Kukula kwa mzere - mavuto ndi mayankho

1. Chitsulo chimakhala ndi kutalika kwa 40 cm pa 20 ^o C. Chiŵerengero cha kukula kwa mzere wachitsulo ndi 12 x 10 ^-6 (Co ⁾ -1 ^. Kuwonjezeka kwa kutalika ndi kutalika komaliza pamene chili pa 70 ^o C kudzakhala…

Zodziwika:

Kusintha kwa kutentha ( ΔT ) = 70 ^o C – 20 ^o C = 50 ^o C

Kutalika koyambirira (L ₁ ) = 40 cm

Koyefifiti ya kukula kolunjika kwa chitsulo (α ) = 12 x 10 ^-6 (Co ^o ) ^-1

Kufunidwa: Kusintha kwa kutalika ( Δ L) ndi kutalika komaliza (L ₂ )

Yankho:

a) Kusintha kwa kutalika ( ΔL)

Δ L = α L ₁ ΔT

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

Δ L = (10 ^-6 )(24 x 10 ³ ) masentimita

Δ L = 24 x 10 ^-3 cm

Δ L = 24 / 10 ³ cm

Δ L = 24 / 1000 cm

Δ L = 0.024 cm

b) Utali womaliza (L ₂ )

L ₂ = L ₁ + ΔL

L ₂ = 40 cm + 0.024 cm

L ₂ = 40.024 cm

[irp]

2. Ndodo yachitsulo yotenthedwa kuyambira 30 ^o C mpaka 80 ^o C. Utali womaliza wa chitsulo ndi 115 cm ndipo coefficient of linear expansion ndi 3 × 10 ^{-3 o} C ^-1 . Kodi kutalika koyambirira ndi kusintha kwa kutalika kwa chitsulo ndi kotani?

Yankho:

Kusintha kwa kutentha ( ΔT) = 80 ^o C – 30 ^o C = 50 ^o C

Kutalika komaliza (L ₂ ) = 115 cm

Chiŵerengero cha kukula kolunjika ( α) = 3×10 ^-3o C ^-1

Kufunidwa: kutalika koyambirira (L ₁ ) ndi kusintha kwa kutalika ( Δ L)

Yankho:

a) Utali woyambirira (L ₁ )

Fomula ya kusintha kwa kutalika kwa kukula kwa mzere:

Δ L = α L ₁ ΔT

Fomula ya kutalika komaliza :

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 cm = L ₁ (1 + 150.10 ^-3 )

115 cm = L ₁ (1 + 0.15)

115 cm = L ₁ (1.15)

L 1 = 115 cm / 1.15 L 1 = 100 cm b) kusintha kwa kutalika ( ΔL ) Δ L = L 2 – L 1 ΔL = 115 cm - 100 cm Δ L = 15 cm

[irp]

3. Pa 25 ^o C, kutalika kwa galasi ndi 50 cm. Pambuyo potenthetsa, kutalika komaliza kwa galasi ndi 50.9 cm. Chiwerengero cha kukula kwa mzere ndi α = 9 x 10 ^-6 C ^-1 . Dziwani kutentha komaliza kwa galasi…

Zodziwika:

Kutalika koyambirira (L ₁ ) = 50 cm

Kutalika komaliza (L ₂ ) = 50.09 cm

Kusintha kwa kutalika ( Δ L) = 50.2 cm – 50 cm = 0.09 cm

Chiŵerengero cha kukula kolunjika (α) = 9 x 10 ^{-6 o} C ^-1

Kutentha koyambirira (T1 ₎ = 25 ^o C

Kufunidwa: Kutentha komaliza ( _T2 )

Yankho:

ΔL = α L ₁ ΔT

Δ L = α L ₁ (T ₂ – T ₁ )

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

Kutentha komaliza ndi 225 ^o C.

[irp]

4. Utali woyambirira wa chitsulo ndi mita imodzi ndipo kutalika komaliza ndi 1.02 m. Kusintha kwa kutentha ndi 50 Kelvin. Dziwani kuchuluka kwa kukula kwa mzere!

Zodziwika:

Kutalika koyambirira (L ₁ ) = mita imodzi

Kutalika komaliza (L ₂ ) = 1.02 mamita

Kusintha kwa kutalika ( Δ L) = L ₂ – L ₁ = 1.02 mamita – 1 mita = 0.02 mamita

Kusintha kwa kutentha (ΔT ) = 50 Kelvin = 50 ^o C

Kufunidwa: Chiwerengero cha kukula kolunjika

Yankho:

Δ L = α L 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

[wpdm_package id='694′]

1. Kusintha miyeso ya kutentha
2. Kukula kwa mzere
3. Kukula kwa dera
4. Kukula kwa voliyumu
5. kutentha
6. Kutentha kofanana ndi makina
7. Kutentha ndi mphamvu ya kutentha yeniyeni
8. Kutentha kobisika, kutentha kwa fusion, kutentha kwa nthunzi
9. Kusunga mphamvu potumiza kutentha