Ballaarinta toosan - dhibaatooyinka iyo xalalka

1. Birtu waa 40 cm dhererkeedu waa 20 ^o C. Isugeynta ballaarinta toosan ee birta waa 12 x 10 ^-6 (C ^o ) ^-1 . Kordhinta dhererka iyo dhererka ugu dambeeya marka uu gaaro 70 ^o C waxay noqon doontaa…

La yaqaan:

Isbeddelka heerkulka ( ΔT ) = 70 ^o C – 20 ^o C = 50 ^o C

Dhererka asalka ah (L ₁ ) = 40 cm

Isugeynta ballaarinta toosan ee birta (α ) = 12 x 10 ^-6 (C ^o ) ^-1

La Rabay: Isbeddelka dhererka ( Δ L) iyo dhererka ugu dambeeya (L ₂ )

Xalka:

a) Isbeddelka dhererka ( 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 ) cm

Δ L = 24 x 10 ^-3 cm

Δ L = 24 / 10 ³ cm

Δ L = 24 / 1000 cm

Δ L = 0.024 cm

b) Dhererka ugu dambeeya (L ₂ )

L ₂ = L ₁ + ΔL

L ₂ = 40 cm + 0.024 cm

L ₂ = 40.024 cm

2. Ul bir ah oo lagu kululeeyo 30 ^o C ilaa 80 ^o C. Dhererka ugu dambeeya ee birtu waa 115 cm, isku-darka ballaarinta toosanna waa 3 × 10 ^{-3 o} C ^-1 . Waa maxay dhererka asalka ah iyo isbeddelka dhererka birta?

Xalka:

Isbeddelka heerkulka ( ΔT) = 80 ^o C – 30 ^o C = 50 ^o C

Dhererka ugu dambeeya (L ₂ ) = 115 cm

Isugeynta ballaarinta toosan ( α ) = 3×10 ^{-3 o} C ^-1

La rabay: dhererka asalka ah (L ₁ ) iyo isbeddelka dhererka ( Δ L)

Xalka:

a) Dhererka asalka ah (L ₁ )

Qaacidada isbeddelka dhererka ee ballaarinta toosan:

Δ L = α L ₁ ΔT

Qaacidda dhererka kama dambaysta ah :

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) isbeddelka dhererka ( ΔL ) Δ L = L 2 – L 1 ΔL = 115 cm – 100 cm Δ L = 15 cm

3. Heerkulka 25 ^o C, dhererka galaaska waa 50 cm. Ka dib marka la kululeeyo, dhererka ugu dambeeya ee galaaska waa 50.9 cm. Isugeynta ballaarinta toosan waa α = 9 x 10 ^-6 C ^-1 . Go'aami heerkulka kama dambaysta ah ee galaaska…

La yaqaan:

Dhererka asalka ah (L ₁ ) = 50 cm

Dhererka ugu dambeeya (L ₂ ) = 50.09 cm

Isbeddelka dhererka ( Δ L) = 50.2 cm – 50 cm = 0.09 cm

Isugeynta ballaarinta toosan (α) = 9 x 10 ^{-6 o} C ^-1

Heerkulka asalka ah (T ₁ ) = 25 ^o C

La Rabay: Heerkulka kama dambaysta ah ( _T2 )

Xalka:

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

Heerkulka kama dambaysta ah waa 225 ^o C.

4. Dhererka asalka ah ee birta waa 1 mitir dhererka kama dambaysta ahna waa 1.02 m. Isbeddelka heerkulka waa 50 Kelvin. Go'aami isku-dhafka ballaarinta toosan!

La yaqaan:

Dhererka bilowga ah (L ₁ ) = 1 mitir

Dhererka ugu dambeeya (L ₂ ) = 1.02 mitir

Isbeddelka dhererka ( Δ L) = L ₂ – L ₁ = 1.02 mitir – 1 mitir = 0.02 mitir

Isbeddelka heerkulka (Δ T ) = 50 Kelvin = 50 ^o C

La Doonayo: Isugeynta ballaarinta toosan

Xalka:

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

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1. Beddelidda miisaanka heerkulka
2. Balaadhinta toosan
3. Ballaarinta aagga
4. Ballaarinta mugga
5. Heat
6. U dhigma farsamo ee kulaylka
7. Awood gaar ah oo kul iyo kulayl ah
8. Kulayl qarsoon, kulayl isku-dhafan, kulayl uumi-baxa
9. Ilaalinta tamarta ee wareejinta kulaylka