Te whānui rārangi – ngā raruraru me ngā otinga

1. E 40 cm te roa o te maitai i te 20 ^° C. Ko te tauwehenga whānui rārangi mō te maitai ko 12 x 10⁻¹ ^-6 ( ^C₂o₃ ) ^-1 . Ko te pikinga o te roa me te roa whakamutunga ina tae ki te 70 ^° C ka…

Mōhiotia:

Ko te huringa o te pāmahana ( ΔT ) = 70 ^° C – 20 ^° C = 50 ^° C

Ko te roa taketake (L ₁ ) = 40 cm

Tauwehenga o te whakawhanuitanga rārangi mō te maitai (α ) = 12 x 10 ^-6 (C ^o ) ^-1

E hiahiatia ana: Te huringa o te roa ( ΔL ) me te roa whakamutunga ( _L2 )

Rongoā:

a) Te panonitanga o te roa ( ΔL)

ΔL = αL ₁ ΔT

Δ L = ( 12×10 ^{-6 o} C ^-1 )(40 cm)(50 ^o C)

Δ L = (10 ^-6 )(24 x 10 ³ ) cm

ΔL = 24 x 10 ^-3 henemita

ΔL = 24 / 10 ³ henimita

ΔL = 24 / 1000 cm

ΔL = 0.024 henimita

b) Te roa whakamutunga (L ₂ )

L ₂ = L ₁ + ΔL

L ₂ = 40 henimita + 0.024 henimita

L ₂ = 40.024 henimita

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2. He tokotoko rino kua whakamahanatia mai i te 30 ^° C ki te 80 ^° C . Ko te roa whakamutunga o te rino he 115 cm, ā, ko te tauwehenga whānui rārangi he 3×10−3−1 ^{. He aha} te roa taketake me te huringa o te roa o te rino?

Rongoā:

Ko te huringa o te pāmahana ( ΔT) = 80 ^° C – 30 ^° C = 50 ^° C

Ko te roa whakamutunga (L ₂ ) = 115 cm

Ko te tauwehenga whānui rārangi ( α) = 3×10 ^{-3 o} C ^-1

E hiahiatia ana: te roa taketake (L ₁ ) me te huringa o te roa ( Δ L)

Rongoā:

a) Te roa taketake (L ₁ )

Te tātai o te huringa roa mō te whānui rārangi:

ΔL = αL ₁ ΔT​

Te tātai o te roa whakamutunga :

L ₂ = L ₁ + ΔL

L ₂ = L ₁ + α L ₁ ΔT

L ₂ = L ₁ (1 + α ΔT)

115 cm = L ₁ (1 + (3.10 ^{-3 o} C ^-1 )(50 ^o C)

115 henimita = L ₁ (1 + 150.10 ^-3 )

115 henimita = L ₁ (1 + 0.15)

115 henimita = L ₁ (1.15)

R 1 = 115 henimita / 1.15 L 1 = 100 henemita b) te huringa o te roa ( ΔL ) ΔL = L2 – L1 ΔL = 115 henimita – 100 henimita ΔL = 15 cm

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3. I te 25 ^o C, ko te roa o te karāhe he 50 cm. I muri i te whakamahana, ko te roa whakamutunga o te karāhe he 50.9 cm. Ko te tauwehenga o te whakawhānui raina ko α = 9 x 10 ^-6 C ^-1 . Tātaihia te pāmahana whakamutunga o te karāhe…

Mōhiotia:

Ko te roa taketake (L ₁ ) = 50 cm

Ko te roa whakamutunga (L ₂ ) = 50.09 cm

Ko te panonitanga o te roa ( ΔL ) = 50.2 cm – 50 cm = 0.09 cm

Ko te tauwehenga o te whakawhānui rārangi (α) = 9 x 10 ^{-6 o} C ^-1

Ko te pāmahana taketake (T ₁ ) = 25 ^° C

E hiahiatia ana: Te pāmahana whakamutunga (T ₂ )

Rongoā:

ΔL = α L ₁ ΔT

ΔL = αL1 ( _T2 – _T1 )​_​

0.09 henimita = ( 9 x 10 ^{-6 o} C) (50 henimita )(T ₂ – 25 ^o C)

0.09 = (45 x 10 ^-5 )(T ₂ – 25)

0.09 / (45 x 10 ^-5 ) = T ₂ – 25

0.002 x 10 ⁵ = T ₂ – 25

2 x 10 ² = T ₂ – 25

200 = T ₂ – 25

T ₂ = 200 + 25

T ₂ = 225 ^° C

Ko te pāmahana whakamutunga he 225 ^° C.

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4. Ko te roa taketake o te konganuku he 1 mita, ā, ko te roa whakamutunga he 1.02 m. Ko te huringa o te pāmahana he 50 Kelvin. Tātaihia te tauwehenga o te whakawhānui rārangi!

Mōhiotia:

Ko te roa tīmatanga (L ₁ ) = 1 mita

Ko te roa whakamutunga (L ₂ ) = 1.02 mita

Ko te panonitanga o te roa ( Δ L) = L ₂ – L ₁ = 1.02 mita – 1 mita = 0.02 mita

Te huringa o te pāmahana (ΔT ) = 50 Kelvin = 50 ^° C

E hiahiatia ana: Te tauwehenga o te whakawhānui raina

Rongoā:

ΔL = αL ₁ ΔT​

0.02 m = α (1 m ) (50 ^° C)

0.02 = α ( 50 ^° C)

α = 0.02 / 50 ^° C

α = 0.0004 ^o C ^-1

α = 4 x 10 ^{-4 o} C ^-1

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1. Te huri i ngā tauine pāmahana
2. Whānuitanga rārangi
3. Te whakawhānui ake i te rohe
4. Whakawhanuitanga rōrahi
5. Heat
6. Te ōrite ā-pūkaha o te wera
7. Te wera motuhake me te kaha wera
8. Te wera huna, te wera o te hanumi, te wera o te mimiti
9. Te tiaki pūngao mō te whakawhiti wera