Tauwehenga whakawhanui rōrahi karāhe (γ) = 3α = 3 (9 x 10 -6 o C -1 ) = 27 x 10 -6 o C -1
Tauwehenga whānui o te rōrahi wai ( γ) = 2,1 x 10 -4 o C -1
I pātaihia: B E hia te nui o te wai i maringi?
Whakautu:
Tātai whakawhanui rōrahi:
V = V o + γ V o ΔT
V – V o = γ V o ΔT
ΔV = γV o ΔT
Ngā Mōhiohio:
V = rōrahi whakamutunga, V o = rōrahi tīmatanga, ΔV = huringa rōrahi, γ = tauwehenga whānui rōrahi, ΔT = huringa pāmahana.
Tātaihia te huringa 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
Tātaihia te huringa o te rōrahi 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 wai i te ipu karāhe, nō reira ka maringi ētahi o te wai.
Tātaihia te nui o te wai i maringi:
0,0168 rita – 0,002160 rita = 0,01464 rita = 0,015 rita
Ko te whakautu tika ko A.
5. He oko i hangaia ki te maitai (te tauwehenga o te whānui raina = 10-5 oC-1) he rahi 6 rita kua whakakiia ki te wai acetone (tau whakawhanui rōrahi = 1,5 x 10-3 oC-1). Ki te whakamahanahia ngā mea e rua kia piki ake te pāmahana o te rūma mai i te 0oC ki te 40oC, kātahi ko te nui o te acetone i maringi ko…
A. 0,35 rita
B. 0,48 rita
C. 0,58 rita
D. 1,36 rita
E. 1,48 rita
Kōrero
E mōhiotia ana:
Te rōrahi tīmatanga o te oko rino me te āketo (V o ) = 6 rita
Te huringa o te pāmahana o te oko rino me te āketo ( ΔT) = 40 o C
Ko te tauwehenga whānui raina o te maitai (α) = 10 -5 o C -1
Tauwehenga whakawhanui rōrahi o te maitai (γ) = 3α = 3 (10 -5 o C -1 ) = 3 x 10 -5 o C -1
Tauwehenga whakawhanui rōrahi āketona ( γ) = 1,5 x 10 -3 o C -1
I pātaihia: B E hia te nui o te wai i maringi?
Whakautu:
Tātai whakawhanui rōrahi:
ΔV = γV o ΔT
Ngā Mōhiohio:
ΔV = huringa o te rōrahi, γ = tauwehenga o te whakawhānui rōrahi, V o = rōrahi tīmatanga, ΔT = huringa o te pāmahana.
Tātaihia te panonitanga o te rōrahi o te oko maitai:
ΔV = γ V o ΔT = ( 3 x 10 -5 )(6)(40) = 720 x 10 -5 = 0,00720 rita
Tātaihia te huringa o te rōrahi 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 tō te oko rino, nō reira ka maringi ētahi o te wai.
Tātaihia te nui o te wai i maringi:
0,360 rita – 0,00720 rita = 0,3528 rita = 0,35 rita
Ko te whakautu tika ko A.
