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An aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. The can’s initial volume at 8 °C is 4.8 × 10-4 m3. The coefficient of volume expansion for aluminum is 69 × 10-6 (C°)-1. When the can and the liquid are heated to 80 °C, 6.1 × 10-6 m3 of liquid spills over. What is the coefficient of volume expansion of the liquid?

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    The volume of liquid that spills over the can is the difference between the increase in the volume of the liquid and that of the aluminum can
    ΔV=β₁VΔT - β ₂VΔT
    β₁=(ΔV/VΔT) + β ₂ =
    =(6.1•10⁻⁶/4.8•10⁻⁴•72) + 69•10⁻⁶ = 1.13•10⁻³ °C⁻¹

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