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1 August, 13:06

A container can be made from steel [β = 36 * 10-6 (C°) - 1] or lead [β = 87 * 10-6 (C°) - 1]. A liquid is poured into the container, filling it to the brim. The liquid is either water [β = 207 * 10-6 (C°) - 1] or ethyl alcohol [β = 1120 * 10-6 (C°) - 1]. When the full container is heated, some liquid spills out. To keep the overflow to a minimum, from what should the container be made and what should the liquid be?

1) Steel, Ethyl alcohol

2) Lead, Water

3) Lead, Ethyl alcohol

4) Steel, Water

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Answers (1)
  1. 1 August, 13:15
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    correct answer 2

    Explanation:

    For this exercise we must calculate the change in volume of the container and the liquid, the education that describes the change in volume is

    ΔV = V₀ β ΔT

    Let's write this equation for each material

    Steel

    ΔV₁ = V₀ 36 10⁻⁶ ΔT

    Lead

    ΔV₂ = V₀ 87 10⁻⁶ ΔT

    We write the same equations for liquids

    Water

    ΔV₃ = V₀ 207 10⁻⁶ ΔT

    Alcohol

    ΔV₄ = V₀ 1120 10⁻⁶ ΔT

    So that the spill is minimal, we can find, the volume of liquid minus the change in volume of content

    Steel-alcohol

    ΔV₁₄ = ΔV₄ - ΔV₁

    ΔV₁₄ = V₀ ΔT 10⁻⁶ (1120-36) =

    ΔV₁₄ = (V₀ ΔT 10⁻⁶) 1084

    Lead - water

    ΔV₂₃ = ΔVw - ΔVpb

    ΔV₂₃ = V₀ ΔT 10⁻⁶ (207-87)

    ΔV₂₃ = V₀ ΔT 10⁻⁶ 120

    Lead - Alcohol

    ΔV₄₃ = ΔV₄ - ΔV₂

    ΔV₄₃ = V₀ ΔT 10⁻⁶ (1120-87)

    ΔV₄₃ = V₀ ΔT 10⁻⁶ 1033

    Steel - Water

    ΔV₃₁ = ΔV₃ - ΔV₁

    ΔV₃₁ = V₀ ΔT 10⁻⁶ (207 - 36)

    ΔV₃₁ = V₀ ΔT 10⁻⁶ 171

    We can see that there is the smallest spill for the combination lead filled with water

    correct answer 2
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