Tātai whakawhanui

Ngā tauira pātai me ngā tātai whakawhanui

1. Ko te wai e whakamahia ana hei whakakī i tētahi inemahana he mea hanga mai i te mercury, i te waipiro rānei. Ko te kaupapa o te huringa te pūtake o te hanga i tēnei inemahana...

A. te tere whakawhanui o te konukōre hei hua o ngā huringa pāmahana
B. te mimiti wera nā ngā huringa o te pāmahana mercury
C. te pēhanga nā te huringa o te pāmahana i roto i te mercury
D. te rōrahi hei hua o ngā huringa o te pāmahana i roto i te mercury

Kōrero
Ka rerekē te rōrahi o tētahi mea ina rerekē tōna pāmahana. I te nuinga o te wā, ki te piki te pāmahana, ka piki anō hoki te rōrahi, ā, ki te heke te pāmahana, ka heke anō hoki te rōrahi. E pā ana hoki tēnei ki te konukōre me te waipiro.
Ko te whakautu tika ko D.

2. Tirohia te pikitia o tētahi konganuku rua i te pāmahana o te 26^oC i raro!

Ina whakamahanahia te bimetal ki te 50^oC, ko ngā kaupapa i puta koia ēnei:

Ko te ahunga o te piko me te take tika e tohuhia ana e….

A. (1) me (2)
B. (1) me (4)
C. (2) me (3)
D. (3) me (4)

Kōrero
Ko te bimetal he huinga o ngā konganuku e rua, he rerekē ngā tauwehenga whānui rārangi, arā, he nui ake te tauwehenga whānui rārangi o tētahi konganuku, ā, he iti ake te tauwehenga whānui rārangi o tētahi atu konganuku.

Ki te piki te pāmahana o te konganuku, ka pāngia te konganuku e te whānui o te roa (ka piki te roa o te konganuku), engari, ki te heke te pāmahana o te konganuku, ka pāngia te konganuku e te whakawhāititanga o te roa (ka heke te roa o te konganuku). Mō te pikinga pāmahana ōrite, ka whānui ngā konganuku e rua me te pikinga roa rerekē. Ko te konganuku he nui ake te tauwehenga whānui rārangi ka pāngia e te pikinga roa nui ake, ko te konganuku he iti ake te tauwehenga whānui rārangi ka pāngia e te pikinga roa iti ake. Waihoki, mō te hekenga pāmahana ōrite, ka mimiti ngā konganuku e rua me te whakahekenga roa rerekē. Ko te konganuku he nui ake te tauwehenga whānui rārangi ka pāngia e te whakaitinga roa nui ake, ko te konganuku he iti ake te tauwehenga whānui rārangi ka pāngia e te whakaitinga roa iti ake.

Nō reira, ina piki ake te pāmahana o te konganuku rua, ka piko te rīpene whakarewa he nui ake te tauwehenga whānui raina ki te rīpene whakarewa he iti ake te tauwehenga. He aha ai tēnei? Nā te mea ka taea e tēnei āhuatanga te rīpene whakarewa he nui ake te tauwehenga whānui raina kia roa ake i te rīpene whakarewa he iti ake te tauwehenga whānui raina.
I tetahi atu taha, ina heke te pāmahana o te konganuku rua, ka piko te rīpene whakarewa he iti ake te tauwehenga whānui raina ki te rīpene whakarewa he nui ake te tauwehenga whānui raina. Mā tēnei āhuatanga ka taea e te rīpene whakarewa he nui ake te tauwehenga whānui raina te poto ake i te rīpene whakarewa he iti ake te tauwehenga whānui raina.
Ko te whakautu tika ko C.

3. E rua ngā tokotoko, i te tīmatanga he 10 m te roa o ia tokotoko. He maitai me te konumohe ngā tokotoko e rua, ā, ko ngā tauwehenga whānui rārangi he 11 x 10.^-6 /^oC me te 24 x 10^-6 /^oC. I muri i te pikinga o te pāmahana mā te 40^oC, ko te roa o ngā tokotoko maitai me te konumohe ka noho hei...
A. 10,044 m me 10,096 m
B. 10,0044 m me 10,0096 m
C. 10,096 m me 10,044 m
D. 10,0096 m me 10,0044 m
Kōrero
E mōhiotia ana:
Te roa tīmatanga (L)_o) te tokotoko maitai = 10 mita
Te roa tīmatanga (L)_o) te tokotoko konumohe = 10 mita
Ko te tauwehenga whānui rārangi o te maitai (α) = 11 x 10^-6 /^oC
Ko te tauwehenga whānui rārangi o te konumohe (α) = 24 x 10^-6 /^oC
Huringa pāmahana (ΔT) = 40^oC
Pātai: Te roa o ngā tokotoko maitai me te konumohe i muri i te pikinga o te pāmahana
Whakautu:
Tātai whakawhanui roa:
R = R_o + ΔL
R = R_o + α L_o ΔT
Ko te roa o te pae maitai i muri i te pikinga o te pāmahana:
R = R_o + α L_o ΔT
R = 10 + (11 x 10^-6)(10)(40)
R = 10 + (11 x 10^-6)(400)
R = 10 + (4400 x 10^-6)
L = 10 + 0,0044
L = 10,0044 mita

Ko te roa o te tokotoko konumohe i muri i te pikinga o te pāmahana:
R = R_o + α L_o ΔT)
R = 10 + (24 x 10^-6)(10)(40)
R = 10 + (24 x 10^-6)(400)
R = 10 + (9600 x 10^-6)
L = 10 + 0,0096
L = 10,0096 mita
Ko te whakautu tika ko B.

4. He roa l te pae whakarewa me te tauwehenga whānui rārangi α i te pāmahana o te 25^oC. Ki te whakamahanatia ki te 30^oC, ka piki ake te roa Δl. Mēnā ka tapahia te konganuku ki te 1/3 o tōna roa taketake, ka piki ake te roa ina whakamahanatia ki te pāmahana o te 35^oKo C te….
A. 2/3 Δl
B. 3/2 Δl
C. 5/3 Δl
D. 5/2 Δl
Kōrero
E mōhiotia ana:
Mena
Tauwehenga o te whānui raina o te konganuku (α) = α
Ko te roa tīmatanga o te konganuku (L^o) = l
Te pikinga o te pāmahana (ΔT) = 30^oC - 25^oC=5^oC
māka
Te pikinga o te roa (ΔL) = Δl
Pātai: Mēnā ko te lo = 1/3 l me te ΔT = 35^oC - 25^oC=10^oC kātahi ka piki te roa = ….. ?
Whakautu:
Tātaihia te tauwehenga whānui rārangi o te konganuku (α) mā te whakamahi i te tātai mō te pikinga o te roa o te konganuku:

Whakamahia tēnei tauwehenga o te uara whānui rārangi hei tatau i te pikinga o te roa o te konganuku ina rerekē tōna pāmahana mai i te 25^oKa huri a C hei 35^oC.

Ko te whakautu tika ko A.

5. I te pāmahana o te 20^oC, ko te roa o te tokotoko konumohe he 200 cm. Mēnā ka whakamahanatia ki te pāmahana o te 100^oC ka piki ake te roa mā te 0,00384 m. Mena i te pāmahana o te 20^oC. He pōro kei reira i hangaia ki te rauemi konumohe kotahi, nō reira, kia piki ake ai te rōrahi o te pōro mā te 1% o te rōrahi o te pōro taketake, me whakamahana te pōro ki te pāmahana...
A. 139^oC
B. 159^oC
C. 208^oC
D. 228^oC
Kōrero
E mōhiotia ana:
Te roa tīmatanga o te tokotoko konumohe (L)_o) = 200 henimita = 2 mita
Huringa pāmahana (ΔT) = 100^oC - 20^oC=80^oC
Te pikinga o te roa (Δl) = 0,00384 mita
Pātai: Kia piki ake ai te rōrahi o te pōro mā te 1% mai i te rōrahi taketake o te pōro, me whakamahana te pōro ki te pāmahana o...
Whakautu:
Tātaihia te tauwehenga roa o te tokotoko konumohe mā te whakamahi i te tātai pikinga roa:

Tauwehenga whānui rōrahi o te konumohe (β) = 3 x tauwehenga whānui roa (α) = 3 (0,000024) = 0,000072

E mōhiotia ana:
Te rōrahi taketake o te pōro = V
Te pikinga o te rōrahi o te pōro konumohe (ΔV) = (1%)(V) = (1/100)(V) = V/100
Te pikinga o te pāmahana (ΔT) = T – 20
I pātaihia: Kua wera te pōro ki te pāmahana (T) = ….. ?
Whakautu:

Ko te whakautu tika ko B.

6. He kōhao porowhita kōpiko kei waenganui o tētahi pereti whakarewa porowhita. Ina whakamahanatia te pereti ka...
A. Ka piki ake te whānui o te pereti, ka heke iho te whānui o te kōhao
B. Ka heke te whānui o te pereti, ka piki ake te whānui o te kōhao
C. ka piki ake te whānui o te pereti, ka piki ake hoki te whānui o te kōhao
D. ka heke te whānui o te pereti, ka heke hoki te whānui o te kōhao
Kōrero
Te tātai mō te horahanga o te porowhita (A):
A = π r²
Tātai whānui porowhita (D):
D = 2 r
Ki te whakamahanahia he pereti whakarewa, ka piki ake te horahanga (A) o te pereti whakarewa. Ki te piki ake te horahanga o te pereti whakarewa, ka piki ake te whānui (D) te pūtoro rānei (r) o te pereti whakarewa. Ki te piki ake te whānui (D) te pūtoro rānei (r) o te pereti whakarewa, ka piki ake te whānui me te pūtoro o te kōhao.
Ko te whakautu tika ko C.

7. He kirihou te anga mōhiti e rua, ā, ko te tauwehenga whānui rārangi he 1,3 x 10^-4 (^oC)^-1He porowhita ngā kōhao arotahi, ā, ko te whānui o te 2,2 cm. Kia uru ai ngā arotahi he whānui o te 2,21 cm ki roto i ngā kōhao arotahi, me whakamahana te anga mōhiti kia huri rā anō te pāmahana mā te….
A. 25^oC
B. 35^oC
C. 45^oC
D. 55^oC
Kōrero
E mōhiotia ana:
Tauwehenga o te whānui raina o te kirihou (α) = 1,3 x 10^-4 (^oC^-1)
Te pūtoro o te kōhao arotahi (r)¹) = te pūtoro o te kōhao arotahi tuatahi = 2,2 cm
Te pūtoro o te kōhao arotahi i muri i te whakamahana (r)²) = 2,21 henemita
Pātai: Te huringa o te pāmahana o te anga mōhiti
Whakautu:
Kia taea ai te whakauru i tētahi karāhe arotahi he 2,21 cm te whānui, i muri i te whakamahana, me piki ake te whānui o te karāhe arotahi mā te 2,21 cm – 2,20 cm = 0,01 cm.
Ko te tauwehenga whānui o te horahanga o te pereti whakarewa (β) = 2 x tauwehenga whānui rārangi (α) = 2 x 1,3 x 10^{-4 o}C^-1 = 2,6x10^{-4 o}C^-1

Ngā huringa pāmahana:

Ko te whakautu tika ko B.

8. I te whakaahua e whai ake nei, he āputa kei waenganui i ngā ara rerewē e rua i hangaia ki te rino. Ko te kaupapa o tēnei āputa he...
A. Ka iti haere te kaha waku ina haere te tereina.
B. Ka iti haere ngā wiri ina hipa te tereina.
C. Kāore ngā ara rerewē e piko ina whakawhanuitia te rino
D. Kāore ngā ara rerewē e piko ina pāhia e te tereina.
Kōrero
He mea hanga ngā reera ki te konganuku, ka ngāwari te whakawhanui ina rerekē te pāmahana. I te rā wera, ka piki te pāmahana o ngā reera, ka whakawhanui. Ina mirimiri ngā reera ki ngā wira tereina, ka piki anō hoki te pāmahana, ka whakawhanui. Nō reira, ko te āputa i waenganui i ngā reera e rua ka ārai i te piko o ngā reera ina whakawhanui te konganuku.
Ko te whakautu tika ko C.

9.
He mea whakamahana te rino hiko e motu aunoa ana i te iahiko ina tae te rino ki tētahi pāmahana. Mā te pikinga o te pāmahana ka piko te rīpene whakarewa rua, e whakaaturia ana i te ahua. Ka puta tēnei nā te mea…
A. He nui ake te wera motuhake o te konganuku (B) i te wera motuhake o te konganuku (A)
B. He iti ake te wera motuhake o te konganuku (B) i te wera motuhake o te konganuku (A)
C. He nui ake te tauwehenga whānui rārangi o te konganuku (B) i te tauwehenga whānui rārangi (A)
D. He iti ake te tauwehenga whānui rārangi o te konganuku (B) i te tauwehenga whānui rārangi (A)
Kōrero
Ko te konganuku rua he mea hanga mai i te konganuku A me te konganuku B, ā, he rerekē ngā tauwehenga whānui rārangi. I runga i te ahua i runga ake nei, ina piki te pāmahana, ka ahua piko te konganuku A ki te konganuku B. Nō reira, ka taea te whakatau ko te pikinga pāmahana ōrite, ka nui ake te whānui rārangi o te konganuku A, engari he iti ake te whānui rārangi o te konganuku B. He nui ake te pikinga o te roa o te konganuku A i te konganuku B, nō reira he nui ake te tauwehenga whānui rārangi o te konganuku A i te konganuku B.
Ko te whakautu tika ko D.

Pūtake pātai:

Ngā Pātai OSN mō te Ahupūngao o te Kura Tuarua