Ka hoʻonui laina - nā pilikia a me nā hoʻonā

1. He 40 kenimika ka lōʻihi o ke kila ma 20 ^o C. ʻO ke koina o ka hoʻonui linear no ke kila he 12 x 10 ^-6 (C ^o ) ^-1 . ʻO ka hoʻonui ʻana o ka lōʻihi a me ka lōʻihi hope loa i ka wā ma 70 ^o C e…

ʻIke ʻia:

ʻO ka loli o ka mahana ( ΔT ) = 70 ^o C – 20 ^o C = 50 ^o C

ʻO ka lōʻihi mua (L ₁ ) = 40 kenimika

ʻO ke koina o ka hoʻonui linear no ke kila (α ) = 12 x 10-6 ⁽ C ^o ) ^-1

Makemake ʻia: ʻO ka loli o ka lōʻihi ( ΔL ) a me ka lōʻihi hope loa ( _L2 )

Lōlā:

a) Ka loli o ka lōʻihi ( ΔL)

ΔL = αL ₁ ΔT

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

Δ L = (10 ^-6 )(24 x 10 ³ ) knm

Δ L = 24 x 10 ^-3 kenimika

Δ L = 24 / 10 ³ kenimika

Δ L = 24 / 1000 kenimika

Δ L = 0.024 kenimika

b) Ka lōʻihi hope loa (L ₂ )

L ₂ = L ₁ + ΔL

L ₂ = 40 kenimika + 0.024 kenimika

L ₂ = 40.024 kenimika

ʻAʻole maopopo

2. He koʻokoʻo hao i hoʻomehana ʻia mai 30 ^° C a i 80 ^{° C .} ʻO ka lōʻihi hope loa o ka hao he 115 cm a ʻo ke koina o ka hoʻonui linear he 3×10−3−1−2 ^{. He} aha ka lōʻihi mua a me ka loli o ka lōʻihi o ka hao?

Lōlā:

ʻO ka loli o ka mahana ( ΔT) = 80 ^o C – 30 ^o C = 50 ^o C

ʻO ka lōʻihi hope loa (L ₂ ) = 115 kenimika

ʻO ke koina o ka hoʻonui linear ( α) = 3 × 10 ^{-3 o} C ^-1

Makemake ʻia: ka lōʻihi mua (L ₁ ) a me ka loli o ka lōʻihi ( Δ L)

Lōlā:

a) Ka lōʻihi mua (L ₁ )

ʻO ke ʻano o ka loli o ka lōʻihi no ka hoʻonui linear:

ΔL = αL ₁ ΔT​

ʻO ke ʻano o ka lōʻihi hope loa :

L ₂ = L ₁ + ΔL

L ₂ = L ₁ + α L ₁ ΔT

L ₂ = L ₁ (1 + α ΔT)

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

115 kenimika = L ₁ (1 + 150.10 ^-3 )

115 kenimika = L ₁ (1 + 0.15)

115 kenimika = L ₁ (1.15)

L 1 = 115 kenimika / 1.15 L 1 = 100 kenimika b) ka loli o ka lōʻihi ( ΔL ) Δ L = L 2 – L 1 ΔL = 115 kenimika – 100 kenimika Δ L = 15 kenimika

ʻAʻole maopopo

3. Ma 25 ^o C, ʻo ka lōʻihi o ke aniani he 50 kenimika. Ma hope o ka hoʻomehana ʻana, ʻo ka lōʻihi hope loa o ke aniani he 50.9 kenimika. ʻO ke koina o ka hoʻonui linear ʻo α = 9 x 10 ^-6 C ^-1 . E hoʻoholo i ka mahana hope loa o ke aniani…

ʻIke ʻia:

ʻO ka lōʻihi mua (L ₁ ) = 50 kenimika

ʻO ka lōʻihi hope loa (L ₂ ) = 50.09 kenimika

ʻO ka loli o ka lōʻihi ( Δ L) = 50.2 kenimika - 50 kenimika = 0.09 kenimika

ʻO ke koina o ka hoʻonui linear (α) = 9 x 10 ^{-6 o} C ^-1

ʻO ka mahana mua (T ₁ ) = 25 ^o C

Makemake ʻia: ʻO ka mahana hope loa (T ₂ )

Lōlā:

ΔL = α L ₁ ΔT

ΔL = αL1 ( _T2 – _T1 )​_​

0.09 kenimika = ( 9 x 10 ^{-6 o} C) (50 kenimika )(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 ^o C

ʻO 225 ^° C ka mahana hope loa .

ʻAʻole maopopo

4. ʻO ka lōʻihi mua o ka metala he 1 mika a ʻo ka lōʻihi hope loa he 1.02 m. ʻO ka loli o ka mahana he 50 Kelvin. E hoʻoholo i ke koina o ka hoʻonui linear!

ʻIke ʻia:

ʻO ka lōʻihi mua (L ₁ ) = 1 mika

ʻO ka lōʻihi hope loa (L ₂ ) = 1.02 mika

ʻO ka loli o ka lōʻihi ( Δ L) = L ₂ – L ₁ = 1.02 mika – 1 mika = 0.02 mika

ʻO ka loli o ka mahana (ΔT ) = 50 Kelvin = 50 ^o C

Makemake ʻia: ʻO ke koina o ka hoʻonui linear

Lōlā:

ΔL = αL ₁ ΔT​

0.02 m = α (1 m ) (50 ^o C)

0.02 = α ( 50 ^o C)

α = 0.02 / 50 ^o C

α = 0.0004 ^o C ^-1

α = 4 x 10 ^{-4 o} C ^-1

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