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23 January, 17:02

A steel bar that is at 10 ° c is 5 meters long, a bar for heated to 120 ° c, how long is that bar? Α = 1.2.10 - ° c

2) A square plate has 50cm side at 40 ° c knowing that α = 1,5-10-⁷ ° c¹

to determine:

A) the surface expansion coefficient β (β = 2.α)

B) Sheet area at 100 ° c (∆a = βAo.∆T)

3) A cube-shaped body has a volume of 1600cm³ at 20 ° c. Knowing that α = 2.7-10-⁵ ° c-¹

To determine

A) The coefficient of volumetric expansion γ. (Γ = 3.α)

B) If the body is heated to 160 ° C, what is the volume of the cube? (∆

V = γ. Vo.∆T)

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Answers (1)
  1. 23 January, 18:10
    0
    1) 5.0066 m

    2A) β = 3*10⁻⁷ / °C

    2B) 2500.045 cm²

    3A) γ = 8.1*10⁻⁵ / °C

    3B) 1618.144 cm³

    Explanation:

    1) Linear thermal expansion is:

    ΔL = α L₀ ΔT

    where ΔL is the change in length,

    α is the linear thermal expansion coefficient,

    L₀ is the original length,

    and ΔT is the change in temperature.

    Given L₀ = 5 m, ΔT = 110°C, and α = 1.2*10⁻⁵ / °C:

    ΔL = (1.2*10⁻⁵ / °C) (5 m) (110°C)

    ΔL = 0.0066 m

    The length increases by, so the new length is:

    L = L₀ + ΔL

    L = 5 m + 0.0066 m

    L = 5.0066 m

    2A) The surface expansion coefficient is:

    β = 2α

    β = 2 (1.5*10⁻⁷ / °C)

    β = 3*10⁻⁷ / °C

    2B) The change in area is:

    ΔA = β A₀ ΔT

    ΔA = (3*10⁻⁷ / °C) (50 cm * 50 cm) (60°C)

    ΔA = 0.045 cm²

    So the new area is:

    A = A + ΔA

    A = 2500 cm² + 0.045 cm²

    A = 2500.045 cm²

    3A) The volumetric expansion coefficient is:

    γ = 3α

    γ = 3 (2.7*10⁻⁵ / °C)

    γ = 8.1*10⁻⁵ / °C

    3B) The change in volume is:

    ΔV = γ V₀ ΔT

    ΔV = (8.1*10⁻⁵ / °C) (1600 cm³) (140°C)

    ΔV = 18.144 cm³

    So the new area is:

    V = V + ΔV

    V = 1600 cm³ + 18.144 cm³

    V = 1618.144 cm³
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