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5 November, 14:47

What is water's density at 93 ∘C? Assume a constant coefficient of volume expansion. Express your answer with the appropriate units.

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  1. 5 November, 16:54
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    982.5 kg/m³

    Explanation:

    When the temperature of a fluid increases, it dilates, and because of the variation of the volume, it's density will vary too. The density can be calculated by the expression:

    ρ₁ = ρ₀ / (1 + β * (t₁ - t₀))

    Where ρ₁ is the final density, ρ₀ the initial density, β is the constant coefficient of volume expansion, t₁ the final temperature, and t₀ the initial temperature.

    At t₀ = 4°C, the water desity is ρ₀ = 1,000 kg/m³. The value of the constant for water is β = 0.0002 m³/m³ °C, so, for t₁ = 93°C

    ρ₁ = 1,000 / (1 + 0.0002 * (93 - 4))

    ρ₁ = 1,000 / (1 + 0.0178)

    ρ₁ = 982.5 kg/m³
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