Chiziqli kengayish – muammolar va yechimlar

1. A steel is 40 cm long at 20 ^oC. The coefficient of chiziqli kengayish for steel is 12 x 10^-6 (C^o)^-1. The increase in length and the final length when it is at 70 ^oC will be…

Ma'lum:

Harorat o'zgarishi (ΔT) = 70^oFZR - 20^oC = 50^oC

The original length (L₁) = 40 sm

Coefficient of linear expansion for steel (α) = 12 x 10^-6 (C^o)^-1

Qidirilgan: Uzunlikning o'zgarishi (ΔL) and the final length (L₂)

yechim:

a) The change in length (ΔL)

ΔL = α L₁ DT

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

ΔL = (10^-6)(24 x 10³) sm

ΔL = 24 x 10^-3 cm

ΔL = 24 / 10³ cm

ΔL = 24 / 1000 cm

ΔL = 0.024 sm

b) The final length (L₂)

L₂ =L₁ + DL

L₂ = 40 cm + 0.024 cm

L₂ = 40.024 sm

2. An iron rod heated from 30 ^oC dan 80 ^oC. The final length of iron is 115 cm and the coefficient of linear expansion is 3×10^{-3 o}C^-1. What is the original length and the change in length of the iron ?

yechim:

O'zgarish harorat (ΔT) = 80 ^oFZR - 30 ^oC = 50 ^oC

The final length (L₂) = 115 sm

Chiziqli kengayish koeffitsienti (α) = 3 × 10^{-3 o}C^-1

Qidirilgan: the original length (L₁) and the change in length (ΔL)

yechim:

a) The original length (L₁)

Formula of the change in length for the linear expansion :

ΔL = α L₁ DT

Formula of the final length :

L₂ = L₁ + DL

L₂ =L₁ + α L₁ DT

L₂ = L₁ (1 + α ΔT)

115 cm = L₁ (1 + (3.10)^{-3 o}C^-1)(50)^oC)

115 cm = L₁ (1 + 150.10^-3)

115 cm = L₁ (1 0.15 + XNUMX XNUMX)

115 cm = L₁ (1.15)

L1 = 115 sm / 1.15 L1 = 100 sm b) the change in length (ΔL) ΔL = L2 - L1 ΔL = 115 cm – 100 cm ΔL = 15 sm

3. 25 yoshda ^oC, the length of the glass is 50 cm. After heated, the final length of the glass is 50.9 cm. The coefficient of linear expansion is α = 9 x 10^-6 C^-1. Determine the final temperature of the glass…

Ma'lum:

The original length (L₁) = 50 sm

The final length (L₂) = 50.09 sm

Uzunlikning o'zgarishi (ΔL) = 50.2 cm – 50 cm = 0.09 cm

Chiziqli kengayish koeffitsienti (α) = 9 x 10^{-6 o}C^-1

The original temperature (T₁) = 25^oC

Qidirilgan: Yakuniy harorat (T₂)

yechim:

ΔL = α L₁ DT

ΔL = α L₁ (T₂ - T₁)

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

0.09 = (45 x 10^-5)(T)₂ - 25)

0.09 / (45 x 10^-5) = T₂ - 25

0.002 x 10⁵ =T₂ - 25

2 x 10² =T₂ - 25

200 = T₂ - 25

T₂ = 200 + 25

T₂ = 225^oC

Yakuniy harorat 225 ^oC.

4. The original length of metal is 1 meter and the final length is 1.02 m. The change in temperature is 50 Kelvin. Determine the coefficient of linear expansion!

Ma'lum:

The initial length (L₁) = 1 metr

The final length (L₂) = 1.02 metr

Uzunlikning o'zgarishi (ΔL) = L₂ - L₁ = 1.02 meter – 1 meter = 0.02 meter

Haroratning o'zgarishi (ΔT) = 50 Kelvin = 50^oC

Qidirilgan: Chiziqli kengayish koeffitsienti

yechim:

ΔL = α L₁ DT

0.02 m = α (1 m)(50^oC)

0.02 = α (50^oC)

α = 0.02 / 50^oC

a = 0.0004 ^oC^-1

α = 4 x 10^{-4 o}C^-1

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1. Harorat shkalalarini konvertatsiya qilish
2. Chiziqli kengayish
3. Hududni kengaytirish
4. Hajmni kengaytirish
5. issiqlik
6. Issiqlikning mexanik ekvivalenti
7. Maxsus issiqlik va issiqlik sig'imi
8. Yashirin issiqlik, erish issiqligi, bug'lanish issiqligi
9. Issiqlik uzatish uchun energiya tejash